Sedimentation devices and methods for determining particle size distribution by water pressure during sedimentation

Abstract

Methods and devices for determining a particle size distribution (PSD) of a mixture of solid particles are provided. Solid particles are introduced into a first end of a liquid-filled sedimentation column fluidly coupled to a secondary column. Liquid height is measured in the secondary column at distinct times as the solid particles pass through the sedimentation column. Further, a PSD of the solid particles is determined based on a plurality of respective settling velocities of the solid particles corresponding in time to the heights of liquid measured at distinct times. The device includes the sedimentation column containing a liquid with a height ≥ about 1 meter, where the secondary column receives a portion of the liquid free of solid particles from the sedimentation column to provide a plurality of height measurements.

Description

Attorney Docket No. 2115-0084818-WO-POBSEDIMENTATION DEVICES AND METHODS FOR DETERMINING PARTICLESIZE DISTRIBUTION BY WATER PRESSURE DURING SEDIMENTATIONGOVERNMENT SUPPORT

[0001] This invention was made with government support under 1825189 awarded by the National Science Foundation. The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 683,293, filed on August 15, 2024. The entire disclosure of the above application is incorporated herein by reference.FIELD

[0003] The present disclosure relates methods and devices for determining a particle size distribution of a mixture of solid particles by sedimentation through a column of liquid and height measurements of liquid in a hydraulically connected secondary column as the solid particles settle past a pressure port in the first column.BACKGROUND

[0004] This section provides background information related to the present disclosure which is not necessarily prior art.

[0005] Determining particle sizes of solid particles is important in many industries. Mixtures of solid particles are typically poly disperse and have different sizes. A particle size distribution (PSD) is a common technique to characterize and compare such solid particle mixtures. Particle size distribution (PSD) serves as a fundamental soil index property in engineering, earth science and agriculture, among others. Every Civil Engineering construction project begins with a site characterization, which includes soil borings and soil sampling from various locations and depths below the surface. The collected specimens are taken to a laboratory for testing.

[0006] Thus, the first and most common test is one that determines the soil specimens’ particle size distributions (PSD). For example, the PSD is essential for soil classification which in turn is the starting point for all geotechnical engineering design. For sands, it is determined in thousands of soil testing laboratories throughout the world using a standard sieve test. By way of example, ASTM International Standard C136-C136M-19 “ Standard Test Method for SieveAttorney Docket No. 2115-0084818-WO-POBAnalysis of Fine and Coarse Aggregates” may be conducted to determine particle size distribution. More specifically, a series of sieves with different sized openings are stacked on one another onto which a sample is placed, followed by inserting it into a sieve shaker to determine particle size distribution of gravel and sand samples as they fall through the series of sieves. Each sieve with a distinct opening size provides a data point for grain size, for example, percent passing (or percent finer) versus percent retained (or percent coarser). The particle size distribution by ASTM Cl 36- C136M-19 test typically provides six to eight standard sieve sizes or data points, which are then fitted into a curve. The determination of particle size distribution (PSD) of sands has remained staunchly reliant on sieve analysis.

[0007] Other tests include hydrometer testing used for solid particles of fine sizes, like silt and clay, by employing a tool to measure the density or specific gravity of a liquid when compared to water by using a calibrated glass tube with a scale, and employing Stokes’ Law. However, hydrometer testing only works for very small solid particles and further is based on the assumption that they are spherical. However, this assumption does not work for sand particles. Besides, the falling velocity of sand particles can be orders of magnitude higher than that of silt and clay. Therefore, the particle size distribution of sands cannot be determined by a hydrometer test. It would be desirable to provide new techniques and devices that rapidly characterize particle size distribution of complex mixtures with larger particles, like sand, without requiring the need for complex sieve shaking tests in a laboratory.SUMMARY

[0008] This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

[0009] In certain aspects the present disclosure relates to a device for determining a particle size distribution of a mixture of solid particles. The device may comprise a sedimentation column for containing a liquid having a height of greater than or equal to about 1 meter. The sedimentation column has a first end that is open for receiving the liquid and a sample of solid particles and a second end that is sealed. The device also a port disposed in a wall of the sedimentation column at a height above where the particles collect at the second end of the sedimentation column. The device comprises a conduit in fluid communication with the port that receives a portion of the liquid in the sedimentation column free of the solid particles. A secondary column associated with the conduit provides a plurality of height measurements of the liquid in the secondary column for a duration that solid particles pass through the sedimentation column from the first end to the second end. A particle size distribution of the solid particles is determinedAttorney Docket No. 2115-0084818-WO-POB based on a plurality of respective settling velocities of the solid particles and the plurality of the height measurements of the liquid.

[0010] In one aspect, the sedimentation column is a cylindrical column that is transmissive to light having wavelengths in the visible region.

[0011] In one aspect, the sedimentation column has a diameter at the first end of greater than or equal to about 25 mm and the height is greater than or equal to about 1.5 meters to less than or equal to about 2 meters. Further, a particle size of the solid particles is greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm.

[0012] In one aspect, the conduit comprises a first region that defines an angle with respect to the sedimentation column so that the first region of the conduit connects to the port and is graded to a first elevation that is above the port.

[0013] In one aspect, the angle is less than or equal to about 30° from vertical corresponding to the sedimentation column.

[0014] In one aspect, the port is disposed greater than or equal to about 16 cm above the second end of the sedimentation column.

[0015] In one aspect, the device further comprises a processor that receives and records the plurality of height measurements of the liquid in the secondary column to determine a specific gravity of the solid particles and a mass of the solid particles.

[0016] In one further aspect, the processor is configured to calculate the plurality of respective calculated settling velocities (v) of the solid particles passing the pressure port on the column at any given time during the settling process by using a settling distance divided by a settling time.

[0017] In one further aspect, the processor is programmed to determine a plurality of particle sizes from previously determined settling velocities (v) by using settling velocity models, such as, but not limited to, the model provided by Jimenez, J. A., and Madsen, O. S. “A simple formula to estimate settling velocity of natural sediments J. Waterw. Port Coastal Ocean Eng. 129 (2): pp.where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, AN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.Attorney Docket No. 2115-0084818-WO-POB

[0018] In one aspect, the device further comprises an indicia of height to provide the plurality of height measurements of the liquid in the secondary column.

[0019] In one aspect, the secondary column is a flexible transparent tube.

[0020] In one aspect, the sedimentation column has a first diameter and the secondary column has a second diameter of less than the first diameter.

[0021] In one aspect, the device further comprises a plurality of mechanical connectors to reversibly secure the secondary column to the sedimentation column.

[0022] In one aspect, the conduit comprises at least one quick connector to reversibly couple with the secondary column.

[0023] In one aspect, the sedimentation column is an assembly comprising multiple segments reversibly coupled together.

[0024] In certain aspects, the present disclosure further relates to a method of determining a particle size distribution of a mixture of solid particles. The method optionally comprises introducing a sample of solid particles into a first end of a sedimentation column containing a liquid. The method also comprises measuring a height of the liquid at distinct times in a secondary column in fluid communication with the sedimentation column as the solid particles pass through the sedimentation column from the first end to a second end to provide a plurality of height measurements. A particle size distribution of the solid particles is determined based on a plurality of respective settling velocities of the solid particles and the plurality of the height measurements of the liquid.

[0025] In one aspect, the measuring the height comprises measuring an initial height of the liquid in the secondary column prior to the introducing of the sample.

[0026] In one aspect, the measuring the height further comprises measuring a plurality of heights of the liquid in the secondary column intermittently while the solid particles are passing through the sedimentation column.

[0027] In one aspect, the measuring the height further comprises measuring a final height of the liquid in the secondary column after the solid particles collect at the second end of the column.

[0028] In one aspect, an indicia of height is associated with the secondary column for the measuring of the height of the liquid at distinct times in the secondary column.

[0029] In one aspect, the measuring the height of the liquid at distinct times in the secondary column occurs by recording a plurality of times at which a plurality of predetermined heights are reached in the secondary column.

[0030] In one further aspect, the predetermined heights are height intervals of about 1 mm.Attorney Docket No. 2115-0084818-WO-POB

[0031] In one aspect, the sedimentation column further comprises a port disposed in a wall of the sedimentation column disposed at a height above where the particles collect at the second end of the sedimentation column. The device further comprises a conduit in fluid communication with the port that receives a portion of the liquid in the sedimentation column free of the solid particles. The device also comprises a quick connector associated with the conduit in which the secondary column seats through which the liquid transfers.

[0032] In one aspect, the determining the particle size distribution includes calculating a plurality of particle sizes by using settling velocity models, such as, but not limited to, the Jimenez and Madsen model (2003):where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, dN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

[0033] In one aspect, the measuring the height of the liquid in the secondary column occurs continuously.

[0034] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.DRAWINGS

[0035] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0036] FIG. 1 shows a side view of a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and an ancillary or secondary column in the form of a manometer (“m-Sed” system) for observation of height measurements of liquid including a scale with indicia of height.

[0037] FIGS. 2A-2D show a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and a pressure measuring component in the form of an ancillary column / tube or manometer for observation having a scale with indicia of height to determineAttorney Docket No. 2115-0084818-WO-POB hydrostatic pressure that may be portable and assembled / disassembled. FIG. 2A shows a lower region of a sedimentation column and the ancillary column or manometer. FIG. 2B shows an upper region of the sedimentation column where the manometer is secured parallel to the main sedimentation column by anchor clips. Further, a view of a scale having indicia for measurement of height that can be used to determine hydrostatic pressure is shown. FIG. 2C shows a magnified view of the lower section with a base and pedestal to support the sedimentation column to which the ancillary column may be connected. FIG. 2D shows an assembly of both the sedimentation column and the manometer together on a base and pedestal for supporting the columns.

[0038] FIGS. 3A-3B show a schematic of a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and a pressure measuring component in the form of a manometer for observation having a scale with indicia of height to determined hydrostatic pressure that may be portable that is disassembled with various components prior to assembly. FIG. 3A shows a top region or section of the sedimentation column and pressure measuring component in the form of a manometer to an upper coupler, while FIG. 3B shows a lower region or section of the sedimentation column and pressure measuring component in the form of a manometer that attaches to the upper coupler and further has a lower coupler that attaches to a pedestal and base.

[0039] FIG. 4 show pressure stages A-D during tests to determine a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, where the measurement device includes a sedimentation column and a water level measuring component (manometer column) for observation having a scale with indicia of height that may be portable and assembled / disassembled. Stage A occurs when only water is in the sedimentation column and manometer. Stage B is where a sample of solid particles is introduced to the sedimentation column and all the solids are above a pressure port. Stage C coincides to when the solids are falling through the sedimentation column past the pressure port. Finally, stage D is where all the solids have passed by and settled below the pressure port.

[0040] FIG. 5 shows measurements for typical manometer water height time histories for fine, medium, coarse and gap-graded sands in a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and a pressure measuring component in the form of a manometer.

[0041] FIG. 6 shows images of eight tested soil specimens with their percentages of coarse, medium and fine sand. Scale bars are 2 mm.Attorney Docket No. 2115-0084818-WO-POB

[0042] FIGS. 7A-7B show comparisons of particle size distributions (PSDs) for the eight tested soil specimens in FIG. 6 comparing those obtained from a conventional sieve shaking test versus those obtained from a device that includes a sedimentation column and a pressure measuring component in the form of a manometer (m-Sed) according to certain aspects of the present disclosure. FIG. 7A shows samples 1 to 6 and FIG. 7B shows sample 7 to 8.

[0043] FIG. 8 shows assessment of repeatability of particle size distribution obtained from a device that includes a sedimentation column and a pressure measuring component in the form of a manometer (m-Sed) according to certain aspects of the present disclosure.

[0044] FIG. 9 shows a comparison of particle size distributions (PSDs) for a soil specimen obtained from a conventional sieve shaking test versus those obtained from a m-Sed device that includes a sedimentation column and a pressure measuring component in the form of a manometer according to certain aspects of the present disclosure and from a u-Scd device including a sedimentation column and a pressure measuring component in the form of a pressure transducer according to certain aspects of the present disclosure.

[0045] FIG. 10 shows the effect of Corey Shape Factor (csf) values on particle settling velocity.

[0046] FIG. 11 shows the effect of Corey Shape Factor (csf) values on particle size distributions (PSDs) for two tested soil specimens obtained from a device that includes a sedimentation column and a pressure measuring component in the form of a manometer (m-Sed) according to certain aspects of the present disclosure.

[0047] FIGS. 12A-12B show how to determine AJM (FIG. 12A) and BJM (FIG. 12B) coefficients based on Jimenez and Madsen, 2003.

[0048] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.DETAILED DESCRIPTION

[0049] Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific compositions, components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.Attorney Docket No. 2115-0084818-WO-POB

[0050] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, elements, compositions, steps, integers, operations, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Although the open-ended term “comprising,” is to be understood as a non-restrictive term used to describe and claim various embodiments set forth herein, in certain aspects, the term may alternatively be understood to instead be a more limiting and restrictive term, such as “consisting of’ or “consisting essentially of.” Thus, for any given embodiment reciting compositions, materials, components, elements, features, integers, operations, and / or process steps, the present disclosure also specifically includes embodiments consisting of, or consisting essentially of, such recited compositions, materials, components, elements, features, integers, operations, and / or process steps. In the case of “consisting of,” the alternative embodiment excludes any additional compositions, materials, components, elements, features, integers, operations, and / or process steps, while in the case of “consisting essentially of,” any additional compositions, materials, components, elements, features, integers, operations, and / or process steps that materially affect the basic and novel characteristics are excluded from such an embodiment, but any compositions, materials, components, elements, features, integers, operations, and / or process steps that do not materially affect the basic and novel characteristics can be included in the embodiment.

[0051] Any method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed, unless otherwise indicated.

[0052] When a component, element, or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other component, element, or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.Attorney Docket No. 2115-0084818-WO-POB

[0053] Although the terms first, second, third, etc. may be used herein to describe various steps, elements, components, regions, layers and / or sections, these steps, elements, components, regions, layers and / or sections should not be limited by these terms, unless otherwise indicated. These terms may be only used to distinguish one step, element, component, region, layer or section from another step, element, component, region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first step, element, component, region, layer or section discussed below could be termed a second step, element, component, region, layer or section without departing from the teachings of the example embodiments.

[0054] Spatially or temporally relative terms, such as “before,” “after,” “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially or temporally relative terms may be intended to encompass different orientations of the device or system in use or operation in addition to the orientation depicted in the figures.

[0055] In this application, the term “processor,” “module” or the term “controller” may be replaced with the term “circuit.” The term “module” may refer to, be part of, or include: an Application Specific Integrated Circuit (ASIC); a digital, analog, or mixed analog / digital discrete circuit; a digital, analog, or mixed analog / digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip.

[0056] The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces that are connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of any given module of the present disclosure may be distributed among multiple modules that are connected via interface circuits. For example, multiple modules may allow load balancing. In a further example, a server (also known as remote, or cloud) module may accomplish some functionality on behalf of a client module.

[0057] The term code, as used above, may include software, firmware, and / or microcode, and may refer to programs, routines, functions, classes, data structures, and / or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses a processor circuit that, inAttorney Docket No. 2115-0084818-WO-POB combination with additional processor circuits, executes some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses a memory circuit that, in combination with additional memories, stores some or all code from one or more modules.

[0058] The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium, as used herein, does not encompass transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered tangible and non-transitory. Nonlimiting examples of a non-transitory, tangible computer-readable medium are nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), volatile memory circuits (such as a static random access memory circuit or a dynamic random access memory circuit), magnetic storage media (such as an analog or digital magnetic tape or a hard disk drive), and optical storage media (such as a CD, a DVD, or a Blu-ray Disc).

[0059] The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in computer programs. Any functional blocks, flowchart components, and other elements described above serve as software specifications, which can be translated into the computer programs by the routine work of a skilled technician or programmer.

[0060] The computer programs include processor-executable instructions that are stored on at least one non-transitory, tangible computer-readable medium. The computer programs may also include or rely on stored data. The computer programs may encompass a basic input / output system (BIOS) that interacts with hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0061] The computer programs may include: (i) descriptive text to be parsed, such as HTML (hypertext markup language), XML (extensible markup language), or JSON (JavaScript Object Notation) (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code may be written using syntax fromAttorney Docket No. 2115-0084818-WO-POB languages including C, C++, C#, Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, Javascript®, HTML5 (Hypertext Markup Language 5th revision), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB, SIMULINK, and Python®.

[0062] None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. § 112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.”

[0063] Throughout this disclosure, the numerical values represent approximate measures or limits to ranges to encompass minor deviations from the given values and embodiments having about the value mentioned as well as those having exactly the value mentioned. Other than in the working examples provided at the end of the detailed description, all numerical values of parameters (e.g., of quantities or conditions) in this specification, including the appended claims, are to be understood as being modified in all instances by the term “about” whether or not “about” actually appears before the numerical value. “About” indicates that the stated numerical value allows some slight imprecision (with some approach to exactness in the value; approximately or reasonably close to the value; nearly). If the imprecision provided by “about” is not otherwise understood in the art with this ordinary meaning, then “about” as used herein indicates at least variations that may arise from ordinary methods of measuring and using such parameters. For example, “about” may comprise a variation of less than or equal to 5%, optionally less than or equal to 4%, optionally less than or equal to 3%, optionally less than or equal to 2%, optionally less than or equal to 1%, optionally less than or equal to 0.5%, and in certain aspects, optionally less than or equal to 0.1%.

[0064] In addition, disclosure of ranges includes disclosure of all values and further divided ranges within the entire range, including endpoints and sub-ranges given for the ranges.

[0065] The disclosure of all patents, patent applications, articles, and literature referenced or cited in this disclosure are hereby incorporated by reference herein.

[0066] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0067] The present disclosure contemplates methods and devices for determining a particle size distribution of a mixture of solid particles where multiple height measurements of liquid in a column are taken as the solid particles pass through. More specifically, the system includes a primary column, also referred to herein as a sedimentation column, and secondary column, also referred to herein as a manometer, that is fluidly coupled to the primary column. InAttorney Docket No. 2115-0084818-WO-POB this manner, the height measurements from the devices of the present teachings can be used to create accurate particle size distributions for mixtures comprising solid particles without any need for traditional sieving tests. The devices provided by certain aspects of the present disclosure will also be referred to interchangeably herein as “m-Sed,” where m is notation for manometer and Sed refers to sedimentation. The m-Sed test and device can thus eliminate the need to do any sieving of samples of solid particles, especially those considered sands. In various aspects, the present disclosure contemplates analyzing mixtures of solid particles, which includes a plurality of particles that may have a range of distinct particle sizes (e.g., average particle diameters), including those having a minimum particle size of greater than or equal to about 0.075 mm and a maximum average particle size of less than or equal to about 4.75 mm, which are typically classified as sands. For example, ASTM-defined sands may have a particle size of greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm. Thus, the methods and devices described herein pertain to determining a particle size distribution of a mixture of solid particles classified as sand and having an average particles size of greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm, in certain aspects.

[0068] The methods of the present disclosure take considerably less time to perform than a traditional sieve test. Further, the devices of the present disclosure require less and smaller equipment, which advantageously occupies a small footprint. Unlike the sieve test which typically provides only 6 to 8 data points, in certain variations, the methods of the present disclosure can generate a continuous or near-continuous PSD curve. Unlike sieves, there is nothing to clean, store or maintain. Further, the systems provided by the present disclosure are portable and can be taken on-site. The devices have no moving parts, make no noise or dust, and consume considerably less energy than sieving.

[0069] In certain aspects, the present disclosure provides a device 50 for conducting such methods and thus for determining a particle size distribution of a mixture of solid particles or (“m- Sed” device), for example, as shown in FIG. 1. The device 50 includes a vessel for holding liquid 52, such as a column 54. The column 54 may have a major axis (longitudinal axis) that is vertically oriented with a circular cross-section and thus cylindrical shape. The wall 56 of the column 54 thus defines an open volume. The column 54 has a first end 60 with an opening 62 that serves as an inlet to the column 54. The opening 62 may receive a liquid 52 within the open volume defined by the column 54, as well as a sample of the solid particles (not shown) to be analyzed for determining a particle size distribution. In this manner, the column 54 serves as a sedimentation column through which the particles may fall at different settling velocities, as described further herein. Notably, an optional funnel 58 or other similar device may be used to feed a sample solidAttorney Docket No. 2115-0084818-WO-POB particles into the opening 62 at the first end 60 of the column 54. The column 54 includes a second end 70 opposite to the first end that is sealed and fluid-tight. By way of example, one or more gaskets or O-ring seals 72 may be used within a pedestal 74 that seats on a base 76.

[0070] The column includes an aperture that serves as a pressure port 78 disposed in the wall 56 of the column 54 disposed at a port height (designated “ho”) above pedestal 74 above which a lower region 80 of the column 54 is defined where the particles will collect to a maximum collection height (designated “he”) at the second end 70 of the column 54. In certain aspects, the pressure port 78 is disposed so that the port height (ho) is greater than or equal to about 16 cm above the terminal / second end 70 of the column 54. A conduit 82 in fluid communication with the pressure port 78 is configured to receive a portion of the liquid 52 in the column 54. The liquid 52 that enters the conduit 82 is free of any solid particles. The conduit 82 comprises an angled first region 84 that defines an angle (9) with respect to the major longitudinal axis (corresponding to wall 56) of column 54, so that the first region 84 of the conduit 82 connects to the pressure port 78 and is graded so that it rises on an incline to a second elevation (designated “hc2) that is greater than a first elevation (designated “hci”) of the pressure port 78. For example, the angle (9) may be less than or equal to about 30° from vertical (corresponding to the wall 56 / major longitudinal axis) of column 54. Such an angle (9) serves to prevent the solid particles from flowing into the angled first region 84 of the conduit and thus only liquid flows therein. Other alternative components, such as filters, may instead be used to prevent the solid particles from entering the conduit 82 with liquid 52.

[0071] The conduit 82 may terminate in a quick connector 88, for example, push-to- connect fitting. As will be appreciated by those of skill in the art and as discussed below, the measuring component may measure a variable that can be used to determine pressure, such as a height of a fluid that can be used as a variable to calculate and determine hydrostatic pressure. As shown in FIG. 1, a measuring component is a height measuring component in the form of an ancillary or secondary column / tube 100 that serves as an observation tube, also referred to herein as a manometer 100, for observation of liquid and having a scale with indicia of height 102 (also referred to herein as the “manometer-sedimentation” or “m-Sed” device). The manometer 100 is in fluid communication with the primary sedimentation column 54 via the pressure port 78 and conduit 82. Thus, the height measuring component or manometer 100 can be used to intermittently or continuously monitor a height of the liquid 52 that has entered into the manometer 100. The height of the liquid 52 in the conduit 82 and thus manometer 100 reflects a corresponding pressure of the liquid 52 within the column 54 at the pressure port 78. As will be described further herein, the height measuring component associated with the manometer 100 provides a plurality of heightAttorney Docket No. 2115-0084818-WO-POB measurements of the liquid 52, including providing height measurements for a duration that solid particles pass through the column 54 from the first end 60 to the second end 70 to determine a particle size distribution of the solid particles based on a plurality of respective settling velocities of the solid particles and the height measurements.

[0072] As shown in FIG. 1, at least one indicia of height or length / height scale 102 can be used to measure a height of the liquid 52 in the manometer 100. While scale 102 is shown as being associated with the sedimentation column 54, which has a longitudinal axis parallel to a corresponding longitudinal axis of the manometer 100, the scale 102 may also be located near, on, or within the manometer 100, as will be appreciated by those of sill in the art. The manometer 100 may be secured to the sedimentation column by reversible connectors or fasteners, such as mechanical connectors or fasteners, like anchor clips 104. In certain variations, the height measurements may be taken by either by photographic / videographic equipment or by visual operation by an operator conducting the test on the device. In certain variations, the height measurements may be taken continuously, for example, by a continuous videographic / video camera recording the height measurements via the scale 102 over time, for example, as the solid particles are passing by the pressure port 78. However, in other variations, the height measurements can be taken intermittently, for example by photographic equipment / camera or an observer. In certain variations, height measurements and the corresponding acquisition times may be taken at given height increments (e.g., at every 1 mm) with the time recorded to reach each height measurement. Notably, in this embodiment, during the sedimentation process for the solid particles, the fluid 52 flows bidirectionally between the sedimentation column 54 (through the pressure port 78 and conduit 82) and the manometer 100 during the test.

[0073] The height measurements taken can thus provide information about a first portion or percentage by weight of the sample of the solid particles above the pressure port 78 and a second portion or percentage by weight of the sample that is below the pressure port 78. As distance is known as to how far the solid particles travel in the column 54, the settling velocity of whatever particles are at the pressure port 78 at any given time can be determined. As described further below, certain equations can be used to determine a particle size at the pressure port 78 at a given point in time that corresponds to a particle settling velocity.

[0074] In certain aspects, the column 54 is formed of a clear or translucent material, for example having a high level of transmissivity (e.g., greater than or equal to about 75%) to light having wavelengths in the visible region. By way of non-limiting example, the column 54 may be formed of a clear plastic, such as an acrylic, glass, or the like. In this manner, after the solid particles have collected in the lower region 80 following processing in the column 54 to determineAttorney Docket No. 2115-0084818-WO-POB a particle size distribution, the solid particles can be further observed, characterized, and / or analyzed, for example, by image analysis systems.

[0075] A major longitudinal axis or height of the column 54 may be greater than or equal to about 1 meter (about 3.3 feet), optionally greater than or equal to about 1.5 meters (about 5 feet), and in certain aspects, optionally greater than or equal to about 1.8 meters (about 6 feet). As discussed above, the sample of solid particles is introduced into the opening 62 at the first end 70 of the column and thus fall through the liquid 52 at different rates or velocities depending on particle size and density. Thus, a height of the column 54 is advantageously high enough so that the particles can establish respective terminal settling velocities and / or sort by size before passing the pressure port 78 at different points in time. Thus, depending on a maximum particle size of the particles in the sample, the height of column 54 may vary to permit an adequate distance for the particles to fall. Stated in another way, the height of the sedimentation column 54 is sized to ensure that the particles in the solid sample have sorted themselves by size by the time they pass an elevation corresponding to the pressure port 78.

[0076] In certain aspects, the column 54 may have a height of greater than or equal to about 1.5 meters to less than or equal to about 2 meters, wherein a maximum particle size of the solid particles is less than or equal to about 4.75 mm and a minimum particle size of the solid particles is greater than or equal to about 0.075 mm. Further, in certain aspects, the column 54 has a diameter greater than or equal to about 25 mm when the mixture of particles introduced to the first end / top of the column has a mass in excess of 50 grams. Again, a diameter of the column 54 may be enlarged to accommodate a larger sample size of solid particles, as necessary.

[0077] The secondary column or manometer 100 may be a flexible tube. An inner diameter of the secondary column / manometer 100 is selected to avoid capillary rise that can inhibit prompt stabilization of water level, while also minimizing pronounced inertial effects. For example, a diameter that is too small amplifies capillary rise, inhibiting the prompt stabilization of the water level at a height reflecting the actual pressure. Conversely, an excessively large diameter introduces pronounced inertial effects, resulting from the larger volume of water that must move between the sedimentation column and the manometer tube during the test. Such inertial effects can potentially cause problems during certain stages of the m-Sed test, as further described below. In certain variations, the sedimentation column has a first diameter (e.g., inner diameter) and the secondary column or manometer has a second diameter (e.g., inner diameter), where the second diameter is less than the first diameter. More specifically, in particularly advantageous variations, the inner diameter of the manometer may be selected to be less than or equal to about 4 mm, forAttorney Docket No. 2115-0084818-WO-POB example, about 3.2 mm. The manometer may have a length along its major longitudinal axis or height similar to and optionally slightly shorter than that of the sedimentation column 54.

[0078] In one variation, the manometer 100 itself may be formed of a transparent and flexible polymer, such as a flexible polyurethane rubber tube having an inside diameter of 3.2 mm (1 / 8 in.) and an outside diameter of 6.4 mm (1 / 4 in.). The selection of the manometer material and diameter are intrinsically linked to the dynamic pressure responses during testing and further discussed below in the examples. As it can be loosely coiled for transport, the manometer tube can be continuous over its entire 1550 mm (61 in.) length. It attaches to the port assembly using a simple push-to-connect fitting. To keep it securely in place, the manometer tube is attached to the main sedimentation column using multiple (e.g., five) clips along its length. These clips are permanently glued to the main sedimentation column. Lastly, a scale with a precision of 1 mm (1 mm intervals of height indicia) is attached to the upper section of the main sedimentation column for reading water levels in the manometer.

[0079] In various aspects, while not shown, the device 50 may be part of a system that furthers include a processor. The processor may be in electrical communication with a detector or camera that records the height measurements, or these height measurements may be inputted. For example, the processor may be a computer processing unit (CPU) that may be operated with various modules, as appreciated by those of skill in the art. The processor is configured to receive and record a plurality of height measurements taken by the height measurement component (scale 102 that measures height of fluid 52 in the manometer 100). As noted above, the height measurements may be intermittent taken at regular intervales or continuous. The processor is optionally further configured to calculate the plurality of respective settling velocities of the solid particles based on the settling distance and settling times, as will be described further herein. Thus, an overall system for determining a particle size distribution including device 50 may be an automated system.

[0080] FIGS. 2A-2D show a specific design of a particle size distribution system / device that includes an ancillary or secondary column in the form of a manometer according to certain aspects of the present disclosure. The system / device thus includes a sedimentation column and the secondary column or manometer (“m-Sed”) in fluid communication with the sedimentation column, as shown in FIG. 2A. The sedimentation column is formed of clear acrylic and measures 1.8 m (6 ft) in height, with an opening diameter of 25.4 mm (1 inch) and having a wall thickness of 3.2 mm (1 / 8 inch). The base of the column sits on a detachable acrylic base and pedestal with two O-rings to ensure water / fluid tightness.Attorney Docket No. 2115-0084818-WO-POB

[0081] A pressure or manometer port is located about 16 cm above the pedestal. The pressure port inlet is angled at 30° from vertical to prevent the falling particles from entering the conduit that connects to the manometer. The elevation of the port ensures that it remains above the top of the fully settled soil specimen. Typically, a 50 g soil specimen would settle to approximately an 8 cm height, but to provide an extra margin, the port may be located 16 cm above the top of the pedestal.

[0082] Thus, the present disclosure contemplates an embodiment of a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and a measuring component in the form of an ancillary or secondary column / tube that serves as an observation tube, also referred to herein as a manometer, for observation of liquid and having a scale with indicia of height. This variation manometer-based system (m-Sed) may be a field-portable sedimentation test device, which requires no electrical power to operate because it utilizes a manometer instead of a pressure transducer. This eliminates problems associated with voltage fluctuations, sensor failures, electrical power outages, and electrical short-circuits in wet environments. Additionally, the absence of electronic components eliminates maintenance needs such as periodic calibration or sensor replacement. These attributes make the m-Sed system embodiment particularly suitable for deployment in remote or resource-limited areas, disaster-affected regions, extreme weather conditions, and environments where electrical or electronic equipment poses safety concerns such as in mines, oilfields, or industrial facilities.

[0083] While the manometer variation presents a simpler method for pressure measurement than an electronic pressure transducer, for example, the mathematics associated with the reduction of data are much more complex. The complexity is because, unlike a system incorporating a pressure transducer, fluid flows bidirectionally between the sedimentation column and the manometer during the test.

[0084] FIGS. 2A-2D, 3A-3B, and 4 show one variation of a portable particle size distribution system / device 50A for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column 54A having multiple assembled segments and further including the measuring component in the form of an ancillary or secondary column / tube or manometer that serves as an observation tube for height. To the extent that the components are the same as those described above in the context of previous embodiment of the system / device (e.g., 50 in FIG. 1), for brevity these will not be discussed further herein unless otherwise notable. The device 50A may be portable having various components that may be assembled and disassembled. Thus, the device 50A can determine aAttorney Docket No. 2115-0084818-WO-POB particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure. FIGS. 2B and 3A show an upper region 110 of the sedimentation column 54A with the manometer column 100 disposed in a parallel orientation and reversibly connected to the sedimentation column 54Aby the plurality of mechanical connectors 104, here in the form of clips into which the manometer column 100 may seat. FIGS. 2A and 3B show a lower region 120 of the sedimentation column 54A where the manometer / secondary column 100 is likewise secured parallel to the main sedimentation column 54A by anchor clips 104. FIGS. 2C and 3B show a view of a portion of the lower section 120 of the device 50A having the base 76 with a pedestal 74 for supporting the sedimentation column 54A and the attached manometer column 100. FIG. 2D shows an assembly of all the components, including the sedimentation column 54A and the manometer column 100 assembled together and secured to the base 76 and pedestal 74 for supporting the two columns.

[0085] The main sedimentation column 54A may be formed in multiple sections that may be joined together at fluid tight connections. For example, as best seen in FIGS. 3A3B, the main sedimentation column 54A may include a first section of column 130 that seats in an upper coupling component 132 (FIG. 3A) that has sealing gaskets 134 (e.g., two O-ring gaskets as shown). In FIG. 3B, a second section of column 140 has a first end 142 that is received in the upper coupling component 132 (not shown in FIG. 3B) and has a second end 144 that is received in a lower coupling component 146. The lower coupling component 146 secures that second section of the column 140 to the pedestal 74 that also has sealing gaskets 72 (e.g., two O-ring gaskets as shown). The pedestal 74 is connected to base 76 that supports the entire assembly 50A, including the main sedimentation column 54A and secondary manometer column 100. In this manner, the column(s) may be portable and broken into sections during transport, but the various components shown in FIGS. 3A-3B, including segments 130, 140 of the main sedimentation column 54A, may be assembled together on site for conducting tests according to the present disclosure. Thus, the conduit 82A in fluid communication with the pressure port 78A receives a portion of liquid (not shown) from the main sedimentation column 54A, where the liquid is substantially free or free of any solid particles present in the column 54A. Again, the conduit 82A comprises the angled first region 84A. As shown in FIG. 3A, the conduit 82A terminates in a quick connector 88 A, for example, a push-to-connect fitting in which the manometer secondary column 100 may be seated.

[0086] The m-Sed test system hardware shown in FIGS. 2A-2D, 3A-3B, thus includes a sedimentation column 54A and the secondary column or manometer 100, where the main sedimentation column 54A may have at least two sections or segments (e.g., 130, 140) for ease ofAttorney Docket No. 2115-0084818-WO-POB packing and transport. In one example, the upper region or top section 110 is 80 cm (31.5 in.) long, while the lower region or bottom section 120 is 100 cm (39.4 in.) in length. The main sedimentation column 54A may be of the dimensions specified previously above, for example, having an inside diameter of 25.4 mm (1 in.) and an outside diameter of 31.8 mm (1.25 in.). The top section 110 is seated within and may optionally be glued into the upper coupling component / coupler 132. The inside of the bottom of the upper coupler is fitted with two O-rings 132 to prevent leakage when it attaches to the bottom section 120 / segment 140 of the sedimentation column 54A. The second segment 140 of the bottom section 120 of the sedimentation column 54A is also seated and may be affixed (e.g., glued) into a lower coupler 146 as shown in FIGS. 2A-2D and 3A-3B. The lower portion of the lower coupling component 146 is fitted onto the pedestal 74, which is fitted with another set of two O-rings 72 to prevent leakage. In this variation, the pedestal 74 is permanently centered atop a 117 mm (4.6 in.) diameter, 25.4 mm (1.0 in.) thick base 76. The secondary column or manometer 100 may be a flexible tube. The manometer tube may have an inner diameter of about 3.2 mm. All of the m-Sed device hardware is formed from a material transparent to visible light, such as a transparent polymeric material like clear acrylic or in the case of the manometer tube, optionally a transparent polyurethane rubber.

[0087] When assembled, the pressure / manometer port 78 A (the main sedimentation column-to-manometer connector) is located 160 mm (6.3 in.) above the pedestal 74. This provides ample volume for all specimen particles to accumulate below the port 78 A. It should also be noted that the connecting bore or first angled region 84A in the manometer port assembly is angled 30 degrees from vertical. As noted above, this helps prevent soil particles from entering and settling in the connector 88A and manometer 100. The manometer 100 itself is a flexible polyurethane rubber tube having an inside diameter of 3.2 mm (1 / 8 in.) and an outside diameter of 6.4 mm (1 / 4 in.). The selections of the manometer material and diameter may be intrinsically linked to the dynamic pressure responses during testing and further discussed below in the examples. As it can be loosely coiled for transport, the manometer tube can be continuous over its entire 1550 mm (61 in.) length. It attaches to the port assembly 78A using a simple push-to-connect fitting 88A. To keep it securely in place, the manometer tube is attached to the main sedimentation column using multiple (e.g., five) clips 104 along its length. These clips 104 may be permanently glued to the main sedimentation column 54A. Lastly, a scale 102, for example, having a precision of 1 mm (1 mm intervals of height indicia), is attached to the upper section of the main sedimentation column 54A for reading water levels in the manometer 100 oriented in parallel to it.

[0088] In this embodiment, a pressure measuring component is in the form of a secondary column / tube or manometer 100 fluidly coupled to the conduit, wherein liquid heightAttorney Docket No. 2115-0084818-WO-POB measurements are taken. The manometer 100 serves as an observation tube / column and may comprise a scale having indicia of height (best seen in FIGS. 2B and 3A as 102) to measure a height or liquid level in the manometer / measuring component, which may correspond to hydrostatic pressure of liquid at the pressure port 78. As discussed above, the scale or indicia of height 102 may be in the adjacent parallel main sedimentation column, disposed next to or near one or both of the columns, or in the manometer secondary column itself. The manometer 100 is attached so that it is parallel to the main sedimentation column 54A and extends along a majority of length of the column 54A, so that the respective major axes (height / length) are co-extensive with one another, as previously described above. The manometer column 100 may be a flexible tube that is connected to the main sedimentation column 54A, for example, by physical attachment via clips or other connectors 104. In this manner, the measuring component in the form of a manometer 100 in this variation can measure a height of the liquid against the scale 102 (e.g., in the observation tube) and these heights can be used for various calculations and may be used to determine hydrostatic pressure. The various heights / pressure measurements can be taken continuously by videographic equipment or can be taken at regular intervals, either by photographic / videographic equipment or by visual operation by an operator conducting the test on the device. These measurements can be input into a processor / a computer processing unit (CPU) that also forms part of the system and can be operated as described above. As described above, a plurality of measurements (e.g., via height measurements, which can be related to hydrostatic head or pressure) are taken during the testing, including as the solid particles pass by the pressure port to be used to determine the weight of solid particles still above the pressure port.

[0089] For example, the processor may be optionally configured to calculate pressures from height inputs and / or further configured to calculate the plurality of respective settling velocities of the solid particles based on a settling distance and a settling time(s). These height / pressure measurements can thus provide information about an amount (% by weight) of solid particles that are above versus below the pressure transducer port. Further, as a distance that the particles fall through the primary sedimentation column is known and a time at which the particles began falling is known, the settling velocity of a given particle at the pressure port at any given time can provide a particle size by using equations such as given by Jimenez and Madsen discussed below.

[0090] FIG. 4 show pressure stages A-D during tests to determine a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, where the measurement device includes a sedimentation column and a water level measuring component (manometer column) for observation having a scale with indicia of height that may beAttorney Docket No. 2115-0084818-WO-POB portable and assembled / disassembled like the variation described just above. The calculations that occur at these stages will be discussed further below. Generally, Stage A occurs when only water is in the sedimentation column and manometer. Stage B is where a sample of solid particles is introduced to the sedimentation column and all the solids are above a pressure / manometer port. Stage C coincides to when the solids are falling through the sedimentation column past the pressure port. Finally, stage D is where all the solids have passed by and settled below the pressure / manometer port.

[0091] Thus, the present disclosure contemplates a new lightweight portable manometersedimentation (m-Sed) system for determining particle size distributions (PSDs). In certain aspects, the m-Sed test is appropriate for solid particles spanning the full sand size range, for example, for particle sizes ranging from about 0.075 mm to about 4.75 mm. Such an embodiment of the m-Sed particle distribution device and test may employ a polyurethane rubber manometer tube connected to and in fluid communication with a main sedimentation column (for example, having a 3.2 mm inner diameter connected to a 25.4 mm diameter main sedimentation column). In this manner, all reliance on electricity can be eliminated to facilitate testing at remote field locations. Particle size distribution (PSD) curves for various sand specimens produced by the m- Sed are in very good agreement with traditional sieve methods. A parametric analysis using the Corey Shape Factor (csf) showed that the influence of particle shape on settling velocities is most pronounced for coarse particles, diminishes for medium sizes, and becomes negligible for fine sand. The m-Sed test also provides very accurate measures of specific gravity and specimen mass. The m-Sed test's operational simplicity, portability, reliability, and accuracy make it a proven alternative to conventional sieving for PSD analysis of sands.

[0092] In certain further aspects, as discussed above, methods for determining a particle size distribution of a mixture of solid particles are provided. The methods may comprise introducing a sample of solid particles into a first end of a sedimentation column containing a liquid. The method also comprises measuring a height or level of the liquid in a secondary column in fluid communication with the sedimentation column at distinct times as the solid particles pass through the sedimentation column from the first end to a second end. The method also includes determining sizes of the solid particles based on a plurality of their respective settling velocities using equations such as by Jimenez and Madsen.

[0093] In certain aspects, the method further comprises measuring height of the liquid (e.g., measuring height at least once) prior to the introducing of the sample. The methods may alternatively comprise measuring a height of the liquid, which is related to pressure of the liquid, at the pressure port elevation. The method may include measuring the height of the liquid in theAttorney Docket No. 2115-0084818-WO-POB manometer after the solid particles collect at the second end of the sedimentation column. Further, in certain aspects, the measuring height of the liquid in the ancillary column / manometer may be intermittent or alternatively continuous.

[0094] In one aspect, the sedimentation column further comprises a port disposed in a wall of the column disposed at a height above where the particles collect at the second end of the sedimentation column. The sedimentation column further includes a conduit in fluid communication with the pressure port that receives a portion of the liquid in the sedimentation column free of the solid particles. There is also a height measuring component in the form of the ancillary column or manometer that is associated with the conduit and is in fluid communication with the sedimentation column so that heights of the liquid can be measured at distinct times as the solid particles pass through the sedimentation column from the first end to a second end.

[0095] In certain aspects, the measuring of the height comprises measuring an initial height of the liquid in the secondary column prior to the introducing of the sample. Thus, prior to the introducing the sample of solid particles into the sedimentation column, the method may further comprise introducing a first portion of the liquid into the sedimentation column as a first height (112, as shown in FIG. 1) where the liquid fills the sedimentation column to below a second height (ha, as shown in FIG. 1) corresponding to the sedimentation column’s overall height. In various aspects, a plurality of height measurements of the liquid in the secondary column / manometer may be taken at distinct times or more specifically, along with a plurality of the times may be observed / recorded. The methods may include measuring a height of the liquid in the secondary column before the solid particles are introduced and a height of the liquid in the secondary column after the solid particles are introduced but before they pass the pressure port, and a plurality of heights of the liquid in the secondary column while the solid particles are passing the pressure port. The measuring of the height of the liquid in the secondary column may occur intermittently or continuously. Further, the measuring the height may also comprise measuring a final height of the liquid in the secondary column after the solid particles collect at the second end of the column.

[0096] As noted above, an indicia of height or scale may be associated with the secondary column for the measuring of the height at distinct times in the secondary column. Thus, the measuring of heights of the liquid at distinct times in the secondary column may occur by recording a plurality of times at which a plurality of predetermined heights are reached in the secondary column. In certain variations, the predetermined height may be at intervals of about 1 mm.Attorney Docket No. 2115-0084818-WO-POB

[0097] As discussed above, the sedimentation column may further comprise a port disposed in a wall of the sedimentation column disposed at a height above where the particles collect at the second end of the sedimentation column, a conduit in fluid communication with the port that receives a portion of the liquid in the sedimentation column free of the solid particles, and a fluid- tight connector, such as a quick connector, associated with the conduit in which the secondary column seats and through which the liquid transfers.

[0098] In certain aspects, the present disclosure contemplates a method of determining a particle size distribution of a mixture of solid particles. The method comprises introducing a sample of solid particles into a first end of a sedimentation column containing a liquid. The method also comprises measuring the height of the liquid at distinct times in a secondary column in fluid communication with the sedimentation column as the solid particles pass through the sedimentation column from the first end to a second end to provide a plurality of height measurements. The method includes determining a particle size distribution of the solid particles based on a plurality of settling velocities of the solid particles correlated in time and the plurality of height measurements of the liquid in the secondary column.

[0099] In accordance with the present disclosure, various models for calculating sedimentation rates and / or settling velocities may be used, as appreciated by those of skill in the art. In certain aspects that will be described further below, the determining the particle sizes from previously determined settling velocities (v) by using settling velocity models, such as, but not limited to, the Jimenez and Madsen model (2003):where g is an acceleration constant due to gravity, t / ^is a nominal particle diameter of a respective solid particle, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particle, and BJM is a second dimensionless coefficient based on a shape and roundness of the solid particle. In this manner, the particle sizes of the solid particles may be determined.

[0100] Various embodiments of the inventive technology can be further understood by the specific examples contained herein. Specific Examples are provided for illustrative purposes of how to make and use the compositions, devices, and methods according to the present teachings.

[0101] Example

[0102] A particle size distribution of a mixture of solid particles may be determined in this example according to certain aspects of the present disclosure, which includes a sedimentation column and a measuring component in the form of an ancillary or secondary column / tube that isAttorney Docket No. 2115-0084818-WO-POB a manometer (manometer sedimentation or m-Sed) described above. With reference to FIG. 4, the calculations made during pressure stages A-D along with an equation such as by Jimenez and Madsen shown above to determine a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure are described herein. The mathematics for the manometer embodiment of the device is particularly complex considering that fluid moves back and forth between the sedimentation column (Se ) and the manometer (Af). FIG. 4 illustrates four key stages of the manometer test, although other stages may be conducted and incorporated.

[0103] In Stage A, a fluid, typically tap water at room temperature, has been introduced into both the sedimentation column and fluidly connected manometer. The sedimentation column is awaiting the soil specimen. At the elevation of the manometer or pressure port, the pressure can be thought of as being due to the fluid in the column, pcor due to the fluid in the manometer, pm. Naturally,Pc Pm (1) or, in terms of the height of fluid:Yfhc = Yfhm (2) where yf is the unit weight of the fluid (e.g., a unit weight of water at 4 °C), whileis the height of liquid above the connection / port in the column (“c”) and h^nis the height of liquid above the connection / port in the manometer (“m”). The superscript (here “A”) indicates the stage that these height readings are taken, here during Stage A. As the fluid is the same in both the column and manometer, the following is applicable: he = / im (3).

[0104] In Stage B, the soil specimen has been introduced into the sedimentation column and the particles are settling and sorting by size, with larger particles falling faster, followed by finer ones, but none have yet arrived at the manometer / pressure port. The height of water in both the column and manometer has risen but if < h^. The increase in water height in the manometer results from water flowing from the column into the manometer, whereas the rise in water level within the column is caused by the introduced soil particles displacing water. These two heights remain constant until the first (z.e., largest) particles arrive at the connector / port.

[0105] During Stage B, the pressure at the connector / port in terms of the weights of the contents of the sedimentation column is:where W, and W are the weights of fluid and solids in the column above the port and Acis the inside cross-sectional area of the column. Equation (4) may be written:Attorney Docket No. 2115-0084818-WO-POBwhere Vf and 1 are the volumes of fluid and solids in the column above the port, Gsis the specific gravity of solids and ywis the unit weight of pure water at 4°C. Generally, y will be different from Yw-

[0106] Meanwhile, from the manometer’s perspective,Pm -mY f (6)

[0107] Invoking Eq. (1):VfYf+GsVsYw _h BiimYf ' )

[0108] As the volume of fluid in the sedimentation column is the total volume less the volume of solids:this can be solved for the water level in the column during Stage B:

[0109] The volume of solids must equal the volume of displaced fluid:where Amis the inside cross-sectional area of the manometer.

[0110] Inserting Eq. (9) into Eq. (10):which reduces to:

[0111] The corresponding total weight of solids is:

[0112] During Stage C, the particles are passing the connector / port thereby decreasing the water pressure at that elevation. Water is now flowing from the manometer back into the column.As such, the fluid level in the manometer progressively drops, and simultaneously rises in the column. The total volume decrease in the manometer at any time (t) must equal the volume increase in the column:

[0113] By analogy to Eq. (8) during Stage B, in Stage C there is:Attorney Docket No. 2115-0084818-WO-POB in which Vsc(t) is the volume of solids still above the connector at any time (t). Equation (15) is solved for the water level in the column during Stage C:(16).

[0114] Next, the expression for / if by Eq. (9) and the expression for / if (t) by Eq. (16) is brought into the volume balance by Eq. (14):which simplifies to the volume of solids that have passed the connector at time t during Stage C:

[0115] The corresponding weight of solids that have passed the connector at time t is:

[0116] Once all of the particles have passed the connector, stage D begins. With reference to Eq. (19), / ifj(t) now becomes a constantand V7(t) becomes W.P . Thus,(20).

[0117] According to Eqs. (19) and (20), the percentage of the particles by weight still above the connection at any given time (t) during Stage C is:(21).

[0118] During stage D, the water levels in both the column and manometer become the same and constant at new levels: h? = hn(22).

[0119] These are higher than the heights during Stage A because of the presence of the accumulated soil solids at the base of the column. The volume of solids is therefore:

[0120] This expression for 1 can be equated to the one given by Eq. (22):which may be solved for the specific gravity of solids:

[0121] As the particles settle, they naturally sort by size. Therefore, at any given time during stage C, the proportion of finer particles relative to those passing the pressure port elevation can be determined using Eq. (21). Furthermore, Eqs. (13) and (21) reveal that Gsis not needed toAttorney Docket No. 2115-0084818-WO-POB determine either the weight of the soil particles or the percentage of particles finer than those passing the port. However, Gsas computed by Eq. (25) will be needed for the particle settling velocity model, which will be used to determine the size of the particles traveling past the pressure port at any time t.

[0122] FIG. 5 presents actual recordings of water height histories in the manometer tube for coarse, medium, fine, and gap-graded sands. Stage A has been omitted from FIG. 5 to facilitate a clearer comparison of the settling behavior of sand particles of different sizes. The remaining task, in order to obtain the PSD, is to convert the time axis in FIG. 5 to particle sizes. In other words, to determine the size of the particles that are passing the pressure port at any given time. To achieve this, the model proposed by Jimenez & Madsen (2003) is utilized for its simplicity and accuracy.

[0123] A settling velocity model is adopted herein. Building upon prior experimental data, Jimenez and Madsen, O. S. “A simple formula to estimate settling velocity of natural sediments J. Waterw. Port Coastal Ocean Eng. 129 (2): pp. 70-78 (2003), https: / / doi.org / 10.1061 / (ASCE) 0733-950X (2003) 129:2(70), (herein “Jimenez and Madsen (2003))” the relevant portions of which are incorporated herein by reference proposed a comprehensive model for settling velocity, v, of sand particles in fluids. As discussed above, it explicitly accounts for particle shape and roundness, and is applicable across the full range of sand sizes:where i9 is the kinematic viscosity of the fluid. The constants A]Mand B}M, which are dependent on particle shape and roundness, can be found from FIGS. 12A-12B. Particle shape is represented by the Corey Shape Factor (csf), defined as csf = c / (ah)0,5where a, b, and c are the longest, intermediate, and shortest axes of the soil particle, respectively, as shown in FIGS. 12A-12B. Regarding roundness, Jimenez and Madsen (2003) categorized it into three simple descriptors: well-rounded, natural, and crushed. In most practical scenarios, natural sand is predominantly composed of quartz subjected to weathering, such that csf « 0.7, for which AJMequals 0.954 and BJMis 5.121. Eastly, the parameter dNrefers to the nominal particle diameter. To align with sieving, dNwas converted into the sieve diameter using a rule of thumb ds= 0.9 dN, where dsis the sieve diameter, as suggested by Raudkivi, A. J., 'Foose Boundary Hydraulics 3rd Ed. Oxford: Pergamon Press (1990). It should be noted that in the Jimenez and Madsen (2003) model (Eq. 26), particle size is the independent variable, while settling velocity is the dependent variable. However, for the m-Sed test, the relationship must be inverted to have the settling velocity reveal the particle size. Eq. (26) is not solvable for dNso iteration is needed to find dNfor any v.Attorney Docket No. 2115-0084818-WO-POB

[0124] Thus, new methods for determining particle size distribution of solid particles, like sands, are presented. The device / system measures heights in a manometer observation column that is in fluid communication with a sedimentation column during sedimentation of samples, e.g., sand specimens, through the sedimentation column. The height time histories contain at least four stages. Based on the heights during the various stages, the m-Sed test yields the weight of solids, the specific gravity of solids and the particle size distribution (PSD). To produce the PSD, the m- Sed test relies on previously developed models for settling velocity of sand-sized particles.

[0125] Various sand specimens with various geologic (or artificial) origins and different gradations and specific gravities were tested. The m-Sed results compare very favorably to ASTM sieving and ASTM specific gravity test results. In various aspects, the present disclosure contemplates systems / devices and methods for conducting an m-Sed test and demonstrates its capabilities for producing accurate PSDs.

[0126] An example of a “manometer-sedimentation” or m-Sed system includes a 180 cm (71 in.) tall sedimentation column with a 25.4 mm (1.0 in.) inside diameter. Further, the system also includes a manometer that is a flexible tube of 3.2 mm (1 / 8 in.) inside diameter. The main sedimentation column is in two connectable sections to facilitate easy packing and transport, while the manometer tube can be continuous but coiled for transport. Approximately 50 g of soil are used for one test. To obtain a continuous PSD curve, time readings are taken at 1 mm increments of fluid level drop in the manometer. For a specimen mass of 50 g, this will generate about 75 equally spaced data points along the % passing axis of a PSD plot, as described further herein.

[0127] The m-Sed test procedure begins with measuring the temperature of the test water and determining the fluid's kinematic viscosity and density using a table provided by Anton Paar (2025) “Viscosity of Water,” https: / / web.archive.org / web / 20250319201727 / https: / / wiki. anton- paar.com / us-en / water / , the relevant portions of which are incorporated herein by reference. The fluid for the column and manometer is typically room-temperature tap water. The water is introduced into the sedimentation column from the top until its level reaches about themark. For the current m-Sed system,is set at 1.40 m, as shown in FIGS. 2A-2D and 4. The upper or top end of the manometer is then bent downward to allow water to flow out through the tube, effectively expelling any air bubbles from the tube. The manometer is then secured adjacent to the scale on the sedimentation column by pressing it into the clips. Additional test water is then carefully introduced into the sedimentation column until the water level reaches themark.

[0128] To develop continuous PSD curves, readings of time are taken at 1 mm interval drops in manometer water level. In certain aspects, taking the time at given heights is more advantageous than taking water level readings at specified times. Taking time readings at equalAttorney Docket No. 2115-0084818-WO-POB increments of water level drop results in PSD data points equally spaced along the vertical (percent passing) axis of a PSD plot. For a 50 g specimen, this translates to about 75 data points. For situations where the manometer water level is expected to drop rapidly, such as for very uniform sands or soils containing appreciable coarse sand, a camera (e.g., mobile device or cell phone camera) may be used to record a video of the water level drop with time. Using a camera also provides immediate data storage and eliminates possible errors in PSDs due to initially missed, imprecise or incorrect readings. For the current m-Sed system, a 50 g sand specimen causes the water level in the manometer tube to rise by approximately 10 cm. Therefore, to ensure full visibility, a video recording should capture the region from the top of the water in the manometer during Stage A to 15 cm above it. In this study, videos of all tests were recorded by a cellphone at a frequency of 60 Hz.

[0129] The 50 g soil specimen is quickly introduced into the top of the sedimentation column using a wide-mouth funnel to ensure that all the particles have almost the same settlement starting time. For the determination of settling velocity of the particles at the manometer / pressure port elevation, the relationship v = L / t was employed, where L is defined as+ h^) / 2, as shown in FIG. 12, and t represents the duration of particle settling. Once the water height history in the manometer is recorded, the size of the particles passing through the pressure port elevation at any given time can be determined using Eq. (26). After that, Eq. (21) is used to determine the percent finer by weight than these particles. Development of the PSD easily follows.

[0130] Eight specimens were engineered from six pre- sieved soils to evaluate the agreement in results between the m-Sed test and traditional sieving methods. To ensure a comprehensive and systematic evaluation, the specimens included various combinations of coarse, medium, and fine fractions, along with pure coarse, pure medium, and pure fine sands, as defined by ASTM D2487-17, Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System). The specimens covered a particle size range from 0.075 mm to 4.75 mm, representing the entire ASTM-defined sand particle size range.Table 1. Tested Soil Specimens and Size CompositionAttorney Docket No. 2115-0084818-WO-POB

[0131] Griffin, IN and Michigan 2NS, both natural glacial soils, were each processed into two different gradations, resulting in specimens 1 through 4, as detailed in Table 1. To create a pure coarse sand specimen, Peanut Sand, a construction material from Ann Arbor, MI was selected due to its uniform coarse particle size distribution. Indiana Beach sand, a naturally occurring shoreline deposit, was chosen to produce a mixed specimen containing both medium and fine sand fractions. Muskegon sand, a coastal and dune sediment from Lake Michigan, was chosen to represent a well-sorted pure medium sand specimen. Lastly, a pure fine sand specimen was formed using Houston TX sand, which originates from fluvial and coastal plain deposits of southeastern Texas.

[0132] FIG. 6 shows images of the eight soil specimens, captured using a camera at a magnification of 245.4 pixels per mm. Each image shows a 1 cm x 1 cm area of the specimen. The percentages of coarse, medium, and fine sand of each specimen are included in parentheses in FIG. 6. The sieve-based particle size compositions of each specimen, along with their maximum and minimum particle sizes are provided in Table 1. Notably, since the sizes reported in Table 1 are based on sieve opening sizes, they may not precisely represent the actual maximum or minimum particle sizes present in the specimens.

[0133] In the tests, a csf value of 0.7, as recommended for natural sands, was used for all specimens except Specimen No. 5 — Peanut sand. As shown in FIG. 6, Peanut sand exhibits a plate-like shape. To account for this, 25 randomly selected particles from the specimen were measured using a caliper to determine their three orthogonal dimensions (a, b, and c). The average csf of these particles was found to be approximately 0.45. Therefore, a csf value of 0.45 was used in the Jimenez and Madsen model for Test No. 5.

[0134] FIGS. 7A-7B presents the PSD curves obtained from the m-Sed test and by sieving. The PSD curves generated by the m-Sed test exhibit almost perfect agreement with the data points from sieving. Given the strong agreement between the m-Sed results and sieving, the fitting curves to the sieve data were omitted in FIGS. 7A-7B. For the gap-graded soils (Specimens 3 and 4), an absence of m-Sed data points is observed in the intermediate particle size range.Attorney Docket No. 2115-0084818-WO-POBWithin this range, no soil particles exist to pass the pressure port, causing the manometer water level to remain constant.Table 2. Comparison of Particle Size Distribution Metrics (D60, D30, Dw), Cuand Cc

[0135] Table 2 quantitatively compares the PSD results from the sieve test and the m-Sed test via the particle size distribution metrics (D60, D3Q. and10) obtained by both methods. Comparisons of the coefficients of uniformity (Cu) and gradation (Cc) are also included in the table. Overall, the results of the m-Sed test show remarkable agreement with the sieve test results.

[0136] Beyond PSD determination, the m-Sed test also enables the measurement of specific gravity (Eq. 25) and soil specimen mass (Eq. 20). Table 3 compares the specific gravity values derived from the m-Sed test and those from the specific gravity test according to ASTM D854-23, Standard Test Methods for Specific Gravity of Soil Solids by the Water Displacement Method. The comparison between the soil specimen mass determined by the m-Sed test and that measured using a laboratory weight scale is also presented in Table 3. As the results show, the m- Sed test provides highly reliable values of specific gravity and soil specimen mass.Attorney Docket No. 2115-0084818-WO-POBTable 3. Comparison of Specific Gravity and Specimen Mass

[0137] Specimen # 1 , with a composition of 34% coarse sand, 33% medium sand, and 33% fine sand, was tested three times to confirm the repeatability of the m-Sed test. As shown in FIG. 8, the three m-Sed tests on the same specimen not only exhibit a strong agreement with the comparatively sparse data points from the sieve test, but also demonstrate consistency among themselves in the regions between the sieve data points, thus confirming the repeatability of the m-Sed test.

[0138] The PSD of Specimen #1 was also determined using the u-Sed test that employs a sedimentation column with a pressure transducer (in contrast to a manometer). A comparison of the PSD results obtained from the m-Sed, u-Sed, and sieve tests is presented in FIG. 9. As shown, both the u-Scd and m-Sed tests not only exhibit excellent agreement with the sieve test, but also show agreement with each other.

[0139] The effect of particle shape is further investigated. As illustrated in FIGS. 12A- 12B reflecting Jimenez and Madsen (2003), the Corey Shape Factor (csf) of sand particles directly affects the coefficients yMand ByMin Eq. (26), which in turn influences the settling velocity and consequently impacts the accuracy of the PSD results. FIG. 10 presents the relationship between settling velocity and particle size by Eq. (26) for natural sand with different csf values. To produce these curves, typical values of Gs= 2.65 and fl = 0.8926 mm2 / s were assumed. The plot illustrates that larger particles exhibit greater sensitivity to variations in csf,Attorney Docket No. 2115-0084818-WO-POB with higher csf values (i.e., more rounded particles) corresponding to higher settling velocities. As particle size decreases, the effect of csf on settling velocity becomes progressively less significant.

[0140] To further investigate the impact of csf values on PSD curves obtained from the m-Sed test, the water height- time histories from the tests on Specimen #1 (Griffin IN) and Specimen #8 (Houston TX) were used in a parametric analysis. FIG. 11 illustrates the influence of different assumed values of csf on the PSD derived from the m-Sed test. As expected, the effect of csf on particle size estimation diminishes with decreasing particle size, indicating that shape- related variations become negligible for finer fractions. Conversely, for coarse sand, differences in csf lead to notable deviations in the computed particle sizes, underscoring the necessity to account for particle shape effects when analyzing coarser sands.

[0141] Small variations in Gs, as well as minor temperature-induced changes in kinematic viscosity, have negligible effects on the PSD results obtained from the u-Scd test. Furthermore, previous studies have shown that dissolved air and typical variations in atmospheric pressure do not significantly impact water density or viscosity. Therefore, the influence of these factors on the PSD results obtained from the m-Sed test is negligible.

[0142] Regarding the specimen mass, a small mass yields low data density and poor PSD resolution. On the other hand, if a much larger specimen mass is used, the time duration over which the specimen’s particles drop through the funnel into the sedimentation column becomes longer. Thus, they would undesirably have much different settlement starting times. In certain aspects, a specimen mass in the range of about 40 g to 60 g produces consistent PSD results and therefore is suitable for sedimentation systems with a 1-inch column diameter. For larger specimen masses, in certain aspects, the mass may scale proportionally with the square of the sedimentation column's inner diameter to ensure rapid and simultaneous initiation of settling for all particles.

[0143] With the test details fully described in the examples above, a further consideration is the selection of manometer tube diameter and material. The inner diameter of the manometer tube influences the accuracy and responsiveness of the m-Sed system. As noted above, a diameter that is too small amplifies capillary rise, inhibiting the prompt stabilization of the water level at a height reflecting the actual pressure. Conversely, an excessively large diameter introduces pronounced inertial effects, resulting from the larger volume of water that must move between the sedimentation column and the manometer tube during the test. These inertial effects can potentially cause problems during Stages B and C of an m-Sed test.

[0144] One consideration is achieving an initial stabile manometer water level in Stage B. Following the initial introduction of soil / sample into the sedimentation column, the water pressureAttorney Docket No. 2115-0084818-WO-POB at the manometer / pressure port rises sharply, driving water from the column into the manometer tube. If the manometer tube diameter is too large, a large volume of water must flow rapidly, creating significant inertia. Consequently, the water level takes longer to stabilize, potentially failing to reach equilibrium before the largest particles arrive at the manometer port. The absence of a stable manometer water height during Stage Bcompromises the analysis, as this initial equilibrium height serves as a baseline reference for subsequent calculation of PSD facilitating the development of accurate PSDs.

[0145] Another consideration is delayed manometer response during Stage C. As sedimentation proceeds and particles pass the measurement port, the water pressure gradually decreases, prompting reverse flow from the manometer tube back into the sedimentation column. A large tube diameter again results in substantial inertial effects, slowing the water's return flow and delaying the reestablishment of equilibrium. This sluggish response can reduce the precision of water-level measurements during the sedimentation, ultimately affecting the precision of the PSD.

[0146] Through experimentation with different manometer diameters, a tube with an inner diameter of 3.2 mm (1 / 8 in.) was found to be optimal for conditions associated with these experiments. This diameter effectively balances the competing effects of capillary force and inertial response, ensuring rapid stabilization and accurate PSD measurement.

[0147] The selection of the manometer tube material can also significantly affect the responsiveness of the m-Sed system. A polyurethane rubber tube was specifically chosen for its high surface wettability which minimizes capillary rise, thereby reducing meniscus curvature. The smoothness of polyurethane rubber also promotes rapid water flow within the tube, providing swift and accurate responses to dynamic pressure changes. Finally, as mentioned earlier, the entire length of a polyurethane rubber tube manometer is easily coiled for packing and transportation, so it can be one continuous tube.

[0148] In this example, a new field-portable testing system for determining particle size distributions (PSDs) of sands is provided according to certain aspects of the present disclosure. It is based on water pressure readings in a soil sedimentation column using a simple manometer. While bidirectional fluid flow between the sedimentation column and the manometer adds somewhat to the complexity of the governing equations to determine PSDs, the embodiment that employs a manometer provides advantages including simple hardware, no electrical power requirements, short test duration, high system portability, and virtually no maintenance needs. If desired, a cell phone camera may be used to record the manometer water levels with time for permanent data storage and later processing.Attorney Docket No. 2115-0084818-WO-POB

[0149] As described in this example, tests on eight engineered sands having various gradations, size fractions and particle shapes showed nearly perfect agreement with PSDs by sieving. Additional tests were performed that confirmed repeatability of results. A test was also performed to compare results using a pressure transducer and a manometer; the results were virtually indistinguishable.

[0150] Determination of particle sizes requires use of a particle settling model that accounts for variations in settling velocity due to particle shape and roundness. Fortunately, the effects of particle shape are only significant for sands with coarse sand fractions. The shapes of coarse particles can be easily determined by a caliper on a representative number of coarse particles.

[0151] Finally, the m-Sed test provides accurate measures of soil specific gravity and the specimen’s mass of solids with no additional effort. These m-Sed results also strongly agree with independent measures of soils mass and specific gravity by ASTM D854-23 testing procedures.

[0152] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

Claims

Attorney Docket No. 2115-0084818-WO-POBCLAIMSWhat is claimed is:

1. A device for determining a particle size distribution of a mixture of solid particles, the device comprising: a sedimentation column for containing a liquid having a height of greater than or equal to about 1 meter, wherein the sedimentation column has a first end that is open for receiving the liquid and a sample of solid particles and a second end that is sealed; a port disposed in a wall of the sedimentation column at a height above where the solid particles collect at the second end of the sedimentation column; a conduit in fluid communication with the port that receives a portion of the liquid in the sedimentation column free of the solid particles; and a secondary column associated with the conduit that provides a plurality of height measurements of the liquid in the secondary column for a duration that solid particles pass through the sedimentation column from the first end to the second end, where a particle size distribution of the solid particles is determined based on a plurality of respective settling velocities of the solid particles and the plurality of the height measurements of the liquid.

2. The device of claim 1, wherein the sedimentation column is a cylindrical column that is transmissive to light having wavelengths in a visible region.

3. The device of claim 1, wherein the sedimentation column has a diameter at the first end of greater than or equal to about 25 mm and wherein the height is greater than or equal to about 1.5 meters to less than or equal to about 2 meters, wherein a particle size of the solid particles is greater than or equal to about 0.075 mm to a less than or equal to about 4.75 mm.

4. The device of claim 1, wherein the conduit comprises a first region that defines an angle with respect to the sedimentation column so that the first region of the conduit connects to the port and is graded to a first elevation that is above the port.

5. The device of claim 4, wherein the angle is less than or equal to about 30° from vertical corresponding to the sedimentation column.

6. The device of claim 1, wherein the port is disposed greater than or equal to about 16 cm above the second end of the sedimentation column.

7. The device of claim 1, further comprising a processor that receives and records the plurality of height measurements of the liquid in the secondary column to determine a specific gravity of the solid particles and a mass of the solid particles.Attorney Docket No. 2115-0084818-WO-POB8. The device of claim 7, wherein the processor is programmed to wherein the processor is programmed to determine particle sizes of the solid particles based on the plurality of respective calculated settling velocities given by:where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, dN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

9. The device of claim 1, wherein the device further comprises an indicia of height to provide the plurality of height measurements of the liquid in the secondary column.

10. The device of claim 1, wherein the secondary column is a flexible transparent tube.

11. The device of claim 1, wherein the sedimentation column has a first diameter and the secondary column has a second diameter of less than or equal to about 4 mm.

12. The device of claim 1, further comprising a plurality of mechanical connectors to reversibly secure the secondary column to the sedimentation column.

13. The device of claim 1, wherein the conduit comprises at least one quick connector to reversibly couple with the secondary column.

14. The device of claim 1, wherein the sedimentation column is an assembly comprising multiple segments reversibly coupled together.

15. A method of determining a particle size distribution of a mixture of solid particles, the method comprising: introducing a sample of solid particles into a first end of a sedimentation column containing a liquid; measuring a height of the liquid at distinct times in a secondary column in fluid communication with the sedimentation column as the solid particles pass through the sedimentation column from the first end to a second end to provide a plurality of height measurements; and determining a particle size distribution of the solid particles based on a plurality of respective settling velocities of the solid particles and the plurality of the height measurements of the liquid.

16. The method of claim 15, wherein the measuring the height comprises measuring an initial height of the liquid in the secondary column prior to the introducing of the sample.Attorney Docket No. 2115-0084818-WO-POB17. The method of claim 16, wherein the measuring the height further comprises measuring a plurality of heights of the liquid in the secondary column intermittently while the solid particles are passing through the sedimentation column.

18. The method of claim 17, wherein the measuring the height further comprises measuring a final height of the liquid in the secondary column after the solid particles collect at the second end of the column.

19. The method of claim 15, wherein an indicia of height is associated with the secondary column for the measuring of the height of the liquid at distinct times in the secondary column.

20. The method of claim 19, wherein the measuring the height of the liquid at distinct times in the secondary column occurs by recording a plurality of times at which a plurality of predetermined heights are reached in the secondary column.

21. The method of claim 20, wherein the predetermined heights are height intervals of about 1 mm.

22. The method of claim 15, wherein the sedimentation column further comprises: a port disposed in a wall of the sedimentation column disposed at a height above where the solid particles collect at the second end of the sedimentation column; a conduit in fluid communication with the port that receives a portion of the liquid in the sedimentation column free of the solid particles; and a quick connector associated with the conduit in which the secondary column seats through which the liquid transfers.

23. The method of claim 15, wherein the determining the particle size distribution further comprises calculating a plurality of particle sizes by using a settling velocity model:where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, t / ,v is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

24. The method of claim 15, wherein the measuring the height of the liquid in the secondary column occurs continuously.

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