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GB2294551A - Apparatus for determining particle size distribution - Google Patents

Apparatus for determining particle size distribution Download PDF

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Publication number
GB2294551A
GB2294551A GB9420872A GB9420872A GB2294551A GB 2294551 A GB2294551 A GB 2294551A GB 9420872 A GB9420872 A GB 9420872A GB 9420872 A GB9420872 A GB 9420872A GB 2294551 A GB2294551 A GB 2294551A
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United Kingdom
Prior art keywords
container
suspension
samples
outlet
particle size
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Granted
Application number
GB9420872A
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GB9420872D0 (en
GB2294551B (en
Inventor
Anthony Simon Place
Leonard Farlam Gate
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Imerys Minerals Ltd
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ECC International Ltd
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Priority to GB9420872A priority Critical patent/GB2294551B/en
Publication of GB9420872D0 publication Critical patent/GB9420872D0/en
Publication of GB2294551A publication Critical patent/GB2294551A/en
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Publication of GB2294551B publication Critical patent/GB2294551B/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/06Investigating concentration of particle suspensions
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/02Analysing fluids
    • G01N29/036Analysing fluids by measuring frequency or resonance of acoustic waves
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/22Details, e.g. general constructional or apparatus details
    • G01N29/222Constructional or flow details for analysing fluids
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/02Investigating particle size or size distribution
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/01Indexing codes associated with the measuring variable
    • G01N2291/014Resonance or resonant frequency
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/01Indexing codes associated with the measuring variable
    • G01N2291/015Attenuation, scattering
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00Indexing codes associated with group G01N29/00
    • G01N2291/02Indexing codes associated with the analysed material
    • G01N2291/024Mixtures
    • G01N2291/02416Solids in liquids

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  • Physics & Mathematics (AREA)
  • Chemical & Material Sciences (AREA)
  • Biochemistry (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Analytical Chemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Acoustics & Sound (AREA)
  • Dispersion Chemistry (AREA)
  • Sampling And Sample Adjustment (AREA)

Abstract

An apparatus for measuring the particle size distribution of a fine particulate solid material in suspension in a liquid comprises a container (1) for the suspension having an outlet (2) near its base. The mass concentration of samples removed from the outlet is measured periodically as the liquid is withdrawn through the outlet (2). The particles in suspension in the liquid have a velocity by virtue of the decreasing liquid level within the container, and by virtue of the settling rate of the particles within the liquid. The container is shaped as an inverted cone, the outlet (2) being provided near the apex of the cone. <IMAGE>

Description

APPARATUS FOR DETERMINING PARTICLE SIZE DISTRIBUTION This invention relates to a method and apparatus for determining the size distribution of fine particles in suspension in a liquid.
In many industries it is required to measure the particle size parameters of particulate solid materials, and, in the research and quality control laboratories of such industries, it is often necessary to obtain information quickly and accurately about the particle size distributions of a large number of samples. Information concerning the proportion by weight of particles having a dimension larger than about 50pm is generally most conveniently obtained by the use of test sieves of different aperture sizes.
However, when it is required to know the percentage by weight of particles smaller than about 50pm, it is generally necessary to use a method based on gravitational or centrifugal sedimentation.
The terminal velocity of sedimentation of a single spherical particle in a gravitational field in a liquid of viscosity n is given by Stokes' Law as U = 1 . D2 (r-r) g E1 18 n where D is the sphere diameter and r and r' are the densities of the particle and liquid respectively.
Settling rates (dependent upon terminal velocity U) determined in fluids of known viscosity n and density r' then enable the diameter of particles of known density r to be determined from El. Even when the shape of the particles in a suspension is known to depart significantly from that of a sphere it is customary to express the size of the particles in terms of an equivalent spherical diameter (e.s.d.), in other words the diameter of a spherical particle which sediments at the same rate as the non-spherical particle under examination.
A particle size distribution is generally determined by the gravitational sedimentation method by preparing a homogeneous, dispersed suspension of particles at low solids concentration (generally less than 5% by weight) and following the change in mass concentration at a fixed depth below the air/liquid interface with time. Using El, the size of the particle which will have settled below the sampling level in a given time is calculated and, together with a determination of the mass per unit volume of sedimenting material present at this level both initially and after the given time t the cumulative mass distribution of particles below this size is determined.
Sedimenting rates for colloidal micron-sized particles are small, however, and a lum diameter quartz particle has a settling rate in water of typically 80pm per second. Thus if a pipette is used to withdraw samples of suspension from a depth 5cm below the surface of the suspension, it will take about 15 hours before these particles will have settled below the sampling zone.
The equation El also indicates that if the size of the particle is halved, then the settling time needed will have expanded by a factor of 4 to make a sampling time of 60 hours necessary.
The relative mass concentration of the solids in the sample suspension can be determined rapidly by any one of several methods such as transmittance of an Xray beam, or of ultrasonic vibration, or by scattering or diffraction of light. Alternatively, a method relying upon the determination of density may be used.
These methods suffer from the disadvantage of yielding relatively poor accuracy with the dilute suspensions which are necessary to minimise hindered settling.
However rapid the method of performing the mass analysis of the material in the sampled zone, there remains a need to reduce the elapsed time after sedimentation begins, especially for small particles.
Methods have been employed in the past for speeding up the sampling of sedimenting particles of colloidal size. These methods generally can be categorised into one or other of the following two approaches.
In a first approach, the depth of the sampling point below the air/liquid interface is progressively reduced. This may be accomplished by progressively moving the sampling point upwards through the liquid.
Methods of this type are described by Russell,E.W., J.Agric.Sci., 33, 147-54, 1943 and by Oliver,J.P., Hickin,G.K. and Clyde Orr, Powder Technology 4, 257263, 1970/71.
In a second approach, the rate of sedimentation is accelerated by the use of a centrifuge. A method of this type is described by Slater,C. and Cohen,L., J.Sci.Inst., 39, 614-617, 1962.
These methods require more complicated and expensive apparatus and there remains a need to shorten the time required for a particle size analysis without introducing unduly complicated apparatus.
According to a first aspect of the present invention, there is provided an apparatus for measuring the particle size distribution of a fine particulate solid material in suspension in a liquid, comprising: a container for the suspension, the cross sectional area of which container decreases towards its base, the container being provided, at or near its base with a fixed outlet for the suspension; and analysis means for successively or continuously obtaining a value which is representative of the mass concentration of the suspension at a constant level within the container.
For ease of manufacture, and to simplify the mathematical calculations involved, it is convenient to provide a container in the shape of an inverted cone.
However, it may also be advantageous to provide a container having a shape such that the rate of decrease of the cross sectional area increases towards the base of the container, for example a paraboloidal shape.
The outlet is located near to the base of the container in a position such that the drawing of sedimented material up into the outlet is minimised. A convenient position is between 5 and 50mm above the bottom of the container. The outlet may be sized such that the flow out of the vessel which is desired is greater than the flow which would be produced by gravity. In such a case, means is provided for pumping fluid out of the vessel at the desired rate. Alternatively, the outlet may be provided with a valve which controls the flow out of the vessel, and the flow out of the vessel produced by gravity may then be greater than that required for the analysis.
Preferably, the value representative of the mass concentration is obtained through analysis of samples withdrawn from the outlet.
According to a second aspect of the present invention, there is provided a method of measuring the particle size distribution of a fine particulate solid material in suspension in a liquid, comprising filling a container according to the first aspect of the invention to a predetermined depth, progressively withdrawing samples of the suspension through the outlet, and obtaining a value representing the mass concentration of each sample.
The sample may be withdrawn continuously or in a sequence of short pulses, but preferably the samples are withdrawn at a continuous volumetric flow rate. It may also, in certain cases, be convenient to decrease the rate of withdrawal of the sample as the analysis proceeds, as this leads to better resolution of the change of mass concentration with time.
Preferably the value representing the mass concentration is determined by a density measuring method. A convenient method is that in which the sample flows through a hollow vibrating U-tube, which acts as a tuning fork, and the resonant frequency of the tube is measured. Other methods which may be used include measuring the refractive index of the sample, or the attenuation of an ultrasonic vibration passing through the sample. From this measurement an updated determination of the density of the sample is available every few seconds.
The effect of progressively drawing off a sample through the outlet is that the vertical distance between the outlet and the air/liquid interface progressively decreases. This means that the time taken for a fine particle of given size to fall to the level of the outlet decreases as the analysis proceeds.
As the air/liquid interface approaches the outlet, the finer particles will be distributed in a size versus depth profile which is given by equation El.
If, at the same time, in accordance with the invention, the cross sectional area of the vessel containing the suspension decreases as it approaches the outlet, the size distribution profile with depth below the free surface is expanded so that better resolution of finer sizes becomes possible.
For a better understanding of the present invention and to show more clearly how it may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 shows a vessel for measuring particle size distribution; Figure 2 shows a graph representing examples of particle size distribution; and Figure 3 shows an alternative embodiment of the vessel in accordance with the invention.
In the apparatus shown in Figure 1, sedimentation takes place in a vessel 1 having the form of a cone.
The cone-shaped vessel 1 has an outlet 2 which is located a small distance from the apex of the cone, the cone being oriented inversely, namely with the apex directed downwardly. The sample is extracted through the outlet 2, which is at a fixed depth below the initial surface level 3 of a homogeneously mixed suspension 4 containing particles with a range of sizes. The liquid is extracted by means of a pump (not shown) which is capable of withdrawing fluid at a desired constant rate with no backf low. An especially suitable type of pump is a peristaltic dosing pump which is provided with additional rollers to damp out the oscillations in flow rate associated with most peristaltic pumps.A trap 7 is provided below the outlet 2 for retaining any especially coarse particles which might happen to be in the suspension under test, but which would not need to be accounted for in the particle size distribution curve. The dimensions of the cone 1 are such that the initial surface is a circle of radius a and the apex semi-angle of the cone is e. Typically the vessel may have a depth of 5 to 50cm. The apex semi-angle e is typically in the range 45 -85 , preferably around 70 .
The advantage of using a conical or other tapering vessel is that, even when only the finest particles remain in suspension, it is still unnecessary to draw samples of suspension from close to the surface. This is advantageous because samples drawn from close to the surface may not be representative of the whole of the remaining suspension.
If the suspension is being extracted at a constant rate K through the outlet 2, after time t the surface of the suspension will be a circle which may be defined as having a radius b at a height h above the apex of the cone.
The volume V of suspension in the cone at this time t is V = 1 . # . b . h 3 b But b = tan e h so V = #.tan#.h 3 Hence dv = tan2.h2 dh If a constant volumetric flow rate is maintained through the outlet, this constant sampling flow rate (K) may be written as K = dV = dV . dh = #.tan#.h. dh dt dh dt dt Hence the vertical velocity of the fluid at a height h above the bottom of the cone is given by dJ2(fluid) K E2 dt s it.tan2.h2 But a particle with an e.s.d. of D will sediment with a constant velocity U relative to the fluid as given by El (which may be written as U = i.D2) and this must be added to the vertical velocity of the fluid E2 at time t to give the actual velocity of fall of the particle relative to the sampling point as dh (particle) K + i.D2 dt #.htan# Hence it is possible to calculate the size of particle of which all particles having that size or above will have reached the extraction zone (set at a height hl) in a time tl from the equation
where the initial height of suspension in the cone is ho when t = 0.
The above equation may be written as
K where a = and B = i.D2 n.tan28 By substituting x = h-1 and dh = (-x-2) dx, the above integral equation may be transformed to a standard form
with the solution
As defined above a is a constant term containing the flow rate at which the vessel is being emptied, while for kaolin particles in water at 20"C, B = 8.71 x 103 .D2. cm At a time tl after liquid is first withdrawn from the vessel, the height hl of the surface will be known, because the volume of liquid withdrawn will be known.
The parameters ho and a will also be known, and so numerical methods can be used to obtain a value for ss from equation E3. Thus, it is possible to determine a size, which is such that all larger particles have already been withdrawn.
Thus, as the analysis of the extracted samples progresses, a cumulative series of results is obtained representing the mass density of samples of the suspension in which all particles of greater than a known diameter have settled out of the suspension.
Each such sample is taken to be representative of the whole of the remaining suspension.
Thus, as the analysis proceeds, the range of sizes of particle which may be present in the most recent sample is reduced. The time taken to empty the vessel is selected such that the last samples to be analyzed must contain only particles having a diameter smaller than the desired minimum threshold. This desired minimum may, for example be approximately 0.5 pm.
The assumption that the particles are homogeneously distributed in the suspension at the outset enables calculation of the particle size distribution once all of the samples have been analyzed. The percentage by weight of solids in each sample is compared with the percentage by weight of solids in the original suspension. It is also possible to perform the calculations necessary to plot the particle size distribution curve in real time, as the samples are analysed while the liquid is being withdrawn from the container.
The solution above has been derived from an assumption that the volumetric flow rate out of the vessel is constant. Also, the calculations are for a cone shaped vessel. Those skilled in the art will appreciate that alternative equations will need to be derived for a non-constant flow rate and for other shaped vessels. These possibilities do not fall outside the scope of this invention.
EXAMPLE 1 As an example of the application of this method consider the case of a conical vessel as in Figure 1 where ho = 6.5 cm and the emptying point is set at 0.75 cm above the apex of the cone. Let the cone semi-angle e = tan-l 2 and let the extraction rate be 1 cm3/sec so that a, as defined above, takes the value of 0.07958 cm3.s~l. The time to empty the cone to the level of the sample extraction point A is 19m 9s and E3 indicates that, for kaolin particles in water, all particles with an e.s.d. of 1 um will have reached the sample point after 18m 31s.
EXAMPLE 2 Figure 2 shows particle size distribution curves 5 and 6 which were obtained using the method and apparatus of the invention with aqueous suspensions containing approximately 5% by weight of, respectively, a ground natural calcium carbonate pigment having a particle size distribution such that 60% by weight consisted bf particles having an equivalent spherical diameter smaller than 2pm, and a ground natural calcium carbonate pigment having a particle size distribution such that 90% by weight consisted of particles having an equivalent spherical diameter smaller than 2pm.
Each suspension was analysed three times using the method described above, and the three results plotted, in each case, as the curves 5, 6. This demonstrates the good repeatability of the method described herein.
Figure 3 is a diagrammatic representation of an alternative embodiment of the apparatus of the invention. A cone-shaped vessel 11 is provided with an upper cylindrical rim 15 and a lower cylindrical rim 16. A lid 17 has a cylindrical rim 18 which fits over the upper rim 15 of the vessel 11, and is provided with a central, downwardly depending frusto-conical projection 19 through which passes an axial bore 20, terminating in a sample outlet 22, which is at a fixed depth below the initial surface level 13 of a homogeneously mixed suspension 14 containing particles with a range of sizes. A flexible tube 21 connects the outlet 22 to the inlet of a density meter 23. A flexible tube 24 is connected to the outlet of the density meter and a sample stream is drawn continuously through the density meter in the direction of the arrow 25 by means of a peristaltic pump (not shown).
The lower rim 16 of the cone-shaped vessel fits into the upper end of a cylindrical sleeve 26, a watertight seal being formed therewith by means of a sealing ring 27. The lower end of the sleeve 26 fits into an upstanding ring 28 provided on a base plate 29. A water-tight seal is provided between the sleeve 26 and the ring 28 by means of a sealing ring 30. The space defined by the sleeve 26 and the base plate 29 forms a trap for especially coarse particles which are present in the initial homogeneously mixed suspension, but which do not require to be accounted for in the particle size distribution which is determined.
The apparatus is easily dismantled for cleaning after a particle size distribution has been determined.
If the semi-vertex angle of the cone-shaped vessel 11 is 81, and the semi-vertex angle of the frustoconical projecting 19 is 62, the angle e in equation E2 is given by the expression; e = tan-l ff(tan2O1 - tan#2) There are thus provided an apparatus and a method which allow quick and accurate measurement of particle size distribution.

Claims (17)

1. An apparatus for measuring the particle size distribution of a fine particulate solid material in suspension in a liquid, comprising: a container for the suspension, the cross sectional area of which container decreases towards its base, the container being provided, at or near its base with a fixed outlet for the suspension; and analysis means for successively or continuously obtaining a value which is representative of the mass concentration of the suspension at a constant level within the container.
2. An apparatus as claimed in claim 1, in which the analysis means is adapted to analyze samples of the suspension removed from the outlet of the container.
3. An apparatus as claimed in claim 1 or 2, in which the container is substantially conical in shape, the apex of the cone comprising the base of the container.
4. An apparatus as claimed in claim 1 or 2, in which the container has a shape such that the rate of decrease of the cross-sectional area increases in a direction towards the base of the container.
5. An apparatus as claimed in claim 4, in which the container has a paraboloidal shape.
6. An apparatus as claimed in any preceding claim, in which the outlet is provided at a level within the container which is a small distance from the base of the container relatively to the depth of the container.
7. An apparatus as claimed in any preceding claim, in which the analysis means comprises means for measuring density.
8. An apparatus as claimed in claim 7, in which the means for measuring density comprises a hollowvibrating U-tube, the resonant frequency of which may be measured to give a determination of the density of the sample.
9. A method of measuring the particle size distribution of a fine particulate solid material in suspension in a liquid, comprising filling a container as claimed in any one of claims 1 to 8 to a predetermined depth, progressively withdrawing samples of the suspension through the outlet, and obtaining a value representing the mass concentration of each sample.
10. A method as claimed in claim 9, in which the samples are withdrawn continuously from the container.
11. A method as claimed in claim 9, in which the samples are withdrawn from the container is a sequence of short pulses.
12. A method as claimed in claim 10, in which the samples are withdrawn at a continuous volumetric flow rate.
13. A method as claimed in claim 10, in which the rate of withdrawal of the samples is decreased over time.
14. A method as claimed in any one of claims 9 to 13, in which the mass concentration of the samples is obtained periodically.
15. A method as claimed in claim 14, in which the mass concentration of the samples is determined every 1 to 30 seconds.
16. An apparatus for measuring the particle size distribution of a fine particulate solid material substantially as described herein with reference to, and as shown in, Figure 1 of the accompanying drawings.
17. A method of measuring the particle size distribution of a fine particulate solid material in suspension in a liquid substantially as described herein with reference to the accompanying drawings.
GB9420872A 1994-10-17 1994-10-17 Apparatus for determining particle size distribution Expired - Lifetime GB2294551B (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0825436A1 (en) * 1996-08-20 1998-02-25 Ngk Insulators, Ltd. Particle sensor

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106706485B (en) * 2017-02-15 2023-06-06 辽宁科技大学 A fast particle size measuring pot and measuring method

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3797319A (en) * 1972-08-08 1974-03-19 Agency Ind Science Techn Process for measuring particle size and concentration of slurries according to on-stream analysis

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FI896245A7 (en) * 1988-04-25 1989-12-22 Krivorozhsky Gornorudny Inst Method for monitoring the parameters of the solid phase of a suspension and apparatus therefor

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3797319A (en) * 1972-08-08 1974-03-19 Agency Ind Science Techn Process for measuring particle size and concentration of slurries according to on-stream analysis

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0825436A1 (en) * 1996-08-20 1998-02-25 Ngk Insulators, Ltd. Particle sensor
US5969236A (en) * 1996-08-20 1999-10-19 Ngk Insulators, Ltd. Particle sensor

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GB2294551B (en) 1998-09-30

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Expiry date: 20141016