Process, method and apparatus for determining equivalent diameter of powder particles

Abstract

The present invention relates to a process for determining the equivalent diameter of particles of a powder, and to an apparatus for carrying out such a process.

Description

[Technical field]

[0001] The present invention relates to a process for determining the equivalent diameter of particles of a powder, and to an apparatus for carrying out such a process. [Background technology]

[0002] Particle size describes the size of individual particles in a mixture and is an essential parameter for the characterization of inorganic powders, such as those used in the metallurgical and cement industries. Particle size serves as an intrinsic property of the material, allowing different qualities of powders to be easily, accurately and reproducibly distinguished.

[0003] In determining particle size, the equivalent diameter is usually used, which takes into account the fact that the particles are not perfectly spherical. The equivalent diameter can be described using the sieve diameter. For example, a sphere with a diameter of 1 mm and an elongated particle with a diameter of 1 mm can both fit into a square hole with a sieve end length of 1 mm. For example, a rounded flattened particle with a diameter of more than 1 mm can also fit into the hole by taking into account the diagonal of the hole. The equivalent diameter of 1 mm is stated even if the shape of the particle is different. In general, the equivalent diameter is based on the diameter of a sphere of the same volume. In particular, for materials with a constant density and approximately spherical shape, theoretically derivable properties of a packing of spheres can be adopted, where all the spheres have the same size. If the properties of a real system, for example hydrodynamic properties, are measured, the obtained values ​​can be assigned according to the theoretical system.

[0004] From today's point of view, many methods are available that allow the determination of the equivalent diameter as a measure of the particle size of solid non-porous particles. For example, laser diffraction methods, sieve analysis, sedimentation analysis or surface area measurements by the BET method are known. Mainly in the field of the carbide industry, the Fisher Sub Sieve Sizer (FSSS) method has been widespread for decades and is the basis for the classification and comparison of different hard materials such as tungsten carbide and metal powders. For the use of such methods, a relatively narrow and unimodal particle size distribution is an important prerequisite.

[0005] The FSSS method, which is widespread on an industrial scale, dates back to the 1940s and is based on the gas permeability of compressed powder samples. It allows the measurement of the average particle size, which corresponds to the diameter of a sphere of the same volume. This measurement method and the corresponding commercial equipment are described in detail in the standard ASTM B330-Standard Test Methods for Estimating Average Particle Size of Metal Powders and Related Compounds Using Air Permeability. To determine the equivalent diameter, a gas stream is passed through a defined powder pellet and the pressure difference is measured (see Figure 5a). Using the Carman-Kozeny equation (1), the equivalent diameter (D) can be calculated from the ratio of the pressure drop to the gas flow rate.

[0006]

number

[0007] where Δp is the pressure difference [Pa], L is the length of the specimen through which the gas is passed [m], μ is the dynamic viscosity of the gas being measured [Pa s], Φ is the form factor (usually set to 1), ε is the porosity [-], and A is the cross-sectional area of ​​the specimen perpendicular to the flow direction [m 2 ], Q is the volumetric flow rate [m 3 / s], and D is the equivalent diameter [m] of a sphere of the same volume.

[0008] To calculate the equivalent diameter, the following equations (2) and (3) are used: where m is the mass of the sample [kg], ρ is the physical density of the material being measured [kg / m 3 ], and L is the length of the sample flowed [m].

[0009]

number

[0010] This gives the following relationship:

[0011]

number

[0012] The general physical relationship between permeability and gas diffusion is summarized in Terence Allen: Chapter 1: “Permeability and gas diffusion”, January 1, 1997, PARTICLE SIZE MEASUREMENT-Vol. 2: SURFACE AREA AND PORE SIZE DETERMINATION, CHAPMAN&HALL, GB, pages 1-38.

[0013] In the paper “Pressure drop characteristics of poly(high internal phase emulsion) monoliths” published in Journal of Chromatography A, 1144 (2007) 48-54, I. Junkar et al. address the effect of porosity on pressure drop in liquid chromatography and focus on models to calculate porosity.

[0014] In “Packing density, permeability, and separation efficiency of packed microchips at different particle-aspect ratios”, Journal of Chromatography A, 1216 (2009) 264-273, S. Jung et al. discuss the packing density, relationship between pressure drop and flow rate, permeability, and separation efficiency of HPLC microchips.

[0015] GB2025069 deals with the problem of sample provision and suggests processes, in particular a process for preparing pressed powder pellets.

[0016] Patent No. 3125263 describes a method for preparing semiconductor ceramics, in which the particle size of ceramic particles is determined using the Carman-Kozeny equation, and the particle size is controlled by adding a particle size control agent.

[0017] Patent No. 5,033,678 discloses a process and apparatus for determining particle size based on the Carman-Kozeny equation. Summary of the Invention [Problem to be solved by the invention]

[0018] The methods described in the prior art are characterized by the Carman-Kozeny equation, which allows for the general calculation of the pressure loss of a flowed powder charge, but have the disadvantage that this equation only applies to steady-state conditions, which means that there is no change in the volumetric flow rate or pressure over time. With the available measurement setups, it is technically impossible to selectively vary the pressure or the volumetric flow rate.

[0019] The term Q / Δp in the Carman-Kozeny equation is the bulk conductance L R It can be called the unit [m 3 / (s·Pa)] conductance L R represents a characteristic quantity that depends on the structure of the particle system being measured and can be compared to Ohm's law R=U / I, where the electrical conductance of a resistor is described as 1 / R=I / U. According to the Carman-Kozeny formula, the conductance L R can be determined by measuring the pressure drop Δp at a defined flow rate, i.e. at a defined constant volumetric flow rate Q. However, it is essential here that all quantities are steady-state and do not undergo time variations. When using conductance, the Carman-Kozeny equation is reduced to the following form:

[0020]

number

[0021] This method of particle size determination allows a rough estimation of particle size. R To obtain a more accurate value for , the measurement must be repeated at different volume flow rates. However, this type of measurement is time consuming and therefore costly, since between each measurement one must wait until steady state is reached in the measurement system. This type of measurement therefore creates an unfavorable trade-off between the time required for a single measurement and the achievable accuracy.

[0022] The measurement systems established in the field of cemented carbide industry, including especially those by the FSSS process, have several drawbacks besides the above mentioned discrepancies. Thus, one parameter adopted to determine the equivalent diameter is the porosity of the sample, which is usually obtained by visual judgment from the height of the compressed cylindrical sample using a nomogram on the measuring device, but has a corresponding inaccuracy, resulting in random errors that contribute to a wide measurement spread. Another drawback is that the measurement method of the FSSS process only provides for a one-point measurement, which may introduce further errors. Moreover, the latest issue of the related standard ASTM B330 points out that the FSSS method will no longer be the standard method in the future, citing the shortage of equipment and spare parts, as well as the lack of technical support, as the reasons.

[0023] Against this background, the object of the present invention is to provide a measurement process and a corresponding device for determining the equivalent diameter of powder particles. It is envisaged that the process provided achieves an increase in the accuracy of the measurements and thus a reduction in the spread of the measurements, without increasing the time required for a single measurement. [Means for solving the problem]

[0024] To this end, the present invention calculates the conductance L without waiting for a steady state for each measurement. RAccording to the invention, this is achieved by the fact that a constant volume flow rate Q is no longer used, but a volume flow rate Q=Q(t) that increases with time. Under conditions of dynamic volume flow, the linear relationship between Q and Δp on which the conventional measurement methods are based is removed. Rather, the determination of the relationship between Q and Δp according to the process according to the invention is made from a non-linear characteristic by multivariate regression, rather than a simple quotient calculation.

[0025] Surprisingly, it has been found that such a measurement method allows for more accurate measurements and results in less measurement spread in shorter measurement times.

[0026] The invention therefore firstly relates to a process for determining the equivalent diameter D of a powder particle, said equivalent diameter being determined by recording a non-linear characteristic from Q(t) versus Δp(t), where Q(t) means the volumetric flow rate as a function of time and Δp(t) means the pressure difference as a function of time, in particular by plotting a set of time-equivalent values ​​of Q(t) versus Δp(t), preferably with Q(t) plotted on the x-axis and Δp(t) plotted on the y-axis.

[0027] In the scope of the present invention, Q denotes the volumetric flow rate of the measurement gas through the compressed powder sample.

[0028] Q(t) denotes the volumetric flow rate as a function of time.

[0029] Δp represents the pressure change that occurs in the flow direction when the measurement gas passes through the compressed powder sample, and p is the pressure upstream of the compressed powder sample. up and the downstream pressure p of the compressed powder sample down It can be calculated from the difference between

[0030] Δp(t) denotes the pressure difference as a function of time.

[0031] According to the process of the invention, the recording of the non-linear characteristics on which the determination of the equivalent diameter is based can be achieved by adjusting the volumetric flow rate Q(t) of the measurement gas which increases with time, or by the pressure difference Δp(t) which varies with time.

[0032] Thus, in a preferred embodiment of the process according to the invention, the characteristic describes a non-linear relationship between the pressure difference Δp(t) and the volumetric flow rate Q(t). where Δp(t) is the difference in the flow direction of the measurement gas through the compressed powder sample, where Q(t) is the volumetric flow rate of the measurement gas, which increases constantly with time, and dQ(t) / dt=q 0 , q 0 = const., and q 0 >0, q 0 is the rate of change of volume flow rate [L / s 2 ] is indicated.

[0033] According to a preferred embodiment, the constantly increasing volume flow rate Q(t)=q 0 × t is imposed on the system, while pressure is continuously measured upstream and simultaneously downstream as the sample is flushed. Thus, the system is not in a steady state, since all quantities vary continuously with time. Rather, pressure and volumetric flow rate are time-dependent quantities, with a constant rate of change of volumetric flow rate q 0 [L / s 2 ] is preferred.

[0034] In an alternatively preferred embodiment of the process according to the invention, the non-linear characteristic describes the relationship between the pressure difference Δp(t) and the volumetric flow rate Q(t), where Δp(t) is the pressure p upstream of the compressed powder sample. up and the downstream pressure of the compressed powder sample, p down is the pressure difference in the flow direction that changes with time at a constant rate between dΔp(t) / dt=p 0 , p 0 = const., p 0 >0, Q(t) stands for the volumetric flow rate of the measurement gas, which increases continuously with time, p 0 means the rate of pressure change [Pa / s].

[0035] According to this preferred embodiment, the pressure difference on the compressed powder sample is applied at a constant rate p 0 [Pa / s]. At the same time, the volumetric flow rate of the measurement gas required to generate the corresponding pressure difference is measured. Since both quantities change continuously with time, the system never reaches a steady state. According to a preferred embodiment, a constant pressure change rate p 0 is preferred.

[0036] As mentioned above, conventional methods for measuring particle size based on equivalent diameter, such as the FSSS method, operate at a constant volumetric flow rate, and therefore have the disadvantage that reliable values ​​cannot be obtained until the gas volume in the measuring device, which varies depending on the structure, and the gas volume in the sample are filled with the measurement gas, i.e., the inlet volumetric flow rate is equal to the outlet volumetric flow rate, and the system is in a steady state. Reaching a steady state can take several minutes for some powder samples. Not waiting until this state is reached will result in an erroneous evaluation. If sufficient time is given for each measurement until the system reaches a steady state, the measurement time will be disproportionately long, especially when performing multiple measurements with different volumetric flow rates.

[0037] Within the scope of the process according to the invention, it has surprisingly been found that the measurement uncertainties arising in conventional methods can be overcome by not setting the volumetric flow rate of the measurement gas constant, but by varying the volumetric flow rate Q or the pressure difference Δp as a function of time.

[0038] The measurement method according to the invention is therefore not based on a constant volume flow rate, but on a defined rate of change of the volume flow rate, as well as on the pressure change. In this way, not only is the measurement accuracy significantly increased, but also the measurement time can be advantageously reduced compared to conventional measurement methods.

[0039] On this basis, in a preferred embodiment, the process according to the invention comprises the following steps: i) Providing a compressed powder sample. ii) Determine the porosity of the compressed powder sample based on the mass and height of the compressed powder sample. iii) The measurement gas is passed through a compressed powder sample, and Δp is continuously changed as a function of time Δp(t) or Q is continuously changed as a function of time Q(t) to obtain a nonlinear characteristic. R Establish. where △p(t) is the pressure p up and the downstream pressure p of the compressed powder sample down This indicates the pressure difference that occurs in the flow direction. Q(t) is the volumetric flow rate of the measurement gas, and L R =Q / △p. iv) Taking into account the porosity of the compressed powder sample established in ii), establish the equivalent diameter D by deriving it from the nonlinear characteristic of Q(t) versus Δp(t).

[0040] The pressure difference Δp is the pressure p of the measurement gas before it flows through the sample. up and the pressure of the measurement gas after it has flowed through the sample, p down It can be determined by measuring

[0041] Preferably, a gas selected from the group consisting of dry air, nitrogen, argon, helium, carbon dioxide is employed as the measurement gas. The measurement gas can be selected as a function of the expected particle size, it having proven advantageous to use a measurement gas with a higher viscosity for coarser particle sizes. The measurement gas is characterized by not undergoing any chemical reaction with the powder sample to be measured.

[0042] Within the scope of the process according to the invention, an improvement in the accuracy of the measured values ​​while the measurement time is reduced is achieved by including a non-linear characteristic Q(t) vs. Δp(t), which is characterized in that its evaluation excludes reference to the zero point. Therefore, an embodiment of the process according to the invention is preferably such that in step iii) at least two different measurement points are established which do not correspond to the zero point of the characteristic (Δp=0 or Q=0). Preferably, within the scope of the process according to the invention, at least 5 measurement points per minute are established, more preferably at least 12 measurement points per minute.

[0043] The measurements required to record the nonlinearity of the relationship between Δp and Q may be obtained by varying a parameter with time t. In a preferred embodiment, the nonlinearity of the relationship between Δp and Q is established by varying the volumetric flow rate Q(t). In an alternative preferred embodiment, the nonlinearity of the relationship between Δp and Q is established by varying the pressure up It is established as the time lapse of (t).

[0044] In a particularly preferred embodiment, the nonlinear characteristic of the relationship between Δp and Q is the pressure p upstream of the powder pellets at a defined volumetric flow rate Q(t) up The pressure is established as a function of time (t), this pressure also being a function of time, and the volumetric flow rate increases by a constant value in a specific time interval. Thus, in a preferred embodiment, the process according to the invention comprises the following steps: i) Providing a compressed powder sample. ii) Determine the porosity of the compressed powder sample based on the mass and height of the compressed powder sample. iii) The constant volumetric flow rate change rate q of the measurement gas flowing through the compressed powder sample 0 where: dQ(t) / dt=q 0 , and q 0 = constant. iv) Conductance L R is determined from the nonlinear characteristic of Q(t) versus Δp(t), where Δp(t) is the pressure p upstream of the compressed powder sample as a function of time.up and the downstream pressure of the compressed powder sample, p down is the pressure difference between iv) Establish the equivalent diameter D by taking into account the porosity of the compressed powder sample established in ii) and deriving it from the non-linear characteristics.

[0045] In another preferred embodiment, the nonlinear characteristic of the relationship between Δp(t) and Q(t) is expressed as the pressure p upstream of the powder pellet when the volume flow rate Q(t) is continuously increased. up (t) as a function of time. Surprisingly, it has been found that in both cases a particularly narrow distribution of the measured values ​​is obtained. Therefore, an embodiment according to the invention is preferred in which the steps according to the invention comprise the following steps: i) Providing a compressed powder sample. ii) Determine the porosity of the compressed powder sample based on the mass and height of the compressed powder sample. iii) The pressure p upstream of the compressed powder sample up and the downstream pressure p of the compressed powder sample down The pressure difference △p(t) between the velocity p 0 The volumetric flow rate Q(t) of the measurement gas flowing through the compressed powder sample is set so that it changes with iv) The nonlinear characteristic of Q(t) vs. Δp(t) gives the conductance L R Establish. iv) Establish the equivalent diameter D by taking into account the porosity of the compressed powder sample established in ii) and deriving it from the non-linear characteristics.

[0046] Within the scope of the present invention, it has surprisingly been found that, compared to conventional measurement methods in which either a constant pressure or a constant volumetric flow rate is set, by varying one of these two quantities in a defined manner, the accuracy of the measurements is improved. Without being bound by theory, it is assumed that the increased accuracy occurs because the measurement errors that occur are measured several times and can then be eliminated. In a preferred embodiment of the present invention, this is done by multivariate regression.

[0047] The porosity of the compressed powder sample can be included as another parameter in the determination of the equivalent diameter according to the present invention.

[0048] For measuring the sample, a geometrically defined powder pellet can be prepared. It is advantageous to choose a shape whose cross-sectional area is constant in the height direction and whose normal vector is parallel to the direction of the pressing force. This requirement is advantageously met by a cube or a cylinder, with preference being given to cylindrical shapes. Therefore, an embodiment is preferred in which the measurement of the porosity of the compressed powder sample in step ii) of the process according to the invention is carried out with a powder pellet of cylindrical shape. As the skilled person knows, the porosity of a compressed powder sample can be determined from its mass, cross-sectional area and height (equation (3)), in which case the size of the powder pellet in the flow direction of the measurement gas is taken as its height. To improve the handling of the powder pellet, the latter is preferably placed in a sample tube.

[0049] It has been found that within the scope of the process according to the invention, measurement errors occur, in particular due to inaccurate determination of the height of the powder pellets. In order to minimize this source of error, it has proven advantageous if the samples to be measured are compressed with a respectively defined force. Therefore, an embodiment of the process according to the invention is preferred in that the compression of the powder samples to be measured is carried out with a defined force. Preferably, a mechanical pressure of 0.5 to 3 MPa, preferably 1 to 2 MPa, is applied for the compression.

[0050] In order to achieve a uniform sample preparation and an accurate measurement of the height of the compressed powder sample, it has proven advantageous if the sample preparation and measurement are at least partially automated. Therefore, an embodiment in which the compression of the powder sample to prepare the compressed powder sample is automated is preferred. In this way, a uniform and reproducible measurement of the porosity is achieved.

[0051] Another difficulty in the determination of the equivalent diameter is the limited availability of suitable devices. Therefore, the present invention further relates to an apparatus for carrying out the process according to the invention, comprising receiving means for receiving a sample tube containing a compressed powder sample, a data p up (t) and p down The measurement gas pressure control system includes a data acquisition means for acquiring Δp(t), or Δp(t) and Q(t), a data processing unit, a data output means, a process computer, at least one pressure control means, inlet and outlet means for the measurement gas, and at least one control device for feedback controlling the volumetric flow rate of the measurement gas.

[0052] Preferably, the pressure control means and the regulator for feedback control of the volumetric flow rate are electronic regulators.

[0053] Preferably, the apparatus according to the invention is operated such that the measurement gas is introduced into the apparatus through the inlet means and flows through the compressed powder sample before exiting the apparatus again through the outlet means.

[0054] In order to ensure the provision of an integrated sample, in a preferred embodiment the device according to the invention further comprises automated pressing means for preparing a compressed powder sample.

[0055] In order to achieve fine adjustment of the pressure and the volume flow rate, the device according to the invention preferably has different regulators for the pressure and / or the volume flow rate of the measuring gas. By using different regulators, different measuring ranges can be covered.

[0056] In a preferred embodiment, the device according to the invention further comprises a plurality of measuring stations connected in parallel, a central control and evaluation unit and a central process computer for managing the measuring stations. In this way, the efficiency of the measuring device can be increased. Furthermore, the simultaneous measurement of samples in parallel measuring stations allows the measurement staff to be employed economically. Depending on the demands imposed on the powder to be measured, the measuring range of the operating measuring stations can be changed. Preferably, the device according to the invention covers a particle size range of 0.2 to 200 μm, more preferably 0.2 to 100 μm. Due to the change in the volume flow rate as a function of time according to the invention, a sufficiently large amount of gas can be supplied, which also allows the measurement of powders that only result in low pressure losses due to coarse particles.

[0057] The present invention can further relate to the following items.

[0058] Item 1: A process for determining the equivalent diameter D of a powder particle, characterized in that said equivalent diameter is determined by multipoint measurements.

[0059] Item 2: The process according to item 1, characterized in that the process comprises the following steps: i) Providing a powder sample in the form of powder pellets. ii) Determine the porosity of the powder pellet based on the mass and height of the powder pellet. iii) The measurement fluid is passed through the powder pellet and the ratio of Δp to Q is established by varying Δp or Q over time to obtain characteristics. Here, Δp is the pressure p of the powder pellet on the upstream side in the flow direction. up and the downstream pressure of the powder pellet p down It represents the difference between Q indicates the volumetric flow rate of the measured fluid. iv) Establish the equivalent diameter D by taking into account the porosity of the powder pellet established in ii) and deriving it from the properties.

[0060] Item 3: The process according to at least one of the preceding items 1, characterized in that in steps iii) and / or iv) at least two different measurement points are obtained which do not correspond to the zero points of the characteristic (Δp=0 and Q=0).

[0061] Item 4: By selectively varying the volumetric flow rate Q(t) or the pressure p up 4. The process according to at least one of the preceding claims, characterized in that by selectively varying (t), a property of the relationship between Δp and Q is established.

[0062] Item 5: The characteristic of the relationship between △p and Q is the pressure p upstream of the powder pellet. up The process according to at least one of items 1 to 3, characterized in that the time course of (t) is established.

[0063] Item 6: The relationship between △p and Q is expressed as the pressure p upstream of the powder pellet when the volume flow rate Q(t) is continuously increasing. up The process according to at least one of the preceding items, characterized in that the time course of (t) is obtained.

[0064] Item 7: The process according to at least one of the preceding items, characterized in that the powder pellets are obtained by pressing a powder sample measured with a defined force.

[0065] Item 8: The process according to item 7, characterized in that the pressing is carried out in an automated manner.

[0066] Item 9: Receiving means for receiving a sample tube with powder pellets to be measured, data p up and p down, or Δp, and Q, a data processing unit, a data output means, a pressure control means, inlet and outlet means for the fluid, and a control device for feedback-controlling the volumetric flow rate of the measurement gas.

[0067] Item 10: The apparatus according to item 9, further comprising an automatic pressing means for preparing powder pellets.

[0068] Item 11: An apparatus according to at least one of items 9 and 10, further comprising a plurality of regulators for pressure and volumetric flow rate.

[0069] Item 12: Apparatus according to at least one of items 9 and 10, characterized in that it has a plurality of measuring stations connected in parallel and a central control and evaluation unit for managing the measuring stations. [Brief description of the drawings]

[0070] [Figure 1a] Plot showing the effect of the time required for the system to move into a steady, linearly increasing state from measurements of 0.8 μm particle size WC powder. [Figure 1b] Plot showing the error resulting from insufficient setup time in a traditional single point measurement. [Diagram 2] A plot showing the characteristics of a multipoint measurement. [Figure 3a] Measurement variance in the form of a Gaussian distribution curve for the conventional FSSS method and the process according to the invention. [Figure 3b] Measurement variance in the form of a Gaussian distribution curve for the conventional FSSS method and the process according to the invention. [Figure 4a] Measurement variance in the form of a Gaussian distribution curve for the conventional FSSS method and the process according to the invention. [Figure 4b] Measurement variance in the form of a Gaussian distribution curve for the conventional FSSS method and the process according to the invention. [Figure 5a] Conventional measurement setup used with Fisher Subsieve Sizers for determining particle size according to the FSSS method. [Figure 5b] 1 is a plot showing typical time courses of pressure difference and volumetric flow measurements relevant to particle size determination, obtained with conventional measurement methods. [Figure 6a] FIG. 2 is a measurement setup for implementing a process according to the invention in an embodiment in which the volume flow rate Q(t) is always increasing. [Figure 6b] 4 is a plot showing pressure and volumetric flow rate over time for a process according to the present invention; [Figure 7a] Measurement setup for implementing the process according to the invention in an embodiment where the pressure is constantly increasing. [Figure 7b] 4A-4D are plots showing the time-dependent change in volumetric flow rate and pressure differential using a process according to the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0071] The advantages of the present invention are illustrated by the following figures, which should not be construed as limiting the scope of the present invention.

[0072] 1a and 1b show the influence of the setup time, i.e. the time required for the system to move from the measurement of WC powder with a particle size of 0.8 μm to a steady, linearly increasing state. In this case, the setup time is set to 8 minutes, while for a conventional one-point measurement with 10 measurements, the measurement time is 80 minutes. The influence of a too short setup time on the measurement can be clearly seen in the different deviations of the ratio Q(t) vs. Δp(t). The boxed area of ​​FIG. 1a is shown in FIG. 1b on an enlarged scale. FIG. 1b shows the error resulting from an insufficient setup time in a conventional one-point measurement. FIG. 1b shows the segment marked in FIG. 1a and the corresponding measured values ​​of a one-point measurement that corresponds to the measurement range of the conventional FSSS method. As can be seen, the conventional one-point measurement gives significantly deviated results even with sufficient setup times (graphs 1 and 2). In contrast, the process according to the invention allows extremely precise measurements even with short measurement times due to the multipoint measurement (graph 3). A relative error of 7% was established for this type of measurement. Deviations of up to 35% were observed for single point measurements.

[0073] FIG. 2 shows the characteristics of a multipoint measurement. Here, by appropriately selecting the segments of the characteristic used to determine the equivalent diameter, the relative error can be reduced to 1.5%. Furthermore, by creating a p(t) curve, the multipoint measurement can reduce the measurement time to 8 minutes. The process according to the invention makes it possible to use the entire characteristic, including the curve area, and therefore eliminates the need to select the appropriate segments of the characteristic and does not require waiting until the system reaches a steady state. This allows the measurement time to be further reduced. Furthermore, there are measurement situations in which the curve is weak but shows a large curvature. In such cases, it takes a very long time to follow a linear course, which is detrimental to the reduction of the measurement time.

[0074] 3a, 3b, 4a and 4b respectively show a comparison of the measurement variance in the form of Gaussian distribution curves between the conventional FSSS method and the process according to the invention.

[0075] To check the accuracy, a statistically significant number of measurements were carried out on samples with known particle size by the FSSS method and by the process according to the invention. For the first measurements, a tungsten carbide powder with a particle size of 0.6 μm was selected. Comparing the two methods, it can be seen that the measurement by the FSSS method (Figure 3a), which uses an apparatus operating at constant upstream pressure, leads to a clearly larger scatter of the measured values. Thus, in the prior art, such an apparatus can only measure the pressure drop versus the volumetric flow rate. In contrast, the measurement of the same powder lot by the process according to the invention leads to a significantly narrower distribution of the measured values ​​(Figure 3b), which proves the high accuracy of the process according to the invention.

[0076] The same is true when measuring tungsten carbide powder with a particle size of 1.50 μm: here again, the FSSS method produces a large scatter in the measured values ​​(Figure 4a), whereas the process according to the invention produces a narrower distribution of the measured values ​​(Figure 4b).

[0077] FIG. 5a shows diagrammatically a conventional measurement setup used in the prior art, e.g. in a Fisher Subsieve Sizer for determining particle size according to the FSSS method. A gas reservoir (1) supplies the measurement gas to the setup. Via a constant pressure regulator (2), a constant upstream pressure p 1 (p up The measurement gas flows through the compressed powder sample (5) in the holder (4), resulting in a pressure p downstream of the sample. 2 increases (p down ). This pressure p 2is indicated by the well manometer (3). The combination of the valve (6) and the well manometer (3) corresponds to a volumetric flow measurement device. By using the valve (6), the system can be preset so that the particle size can be read off from the analog display panel. The use of the well manometer (3) has the disadvantage that the gas volume downstream of the sample gradually increases and additional gas must be flowed through the sample to counteract this effect. This causes a delay in setting up the measurement. Therefore, to determine the measurement with this system, one must wait until all measurements have reached steady state.

[0078] Figure 5b shows a typical time course of the pressure difference and volume flow measurements relevant for particle size determination, obtained with a conventional measurement method. After some time, the system reaches a steady state and the values ​​become constant. At this point, the values ​​can be read off using the quotient ΔQ / p of the Kármán-Kozeny equation and used for evaluation. As can be seen from the graph, generally correct results are obtained from a measurement time of about 300 seconds.

[0079] Figure 6a shows a schematic representation of the realisation of the process according to the invention in an embodiment with a constantly increasing volumetric flow rate Q(t). A gas reservoir (1) supplies the setup with the measurement gas. The constantly increasing volumetric flow rate of the measurement gas is set by a volumetric flow controller (8). The measurement gas flows through a compressed powder sample (5) in a holder (4). Two electronic manometers measure the pressure p of the measurement gas before it flows through the sample (5). 1 (=p up ) and the pressure p of the measurement gas after it has flowed through the sample (5) 2 (=p down ) are measured simultaneously. Thus, the time-dependent pressure difference Δp(t) = (p1(t) - p2(t)) versus the time-varying volumetric flow rate Q(t) can be established using this setup. From the established Δp(t) and Q(t) values, the nonlinear characteristics of Q(t) versus Δp(t) for determining the equivalent diameter can be derived.

[0080] Figure 6b shows the time evolution of pressure and volumetric flow rate by the process according to the invention. Since the volumetric flow rate Q(t) increases constantly with time, the volumetric flow rate Q(t) can be used directly as the horizontal axis instead of time (t). The determination of the equivalent diameter is then performed using the full characteristic of Q(t) vs. Δp(t). Thus, the process according to the invention has the advantage that it is not necessary to wait until the steady state of the system is obtained.

[0081] Figure 7a shows a schematic representation of the realisation of the process according to the invention in an embodiment with constantly increasing pressure. A gas reservoir (1) supplies the measurement gas to the setup. By using a control unit (7), a constantly increasing pressure is applied to the system. At the same time, the system response is measured by means of a flow meter (6) to measure the volumetric flow rate of the measurement gas and the pressure p after the gas has passed through the compressed powder sample (5) in the holder (4). 2 Measure (p down ). All property values ​​are recorded as time-dependent quantities.

[0082] Figure 7b shows the time-dependent evolution of the volumetric flow rate and the pressure difference when using the process according to the invention. The determination of the equivalent diameter is performed using the entire nonlinear characteristic of Q(t) vs. Δp(t). Thus, the process according to the invention has the advantage that it is not necessary to wait until the steady state of the system is obtained.

Claims

1. A process for determining the equivalent diameter D of a powder sample, wherein the equivalent diameter is determined by recording the nonlinear characteristic of Q(t) versus Δp(t), where Q(t) is the volumetric flow rate as a function of time and Δp(t) is the pressure difference as a function of time.

2. The pressure difference Δp(t) represents a time-dependent difference occurring in the flow direction of the measurement gas flowing through the compressed powder sample, the volumetric flow rate Q(t) represents the volumetric flow rate of the measurement gas, which increases steadily with time; dQ(t) / dt=q ０ , q ０ = const., q ０ >0, and q ０ 10. The process of claim 1, wherein ≈(V) denotes the rate of change of the volumetric flow rate.

3. The pressure difference Δp(t) is the pressure p ｕｐ and downstream pressure p ｄｏｗｎ and the pressure difference between the measured gas ... dΔp(t) / dt=p ０ , p ０ = const., p ０ >0, The volumetric flow rate Q(t) represents the time-dependent volumetric flow rate of the measurement gas, and p ０ 3. The process of claim 2, wherein ≈ represents a rate of change of pressure of the measurement gas.

4. A method for determining the equivalent diameter D of a powder sample, comprising: The following steps: i) providing a compressed powder sample; ii) determining the porosity of the compressed powder sample based on the mass and height of the compressed powder sample; iii) A measurement gas is passed through the compressed powder sample, and Δp is continuously changed as a function of time Δp(t) or Q is continuously changed as a function of time Q(t) to obtain a nonlinear characteristic, thereby obtaining a conductance L Ｒ where the function Δp(t) is the pressure p upstream of the compressed powder sample. ｕｐ and downstream pressure p ｄｏｗｎ The function Q(t) represents the time-dependent pressure difference occurring in the flow direction of the measurement gas between the pressure difference and the volumetric flow rate of the measurement gas, and L Ｒ = Q / Δp, iv) determining the equivalent diameter D by deriving it from the nonlinear characteristics of the function Q(t) versus the function Δp(t) taking into account the porosity of the compressed powder sample determined in step ii); A method comprising:

5. The method described in claim 4, further comprising, in steps iii) and / or iv), obtaining at least two different measurement points that do not correspond to the zero points (Δp = 0, Q = 0) of the nonlinear characteristic.

6. 5. The method of claim 4, wherein the equivalent diameter D is measured at least five times per minute.

7. By selectively varying the volumetric flow rate Q(t) or the pressure p ｕｐ 5. The method of claim 4, wherein the nonlinearity of the relationship between the function .DELTA.p(t) and the function Q(t) is established by selectively varying .DELTA.p(t).

8. The nonlinear characteristic of the relationship between the function Q(t) and the function Δp(t) is such that the pressure p ｕｐ The method of claim 7, wherein the time t is established as a function of time.

9. A process for determining the equivalent diameter D of a powder sample, comprising: The following steps: i) providing a compressed powder sample; ii) determining the porosity of the compressed powder sample based on the mass and height of the compressed powder sample; iii) the pressure p upstream of the compressed powder sample ｕｐ and the pressure p downstream of the compressed powder sample ｄｏｗｎ The pressure difference Δp(t) between ０ Setting the volumetric flow rate Q(t) of the measurement gas flowing through the compressed powder sample to vary as follows: ０ = dΔp(t) / dt, iv) Conductance L from the nonlinear characteristics of the relationship between the volume flow rate Q(t) and the pressure difference Δp(t) Ｒ To obtain v) determining an equivalent diameter D by taking into account the porosity of the compressed powder sample determined in step ii) and deriving it from the non-linear characteristics.

10. The nonlinear characteristic of the relationship between the pressure difference Δp(t) and the volumetric flow rate Q(t) is determined by the upstream pressure p of the powder sample as the volumetric flow rate Q(t) increases. ｕｐ 10. The process of claim 9, further comprising obtaining as a time course of (t).

11. A process for determining the equivalent diameter D of a powder sample, comprising: The following steps: i) providing a compressed powder sample; ii) determining the porosity of the compressed powder sample based on the mass and height of the compressed powder sample; iii) A constant rate of change q of the volumetric flow rate Q(t) of the measurement gas flowing through the compressed powder sample ０ where dQ(t) / dt=q ０ and q ０ = const, iv) Conductance L Ｒ from the nonlinear characteristics of the relationship between the volume flow rate Q(t) and Δp(t), where Δp(t) is the pressure p of the measurement gas upstream of the compressed powder sample as a function of time. ｕｐ (t) and the pressure p of the compressed powder sample downstream of the measurement gas ｄｏｗｎ (t) is the pressure difference between v) determining the equivalent diameter D by taking into account the porosity of the compressed powder sample determined in step ii) and deriving it from the non-linear characteristic.

12. 12. The process of claim 3, 9, or 11, wherein the compression of the powder sample is carried out at a force of 0.5 MPa to 3 MPa.

13. The method of claim 4, wherein the powder sample is compressed at a force of 0.5 MPa to 3 MPa.

14. 13. The process of claim 12, wherein the compaction is performed in an automated manner.

15. The method of claim 13, wherein the compression is performed in an automated manner.

16. receiving means for receiving a sample tube containing the compressed powder sample to be measured; ｕｐ (t), and the pressure p ｄｏｗｎ 12. An apparatus for determining the equivalent diameter D of the powder sample by the process of claims 3, 9 or 11 or the method of claim 4, comprising data acquisition means for acquiring the pressure difference Δp(t) and the volumetric flow rate Q(t), a data processing unit, data output means, a process computer, pressure control means, inlet and outlet means for the measurement gas, and a controller for feedback controlling the volumetric flow rate of the measurement gas.

17. 17. The apparatus of claim 16, further comprising automated compaction means for preparing the compacted powder sample.

18. The apparatus of claim 16, further comprising a plurality of regulators for adjusting the pressure and the volumetric flow rate of the measurement gas.

19. 17. The apparatus according to claim 16, further comprising a plurality of measuring stations connected in parallel, a central control and evaluation unit and a central process computer for managing said measuring stations.

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