Magnetic resonance methods and apparatus for measuring viscosity in fluids

Abstract

A method of non-contact measurement of viscosity using a portable nuclear magnetic resonance ("NMR") apparatus Including i) providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient; ii) accelerating the fluid from a first state of rotation to a second state of rotation; iii) during the period of acceleration of the fluid, generating a series of NMR spin-echo pulse sequences with a delay between sequences to allow for recovery of the NMR magnetization; iv) acquiring spin echo data from each of the pulse sequences from the sensitive region; v) extracting echo intensity values from the spin echo data; vi) determining a transition time from the echo intensity values; and vii) relating the transition time to viscosity to determine the viscosity of the fluid sample.

Description

MAGNETIC RESONANCE METHODS AND APPARATUS FOR MEASURING VISCOSITY IN FLUIDSFIELD

[0001] In one of its aspects, the present disclosure relates generally to a method and apparatus for measuring viscosity in fluids.BACKGROUND

[0002] Finding the viscosity of a fluid is commonly done with a rheometer where the fluid resistance to an inserted probe is measured. The insertion of the probe is intrusive, and the fluid is in direct contact with the probe. While generally not a problem, the use of an intrusive measurement is sometimes not possible or could have unwanted effects, such as a separation of the solution in response to the movement of the probe. Therefore, a non-intrusive, non-contact measurement is desirable. However, existing non-contact methods such as Laser-Doppler- Velocimetry (LDV) [1] or Particle Image Velocimetry (PIV) [2] require transparent samples and in some cases the addition of scatterers to the fluid.SUMMARY

[0003] The present invention, in one embodiment, relates to a method of non-contact measurement of viscosity using a portable nuclear magnetic resonance ("NMR") apparatus, including the steps of i) providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient; ii) accelerating the fluid from a first state of rotation to a second state of rotation; iii) during the period of acceleration of the fluid, generating a series of NMR spin-echo pulse sequences with a delay between sequences to allow for recovery of the NMR magnetization; iv) acquiring spin echo data from each of the pulse sequences from the sensitive region; v) extracting echo intensity values from the spin echo data; vi) determining a transition time from the echo intensity values; and vii) relating the transition time to viscosity to determine the viscosity of the fluid sample.

[0004] An NMR system including a portable unilateral magnet having a constant gradient perpendicular to a surface of the magnet; a tubular vessel suitable for holding a sample fluid; a motor operably connected to the tubular vessel for rotating the tubular vessel around the central axis and for spinning up and spinning down the tubular vessel; a radio frequency coil around therotating sample; an NMR console operably connected to the radio frequency coil; the NMR console comprising a radio frequency generator and a radio frequency detector both operably connected to the radio frequency coil, and a computer system operably connected to the radio frequency detector, wherein the computer system comprising computer program instructions for computer implemented steps including generating a series of NMR spin-echo pulse sequences with a delay between sequences to allow for recovery of the NMR magnetization; acquiring spin echo data from each of the pulse sequences from the sensitive region; extracting echo intensity values from the spin echo data; determining a transition time from the echo intensity values; and relating the transition time to viscosity to determine the viscosity of the fluid sample.

[0005] Other advantages of the present teachings may become apparent to those of skill in the art upon reviewing the present specification.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Embodiments of the present invention will be described with reference to the accompanying drawings, wherein like reference numerals denote like parts, and in which:

[0007] FIG. 1 is a diagram of a fluid between rest and full body rotation (left) with fluid at full body rotation (right);

[0008] FIG. 2 is a graph of the effects of spin-up and spin-down on acquired signal;

[0009] FIG. 3 is a graph of first protocol data: echo intensities vs the number of echo sequence;

[0010] FIG. 4 are graphs of data obtained with the first and second protocol;

[0011] FIG. 5 are graphs of measurement of NMR signal decay for different viscosities;

[0012] FIG. 6 are graphs of fitted data of 25% sample;

[0013] FIG. 7 are graphs of spin-up and spin-down transition times for different RPM;

[0014] FIG. 8 is a diagram of Ekman pumping;

[0015] FIG 9. is a schematic of an experimental setup according to an embodiment of the present invention; and

[0016] FIG 10. is a diagram of the pulse sequence used in the second protocol according to an embodiment of the present invention.DETAILED DESCRIPTION

[0017] Various apparatuses or processes will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover processes or apparatuses that differ from those described below. The claimed inventions are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses described below. It is possible that an apparatus or process described below is not an embodiment of any claimed invention. Any invention disclosed in an apparatus or process described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim, or dedicate to the public any such invention by its disclosure in this document.

[0018] A rotating fluid in a cylindrical container will eventually reach full body rotation, which is when any point of the fluid has the same angular velocity as any other point of the fluid. While not much information can be extracted from a fluid that has reached full body rotation, the time it takes for a fluid to reach or recover from this rotation, the transition time, can be exploited. The transition time has been discussed in several theoretical and experimental publications, and it is shown to depend on the fluid’s viscosity [3], Therefore, if there is a way to find the transition time, the viscosity can be estimated.

[0019] With a portable NMR instrument, a portion of a fluid sample, or the whole fluid sample, is excited to generate an NMR signal. Referring to FIG. 1 , in one embodiment, an NMR signal was generated in a vertical slice passing through the middle of the fluid sample along the longitudinal axis of the vertical tube holding the fluid sample. The vertical slice is represented by the solid horizontal line 2 shown in FIG.1. Different parts of the sample will rotate with different speeds. While in presence of a constant gradient, that will result in a distribution of NMR signal phases in the excited volume, causing a so-called phase interference [4],

[0020] The change in phase interference is the key to finding the transition time. When a sample has a constant velocity profile, phase interference is constant. If the velocity profile is not constant,like in the case of solid body rotation, then phase interference will significantly reduce the signal acquired. Altogether, this means that as the fluid accelerates from one state of full-body rotation (or from rest) to another (or to rest), the signal acquired will decrease (or increase) to a minimum at full-body rotation. The transition time can then be extracted from the data and the viscosity could be estimated.

[0021] To evaluate the viscosity, two dimensionless parameters were used: the Rossby and Ekman number. A detailed analysis of these two parameters is beyond the scope of this application, but there are the important things to note. If the Rossby number is small, then a linear analysis can be performed [5], In the linear analysis, the transition time is inversely proportional to the square root of the Ekman number, while in the non-linear analysis, the transition time is inversely proportional to the Ekman number. Under the heading "Experimental Measurements" below, are three equations to estimate viscosity.

[0022] Referring to FIG. 2, in one embodiment, the method to acquire NMR signal of a sample while it undergoes a change in its rotation speed, including starting from rest to the solid body rotation, and from the solid body rotation to rest, is shown. Due to phase interference, the signal decays as the rotation rate changes, enabling a measurement of the transition time.

[0023] The process of spinning a fluid and letting it recover is often called spin-up and spindown in most papers and documentation. When the spinning starts and the fluid accelerates to full body rotation, it is referred to as spin-up, and when the spinning stops and the fluid recovers back to rest, it is referred to as spin-down. Both spin-up and spin-down have their own transition times that are the same in a linear theoretical treatment (if the Rossby number is small). FIG. 5 shows MR signal magnitude for samples with different viscosities.Rossby Number Linear AnalysisTransition timeEkman Number Kinematic viscosityCylinder heightRotation rate1 BExperimental measurements

[0024] In one embodiment of a rotating apparatus set-up according to the present invention (see FIG. 9), an alternating current (AC) stepper motor 10 powered by a power supply (not shown) is connected to a rotor shaft 12; an Arduino board 14 is used to send commands to motor controller 11 to control motor 10. Rotor shaft 12 rotates a cylindrical glass vessel 16 filled with a fluid (not shown) under investigation. Cylindrical glass vessel 16 is supported by sample holder 22 on bearing 24 which permits cylindrical glass vessel 16 to rotate. Cylindrical glass vessel 16 is positioned next to a portable NMR instrument magnet array indicated generally at 18 including magnets 18a, 18b and 18c which are polarized in the same direction, in such a way that cylindrical glass vessel 16 is positioned adjacent a sensitive region indicated generally at 19 (defined as the area between the pair of grey hatched lines 19a) of NMR instrument magnet array 18. In another embodiment, three-magnet array 18 can be replaced with a single magnet (or other magnet arrays). The advantage of a magnet array is that the configuration can be optimized to give a specific magnetic field profile (therefore, a well-defined excited volume / motion sensitivity). Other magnets can be used provided there is a well-defined magnetic field gradient. Radio frequency (RF) coil 20 of NMR instrument 18is connected to Techmag™ LapNMR 21 to run NMR measurements. In one embodiment, coil 20 is tuned to a frequency of 5.71 MHz and excites an approx. 2 mm rectangular slice of the sample.

[0025] The signal acquisition was synchronized with motor 10 speeding up the rotation speed of the sample in cylindrical glass vessel 16 to observe the spin-up effect on the NMR signal decay. Halfway through the signal acquisition, motor 10 was slowed down to permit the spin-down effect on the NMR signal decay. For all measurements, motor 10 was sped up and slowed down for 7 seconds at each stage, with 14 seconds in total. This number is arbitrary and doesn’t have any specific significance, it was simply enough time for the transition time to be seen. This period can be fine-tuned to speed up the overall acquisition time of the measurement.

[0026] The most important experimental NMR parameter to control the effects of phase interference is the duration of the echo time. It is also common in the NMR community to use the half of the echo time, tau, instead of the echo time, and in one embodiment, the present inventors use the tau time from this point on. During the experiments, a range of tau times was tested. For the lowest tau time of 0.1 milliseconds, the effects of rotation were not detectable. At longer tau times, they were easily detectable; in most experiments, the tau time of 0.5 milliseconds was used along with a range of rotation rates going from 50 to 200 RPM.

[0027] Two measurement protocols were tested, with the focus on a greater Signal-to-Noise Ratio and, therefore, a shorter experiment time.First Protocol

[0028] Referring to FIG. 3, the first protocol consisted of a series of spin echo sequences repeated after a delay necessary to recover the NMR magnetization, which the present inventors call a “last delay”. The last delay determines the temporal resolution of the spin-up / spin-down transition curves. The measurements were done using a sample of doped water with tau of 0.5 ms and a last delay of 50 ms. In total, there were 270 spin echo sequences acquired per scan. The echo intensity data were extracted and processed (See FIG. 3).

[0029] With the first protocol came the confirmation that the spin-up and spin-down transition times could be observed (see the first plot of FIG. 4). To improve the Signal-to-Noise ratio of the acquired data, a second measurement protocol was designed.Second Protocol

[0030] The second protocol (see FIG. 10) resembles the first one except for one key difference: instead of having a series of spin echo sequences with only one echo acquired in each sequence, there was now a series of Car-Purcell-Meiboom-Gill (CPMG) trains. The new sequence has two different tau values: one for the first echo of each CPMG train, and one for the remaining 35 echoes of each CPMG. This is done so that the first echo can have a longer tau value and thus be affected by phase interference while the rest of the echoes can be used to average noise. The last delay between CPMG trains was kept at 50 ms. The tau times of the first echoes were also kept at 0.5ms and the tau times of the remaining echoes were set at 0.1 ms. In total, there were 240 CPMG trains acquired per scan. The second plot of FIG. 4 shows the first echo intensity of the CPMG trains.

[0031] Referring to the third plot of FIG. 4, each CPMG train had all its 36 echoes averaged to yield one data point, with a significantly reduced noise.

[0032] So far, both the new and old sequences have only used doped water to see if the measurement would even work in the first place. With confirmation, new samples of different viscosities were made to see if a difference in viscosity would affect the observed transition times. 6 samples consisting of doped water and glycerol were prepared (10%, 15%, 20%, 25%, 50%,and 75% glycerol). They were then put through the measurement as described above, with the data processed.

[0033] As the viscosity increases, a significant change in the transition time can be observed. The transition time of both spin-up and spin-down gets smaller as the viscosity increases, which agrees with theoretical predictions.

[0034] Although not an issue for most samples, the 75% glycerol sample had transition times so fast that the current sequence could not properly capture it. To fix this, the number of echoes per CPMG could be lowered or the number of CPMGs could be lowered. The parameters can be changed around as needed; the only restriction is that the full sequence needs to last the same amount of time as the motor rotation cycle.

[0035] Referring to FIG. 6, to find the transition time, the spin-up and spin-down signal decays were fitted monoexponentially. A point at which 98% of the signal had decayed / recovered was found using the fitted data, and the time coordinate of this point was estimated to be the transition time.

[0036] In general, the data follows an expected behavior for both spin-up and spin-down experiments. It can also be seen that the transition times depend monotonously on the viscosity. Higher viscosity samples demonstrate consistently shorter transition times that confirms the premise of the proposed method: the viscosity of a fluid sample can be measured by using the spin-up and / or spin-down rotation and detecting the transition time to the dynamic equilibrium. In this implementation, a sensitivity of bulk NMR signal to the time-dependent distribution of velocities in the fluid was employed to measure the transition times (see FIG. 7).

[0037] All the data that has been shown is experimental, but the theoretical values of the transition time can also be estimated, as mentioned in the theory section above. The only variable that changes from sample to sample is the viscosity. The other variables present in the Ekman number and transition time equation are known or constant.Conclusion

[0038] The experimental evidence thus collected is a strong indication that transition times both for the spin-up and spin-down rotations depend on the viscosity monotonously, and thus they canbe used for non-invasive measurements of a sample viscosity with a portable NMR device, with various implementations of the measurement possible.

[0039] In these embodiments, the NMR signal was generated from within the sensitive slice passing vertically through the sample. This permitted to use the velocity distribution in the tangential direction of the rotating sample due to the permanent gradient orientation sensitizing the NMR signal to displacements in that direction. Another possible implementation can involve rotating the magnet array so that the sensitive slice passes horizontally through the bottom of the sample. This will sensitize the NMR signal to displacements in vertical direction, thus making it possible to utilize the vertically oriented circulation due to Ekman pumping as a potential mechanism for measuring the transition time (see FIG. 8). In FIG. 8, the boundary layer is indicated generally at 4 and the Ekman pumping is indicated generally at 6.

[0040] While the teaching herein includes illustrative embodiments and examples of some aspects of an invention, the description is not intended to be construed in a limiting sense. Thus, various modifications of the illustrative embodiments, as well as other embodiments of the invention, may be apparent to persons skilled in the art upon reference to this description. It is therefore contemplated that the appended claims will cover any such modifications or embodiments.

[0041] All publications, patents, and patent applications referred to herein are incorporated by reference in their entirety to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference in its entirety.

[0042] While the teaching herein includes illustrative embodiments and examples of some aspects of an invention, the description is not intended to be construed in a limiting sense. Thus, various modifications of the illustrative embodiments, as well as other embodiments of the invention, may be apparent to persons skilled in the art upon reference to this description. It is therefore contemplated that the appended claims will cover any such modifications or embodiments.

[0043] One or more methods described herein can be implemented by computer program instructions or code, which can be executed on a computer. For example, the code can be implemented by one or more digital processors (e.g., microprocessors or other processing circuitry), and can be stored on a computer program product including a non-transitory computer-readable medium (e.g., storage medium), e.g., a magnetic, optical, electromagnetic, or semiconductor storage medium, including semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), flash memory, a rigid magnetic disk, an optical disk, a solid-state memory drive, etc.

[0044] The program instructions can also be contained in, and provided as an electronic signal, for example in the form of software as a service (SaaS) delivered from a server (e.g., a distributed system and / or a cloud computing system). Alternatively, one or more methods can be implemented in hardware (logic gates, etc.), or in a combination of hardware and software. Example hardware can be programmable processors (e.g. Field-Programmable Gate Array (FPGA), Complex Programmable Logic Device), general purpose processors, graphics processing units (or GPUs) Application Specific Integrated Circuits (ASICs), and the like. One or more methods can be performed as part of or component of an application running on the system, or as an application or software running in conjunction with other applications and operating system.

[0045] One or more methods described herein can be run as a program in an NMR device or as a standalone program connected to an NMR device. Although the description has been described with respect to particular implementations thereof, these particular implementations are merely illustrative, and not restrictive. Concepts illustrated in the examples may be applied to other examples and implementations. Note that the functional blocks, operations, features, methods, devices, and systems described in the present disclosure may be integrated or divided into different combinations of systems, devices, and functional blocks as would be known to those skilled in the art. Any suitable programming language and programming techniques may be used to implement the routines and processing of particular implementations. Different programming techniques may be employed, e.g., procedural or object-oriented. The routines may execute on a single processing device or multiple processors. Although the steps, operations, or computations may be presented in a specific order, the order may be changed in different particular implementations. In some implementations, multiple steps or operations shown as sequential in this specification may be performed at the same time.

[0046] It will be appreciated that the various operations, processes, and methods disclosed herein can be embodied in a machine-readable medium and / or a machine accessible medium compatible with a data processing system (e.g., a computer system), and can be performed in any order (e.g., including using means for achieving the various operations). Accordingly, thespecification and drawings are to be regarded in an illustrative rather than a restrictive sense. In some embodiments, the machine-readable medium can be a non-transitory form of machine- readable medium.

[0047] References:[1] William B. Watkins, R. G. Hussey; Spin-up from rest in a cylinder. Phys. Fluids 1 October 1977; 20 (10): 1596-1604. https: / / doi.Org / 10.1063 / 1.861781[2] Fabian Burmann, Jerome Noir; Effects of bottom topography on the spin-up in a cylinder. Physics of Fluids 1 October 2018; 30 (10): 106601. https: / / doi.Org / 10.1063 / 1.5051 1 1 1[3] Greenspan, H. P. (1990). The Theory of Rotating Fluids.[4] Selby, W., Balcom, B.J., Newling, B., and Mastikhin, I. "Using Phase Interference to Characterize Dynamic Properties-A Review of Constant Gradient, Portable Magnetic Resonance Methods", Frontiers in Physics (2023) 11 (19 pages).[5] Hyun, J. M. (1998). Spin-up Flows in a Rotating Cylindrical Container. International Journal of Fluid Mechanics Research, 25(1-3), 305-313.

Claims

What is claimed is:

1. A method of determining viscosity of a fluid sample comprising: i) providing a magnet with a static magnetic field and a constant gradient where at least a portion of the sample defining a sensitive region is in the constant gradient; ii) accelerating the fluid from a first state of rotation to a second state of rotation; iii) during the period of acceleration of the fluid, generating a series of NMR spin-echo pulse sequences with a delay between sequences to allow for recovery of the NMR magnetization; iv) acquiring spin echo data from each of the pulse sequences from the sensitive region; v) extracting echo intensity values from the spin echo data; vi) determining a transition time from the echo intensity values; and vii) relating the transition time to viscosity to determine the viscosity of the fluid sample.

2. The method of claim 1 , wherein the step of determining the transition time comprises fitting the echo intensity values monoexponentially.

3. The method of claim 1, wherein the acceleration is a spin-up transition.

4. The method of claim 1, wherein the acceleration is a spin-down transition.

5. The method of claim 1, wherein the series of NMR spin-echo pulse sequences comprises a series of pulse sequence trains with a first echo time for the first echo of each train and a second echo time for the subsequent echoes of each of the trains.

6. The method of claim 5, wherein the pulse sequence trains are Car-Purcell-Meiboom-Gill trains.

7. The method of claim 5, wherein the subsequent echoes are averaged to yield a single value.

8. An NMR system comprising: a portable unilateral magnetic having a constant gradient perpendicular to a surface of the magnet; a tubular vessel suitable for holding a sample fluid; a motor operably connected to the tubular vessel for rotating the tubular vessel around the central axis and for spinning up and spinning down the tubular vessel; a radio frequency coil around the rotating sample; an NMR console operably connected to the radio frequency coil; the NMR console comprising a radio frequency generator and a radio frequency detector both operably connected to the radio frequency coil, and a computer system operably connected to the radio frequency detector, wherein the computer system comprising computer program instructions for computer implemented steps comprising generating a series of NMR spin-echo pulse sequences with a delay between sequences to allow for recovery of the NMR magnetization; acquiring spin echo data from each of the pulse sequences from the sensitive region; extracting echo intensity values from the spin echo data; determining a transition time from the echo intensity values; and relating the transition time to viscosity to determine the viscosity of the fluid sample.

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