Automatic dilution system for high-resolution particle size analysis

I claim:

1. An automatic dilution system for providing an optimal value of dilution factor DF for a sample suspension containing particles mixed with a diluent, comprising:

means for providing a continuous flow of said diluent into mixing means;

means for injecting a continuous flow of said sample together with said diluent in said mixing means to provide a net combined flow of diluent and sample from said mixing means, said flow of said diluent being substantially larger than said flow of said sample, whereby said flow of said sample has a relatively minor effect on said net combined flow of said diluent and said sample and said net combined flow is substantially the value of said flow of diluent;

sensor means for measuring a value of a particular characteristic related to particle concentration of said diluted sample leaving said mixing means, said sensor means having a particle coincidence concentration limit;

controller means for determining from said value of said particular characteristic an optimal value of dilution factor DF needed to provide an optimal particle concentration in said diluted sample, said optimal particle concentration being the maximum particle concentration which does not exceed a desired percentage of said coincidence concentration limit of said sensor means, said controller means generating a control signal from said determined optimal value of dilution factor DF; and

means responsive to said control signal for adjusting at least one of said flow of said sample and said flow of said diluent to provide said optimal value of dilution factor DF for said diluted sample in said mixing means.

2. An automatic dilution system for providing an optimal value of dilution factor DF for a sample suspension containing particles mixed with a diluent, comprising:

means for providing a continuous flow of said diluent into mixing means;

means for injecting a continuous flow of said sample together with said diluent in said mixing means;

sensor means for measuring a value of a particular characteristic related to particle concentration of said diluted sample leaving said mixing means, said sensor means having a particle coincidence concentration limit;

controller means for determining from said value of said particular characteristic an optimal value of dilution factor DF needed to provide an optimal particle concentration in said diluted sample, said optimal particle concentration being the maximum particle concentration which does not exceed a desired percentage of said coincidence concentration limit of said sensor means, said controller means generating a control signal from said determined optimal value of dilution factor DF; and

means responsive to said control signal for adjusting at least one of said flow of said sample and said flow of said diluent to provide said optimal value of dilution factor DF for said diluted sample in said mixing means, wherein said particular characteristic of said diluted sample comprises the initial rate of increase R.sub.max (0) of a quantity related to particle concentration in said diluted sample in said mixing means.

3. The automatic dilution system of claim 2, wherein said particle concentration in said diluted sample is the particle concentration of a given range of particle sizes.

4. The automatic dilution system of claim 3, wherein said given range of sizes includes all particle sizes.

5. The automatic dilution system of claim 2, wherein said controller means calculates from the value of R.sub.max (0) the approximate final concentration of particles C.sub.0 /DF expected when equilibrium is achieved in said mixing means, where C.sub.0 is the initial concentration before dilution of given range of particle sizes, compares the computed value of C.sub.0 /DF with said optimal particle concentration, determines from the comparison said optimal value of DF needed to achieve said optimal particle concentration, and generate said control signal.

6. The automatic dilution system of claim 1, wherein said mixing means comprises a mixing chamber including stirrer means.

7. The automatic dilution system of claim 1, wherein said sensor means is based on the principle of single-particle optical sensing.

8. The automatic dilution system of claim 7, wherein said means for injecting a flow of said sample into said mixing means comprises a sample delivery pump, and wherein said means for providing a flow of said diluent comprises a diluent delivery pump.

9. The automatic dilution system of claim 8, wherein said sample delivery pump is a variable output syringe pump.

10. The automatic dilution system of claim 1, wherein said adjusted flow of at least one of said sample and said diluent continues for a time sufficient to achieve equilibrium in the particle concentration in said diluted sample leaving said mixing means, and wherein said sensor means generates data for the construction of a particle size distribution of the sample.

11. The automatic dilution system of claim 1, wherein said mixing means comprises a mixing chamber, and wherein flow means causes a portion of the diluted sample in said mixing chamber to be directed to said sensing means, the remaining portion of said diluted sample being discarded.

12. The automatic dilution system of claim 11, wherein said flow means comprises a diluted sample pump.

13. The automatic dilution system of claim 12, wherein said diluted sample pump comprises a metering pump.

14. The automatic dilution system of claim 12, wherein said diluted sample pump is positioned between said mixing chamber and said sensing means.

15. The automatic dilution system of claim 12, wherein said sensing means is positioned between said mixing chamber and said diluted sample pump.

16. The automatic dilution system of claim 11, wherein said means for injecting a flow of said sample comprises a metering pump.

17. The automatic dilution system of claim 1, wherein said diluent flows in a diluent flow tube, wherein said mixing means comprises a static mixer of relatively small effective volume in series with said flow tube, wherein said means for injecting a flow of said sample comprises means for injecting said sample into said flow tube upstream from said static mixer, and wherein said sensor means is located downstream from said static mixer and receives said diluted sample from said static mixer.

18. The automatic dilution system of claim 17, wherein said means for injecting a flow of said sample further comprises a sample metering pump.

19. The automatic dilution system of claim 1, wherein said mixing means comprises a first mixing means for prediluting said sample and a second mixing means, flow means feeding the prediluted sample in said first mixing means to said second mixing means, wherein said means for injecting a flow of said sample feeds said sample into said first mixing means, and wherein said means for providing a flow of diluent includes first means to feed diluent to said first mixing means and second means for feeding diluent to said second mixing means.

20. The automatic dilution system of claim 19, wherein said flow means for feeding said prediluted sample to said second mixing means feeds diluent to said first mixing chamber means after it is filled with said sample and diluent supplied by said first means to push said prediluted sample into said second mixing means.

21. The automatic dilution system of claim 20, further comprising sample injection valve means and a length of tubing, and wherein said means for injecting a flow of sample fills said length of tubing with said sample, wherein said first means delivers diluent through said sample injection valve means and a diluent fluid path into said first mixing chamber means, and said means for injecting a flow of sample places said length of tubing in series with said diluent fluid path permitting injection of said sample in said loop of tubing into said first mixing chamber means as diluent fluid flows through said path.

22. The automatic dilution system of claim 21, wherein said flow means for feeding said prediluted sample comprises a syringe pump.

23. The automatic dilution system of claim 21, wherein said second mixing means feeds diluted sample to said sensor means.

24. The automatic dilution system of claim 23, further comprising an assisted-drain pump for draining diluted sample from said sensor means.

25. The automatic dilution system of claim 19, wherein diluent flow to said second mixing means flows in a diluent flow tube, wherein said second mixing means comprises a static mixer of relatively small volume in series with said diluent flow tube, and wherein said means for injecting a flow of sample comprises means for injecting said sample into said flow tube upstream from said static mixer, and wherein said sensor means is located downstream from said static mixer and receives said diluted sample from said static mixer.

26. The automatic dilution system of claim 1, wherein said diluted sample leaving said mixing me ans is fed to one of a pair of branches, first sensor means for measuring the value of a first said particular characteristic of said diluted sample in one of said branches and second sensor means for measuring a second said particular characteristic of said diluted sample in the other of said branches.

27. The automatic dilution system of claim 26, wherein said second sensor means senses light scattering and said second said particular characteristic is the initial rate of increase of light intensity in said diluted sample.

28. The automatic dilution system of claim 27, wherein said first sensor means is a single particle optical sensor and said first characteristic is the initial rate of increase of particle concentration in said diluted sample.

29. The automatic dilution system of claim 1, wherein said mixing means has a relatively short equilibrium time, and wherein said means responsive to said control signal responds so quickly that it operates virtually in a negative feedback mode.

30. The automatic dilution system of claim 29, wherein said mixing means is a static mixer having a relatively small volume.

31. The automatic dilution system of claim 29, wherein said mixing means comprises a first predilution chamber feeding a prediluted sample to a second dilution stage comprising a static mixer of relatively small volume, providing said short equilibrium time.

32. A method for automatically diluting a sample suspension containing particles with an optimal value of dilution factor DF, comprising:

providing a continuous flow of diluent into mixing means;

injecting a continuous flow of said sample into said mixing means;

mixing said diluent and said sample in said mixing means to provide a diluted sample;

measuring a value of a particular characteristic related to particle concentration of said diluted sample;

determining from said value of said particular characteristic an optimal value of dilution factor DF to provide an optimal particle concentration in said diluted sample;

generating a control signal from said determined optimal value of dilution factor DF; and

in response to said control signal adjusting said flow of said sample to provide said optimal value of dilution factor DF in said mixing means.

33. The method of claim 32, wherein said particular characteristic of said diluted sample comprises the initial rate of increase R.sub.max (0) of a quantity related to particle concentration in said diluted sample in said mixing means.

34. The method of claim 33, wherein said particle concentration in, said diluted sample is the particle concentration of a given range of particle sizes.

35. The method of claim 34, wherein said given range of sizes include all particle sizes.

36. The method of claim 33, wherein said step of determining an optimal value of dilution factor DF from said value of said particular characteristic comprises calculating from the value of R.sub.max (0) the approximate final concentration of particles C.sub.0 /DF expected when equilibrium is achieved in said mixing means, where C.sub.0 is the initial concentration before dilution, comparing the computed value of C.sub.0 /DF with said optimal particle concentration, determining from the comparison said optimal value of DF needed to achieve said optimal particle concentration, developing a control signal for adjusting said flow of sample to provide a new flow rate of sample to provide said optimal value of DF.

37. The method of claim 32, wherein said mixing means comprises a mixing chamber.

38. The method of claim 32, wherein said measuring step is based on the principal of single-particle optical sensing.

39. The method of claim 32, wherein said adjusted flow of sample and said flow of diluent is permitted to continue until equilibrium is achieved in the particle concentration and wherein said measuring step generates data for the construction of a particle size distribution of the sample.

40. The method of claim 32, further comprising the steps of withdrawing a portion of the dilute sample wherein said measuring step is applied to said portion.

41. The method of claim 32, wherein said mixing means comprises a static mixer connected in series with a flow tube, wherein said diluent is directed through said flow tube, wherein said sample is injected directly into said flow tube, upstream from said static mixer, and wherein said sample and said diluent are mixed in said static mixer.

42. The method of claim 32, wherein said mixing means comprises a first mixing means and a second mixing means, and wherein said method comprises prediluting said sample with said diluent in said first mixing means, feeding said prediluted sample to said second mixing means, and further diluting said prediluted sample in said second mixing means.

43. The method of claim 42, wherein said sample is placed in a length of tubing in series with said diluent, and wherein said sample and diluent are injected into said first mxng chamber, through a common flow tube.

44. The method of claim 42, further comprising the step of feeding additional diluent to said first mixing means after it is filled with prediluted sample to force said prediluted sample from said first mixing chamber to said second mixing chamber.

45. The method of claim 32, wherein said sample is prediluted and then further diluted.

46. An automatic diluting system for controlling the value of dilution factor DF for a concentrated sample suspension containing particles mixed with a diluent, comprising:

means for providing a flow of diluent into mixing means;

means for injecting a flow of a concentrated sample suspension into said mixing means to dilute said sample;

sensor means for determining the particle count rate of said diluted sample leaving said mixing means;

means for deriving a control signal from said count rate; and

means responsive to said control signal for adjusting one of said flow of concentrated sample suspension and said flow of diluent to adjust said dilution factor DF, said flows of diluent and sample suspension into said mixing means being continuous.

47. The automatic dilution system of claim 46, wherein said means for deriving a control signal comprises means for determining the initial rate of increase of particle concentration after mixing of said sample in said diluent begins.

48. The automatic dilution system of claim 47, wherein said means for deriving a control signal further comprises computing from said initial rate of increase of particles the approximate final concentration of particles expected when equilibrium is achieved in said mixing means, comparing said computed approximate final concentration of particles with an optimum particle concentration for said sensor means and, determining from said comparison the optimum value of dilution factor needed to achieve said optimal particle concentration.

49. An automatic dilution system for controlling the dilution factor DF for a concentrated sample suspension containing particles mixed with a diluent, comprising,

means providing a continuous flow of diluent into mixing means;

sample delivery means for delivering a flow of said concentrated sample suspension at a continuous flow rate F.sub.S into said mixing means to dilute said sample;

sensor means for determining the particle concentration per unit volume of said diluted sample leaving said mixing means; and

means for deriving a control signal from said particle concentration per unit volume;

said sample delivery means being responsive to said control signal for adjusting said flow rate F.sub.S of said concentrated sample suspension to adjust said dilution factor DF.

50. A method for automatically diluting a sample suspension, comprising:

feeding a diluent fluid into mixing means;

initially injecting a sample suspension to be diluted into a capture loop; and

then feeding a diluent fluid at a controlled, adjustable flow rate into one end of said capture loop to force said sample suspension undiluted from said the other end of said capture loop into said mixing means.

51. A method for automatically diluting a sample suspension, comprising:

prediluting said sample suspension in first mixing means with a diluent fluid to provide a prediluted sample suspension;

continuously adding diluent fluid at a controlled, adjustable rate to said mixing means to force said prediluted sample out of said first mixing means into second mixing means; and

further diluting said prediluted sample in said second mixing means by continuously feeding a diluent at a controlled, adjustable flow rate into said second mixing means.

52. A method for automatically diluting a sample suspension having a particle size distribution characteristic with tail portions at its upper and lower ends, comprising:

setting the starting threshold diameter to limit examination of said sample suspension to a range of particle sizes in one of said tail portions;

measuring the particle concentration in said range of particle sizes in said one of said tail portions; and

adjusting the dilution factor of said sample in response to said measurement.

53. The method of claim 32, wherein said mixing means has a relatively short equilibrium time, and wherein said adjustment of said flow of said sample responds so quickly that it operates virtually in a negative feedback mode.

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and apparatus for automatic dilution of a starting concentrated fluid suspension of particles for the purpose of optimizing a measurement of the particle size distribution, where the measurement technique chosen is sensitive to individual particles in the suspension over some appropriate range of particle size.

2. Description of the Prior Art

There are many intermediate process materials and final products of technical and/or commercial significance which exist either as a relatively high concentration of solid particles or liquid droplets suspended in a fluid, or as powders, which can be suspended in an appropriate liquid. The physical and/or chemical characteristics of these particle suspensions or dispersions (referred to herein as "sample suspensions"), or of the final products derived from them, often depend critically on the particle size distribution (PSD). Hence, it has become increasingly important to determine the PSD of these particle suspensions with high accuracy, resolution and reproducibility, often in the early stages of production. The solid particles or liquid droplets (in the case of oil-in-water or water-in-oil emulsions)--known as the "dispersed phase"--are suspended in an appropriate fluid, consisting of a simple liquid (e.g. water or an organic solvent) or mixture of liquids, perhaps containing one or more additives of various kinds (e.g. surfactants)--known as the "continuous phase". Typically, the starting particle suspensions to be analyzed contain a relatively high concentration of the dispersed phase--usually exceeding 10% by weight or volume of the overall fluid suspension, and sometimes reaching 40-50%.

Most methods of particle size analysis (PSA) require that the sample presented to the analyzer be much less concentrated than that which is typically available from an intermediate process stream or final product. This requirement that the starting sample be diluted, sometimes very substantially, prior to determination of its PSD is particularly critical for methods known as single-particle sensing (SPS) techniques. Because these methods demand relatively low concentrations of suspended particles in order to produce PSD results of high accuracy and minimal distortion, they are effective in providing a motivation for the present invention.

The well-known method of single-particle optical sensing (SPOS), described extensively elsewhere, is one particular kind of SPS method. It utilizes the principle of either light extinction or scattering to determine the mean diameters of suspended particles as they pass individually through a very small sensing "zone" or "view volume". In the recent invention of Wells et al (pending U.S. patent application Ser. No. 08/625,540, filed May 28, 1996, now U.S. Pat. No. 5,835,211), the physical principle of light scattering is combined with that of light extinction in order to increase the sensitivity and dynamic size range of the sensor. The resulting hybrid design thus extends the applicability of the SPOS method to particles smaller than those which would be detectable using only the light extinction technique, while preserving the large size range offered by the latter. This improvement increases the usefulness and overall effectiveness of the SPOS method.

There is another well-known SPS method for particle size analysis which is based on a different physical principle--the "electro-zone", or "Coulter counter", method. In this well-known technique, one monitors the conductivity between two volumes of partially conducting liquid, one of which contains the suspended sample particles at relatively low concentration, connected together by a small pore. The conductivity decreases momentarily whenever a particle passes through the connecting pore, caused by a pressure differential applied between the two liquid volumes. The magnitude of the conductivity decrease is proportional to the volume of the particle which momentarily interrupts the current flow through the pore. This represents another viable SPS method which can be used in conjunction with an autodilution system based on the present invention.

Regardless of the specific SPS method which is used to perform a PSA measurement, a concentrated particle suspension typically requires extensive predilution in order to ensure accurate PSD results with minimum distortion and artifacts. Specifically, this step is needed to ensure that the particles pass through the active sensing volume, or zone, one at a time, thereby avoiding all but occasional "coincidences" and consequent distortions of the output signal pulses and resulting PSD. For the purpose of explaining the underlying principles of this invention, it is convenient to focus exclusively on the use of an SPOS-type sensor in conjunction with the automatic dilution method and apparatus to be described. However, no loss of generality is thereby intended or implied. Rather, it is implicitly assumed that other methods of particle size analysis, including but not limited to other SPS methods, such as the electro-zone technique, may be used in place of the SPOS method in conjunction with this invention. Examples include "ensemble-type" methods for PSA, which respond to many particles at the same time, such as dynamic light scattering (DLS) and Fraunhofer diffraction (FD), also known as "laser" diffraction (LD). These techniques also usually require substantial dilution of concentrated particle suspensions, depending on their composition and particle size range (i.e. PSD). However, the extent of dilution typically required for these ensemble techniques is often considerably smaller than that needed for SPS techniques, such as SPOS and electro-zone sensing.

Therefore, PSA measurements, including those performed using the SPOS method, generally require substantial dilution of the original concentrated particle suspension, using an appropriate fluid, or mixture of fluids, as a diluent. This is especially required for automatic "online" particle size analysis of process suspensions in a production environment. In this case a dilution system should be able to accommodate samples with greatly differing PSDs, without requiring knowledge of their concentration, composition or PSD characteristics. The extent of dilution of the starting sample should be arrived at quickly and be optimal for the particle size analysis method being utilized--e.g. SPOS.

There are numerous applications for PSA in which the concentration of the starting particle suspension changes relatively little from one sample to the next. In such cases, it may be sufficient to dilute the starting particle suspension using a fixed, predetermined dilution factor, DF. This fixed DF value can be determined ahead of time, in trial-and-error fashion, for each kind of sample or application. A variety of prior art methods and devices exist for diluting a fluid sample with a predetermined dilution factor. By definition, these prior art methods and devices cannot provide for variable dilution when such would be more useful than the fixed, predetermined dilution which they provide, and therefore they are of limited utility.

Examples of prior art methods and/or devices which can be used to provide a fixed, predetermined dilution of fluid samples are described in: Cruzan, U.S. Pat. No. 4,036,062, Roof et al, U.S. Pat. No. 4,036,063, and Roof, U.S. Pat. No. 4,070,913. All of these patents describe means for diluting a fluid sample with a diluent fluid in which each of the fluids is initially contained in separate conduits. At the start of the dilution process the two conduits are connected together to permit closed-loop circulation and mixing of the two fluids. The extent of dilution--i.e. the value of the dilution factor, DF--is determined ahead of time by preselecting the volumetric relationship (relative volumes) of the two conduits.

This traditional approach to diluting a starting concentrated particle suspension is, by definition, inflexible and therefore quite limited. It is also potentially inaccurate when relatively large dilution factors are required. In such situations it may be problematic to inject, or meter out accurately, a very small volume of starting particle suspension into a much larger volume of diluent fluid. This limitation can in general be overcome by performing multiple dilutions in succession, where each dilution step has a fixed, relatively small DF value, able in principle to be accurately controlled. The final dilution factor is then equal to the product of all of the individual, intermediate DF values. However, the apparatus needed to implement this multiple-dilution approach is necessarily more complex and difficult to maintain than a simple, single-stage dilution device.

There exist prior art dilution systems which introduce both the starting concentrated fluid sample and diluent fluid into a mixing chamber on a continuous basis. The rates of flow of each of these input components can be adjusted to fixed, known values so as to yield a final diluted fluid sample having a known dilution factor DF equal to the ratio of the total fluid flow rate (diluent plus starting concentrated sample) to that of the starting concentrated sample alone. The final diluted sample suspension is typically extracted from the mixing chamber at a steady flow rate. Such a dilution system, having a known, but adjustable, dilution factor, is described in the invention of Mowery, Jr., U.S. Pat. No. 4,095,472. In this patent a fixed dilution factor is established at the start of the dilution process. In principle, the dilution factor can range from a relatively low value to a very high one. This method will be described in greater detail subsequently. The invention of Culbertson, U.S. Pat. No. 3,805,831, describes an apparatus for continuously and proportionately mixing one fluid stream, containing concentrated solute, with another, acting as the diluent. The final solute concentration which emerges in the resulting fluid stream is determined by the composition of each individual fluid stream and their relative rates of flow.

Automatic dilution systems which rely on the principle of negative feedback have also been described. In these systems, one or both of the flow rates of the starting, concentrated solute sample and the diluent fluid which enter the mixing chamber are continuously adjusted so as to yield an approximately unchanging solute concentration in the fluid mixture which exits the chamber. Mechanisms for adjusting the flow rate(s) have been proposed which respond to a measurement of the turbidity (i.e. optical density, or absorbence, at a particular wavelength or range of wavelengths) or scattered light intensity (over a particular range of angles) or diffracted light intensity obtained from the diluted fluid mixture residing in, or exiting from, the mixing chamber. A dilution system which responds to one of these measurements is implied by the invention of Pardikes, U.S. Pat. No. 4,279,759, which describes the use of optical sensing devices to measure the presence of a treatment chemical in a liquid process stream. Using negative feedback, this invention controls the rate of introduction of the treatment chemical into the continuously flowing stream so as to establish a relatively fixed, but adjustable, concentration of the chemical in the stream. By extension, sensing techniques based on light scattering and/or diffraction, as described in the inventions of Moreaud et al, U.S. Pat. No. 4,348,112, Tsuji et al, U.S. Pat. No. 4,408,880, and Brenholdt, U.S. Pat. No. 4,507,556, can be used to adjust the flow rate(s) of one or both of the starting concentrated fluid sample and diluent fluid entering a mixing chamber for the purpose of holding relatively constant the solute concentration in the resulting diluted sample fluid.

Finally, the method and apparatus described in the invention of Nicoli et al, U.S. Pat. No. 4,794,806, is able to dilute a starting concentrated particle suspension, using the principle of (approximate) exponential dilution of particles suspended in fluid in a mixing chamber of fixed volume due to the continuous addition of a diluent fluid at a known flow rate. Unlike the methods and devices described above, based on continuous mixing of both the concentrated sample fluid and the diluent fluid, the method described by Nicoli et al is based on injection of a fixed amount of sample into the mixing chamber. Hence, the amount of diluted sample material (i.e. suspended particles) available for the PSA measurement process at the output of the mixing chamber is limited by the amount which was originally injected into the chamber at the start of the automatic dilution process.

SUMMARY OF THE INVENTION

This invention is directed toward a new and novel method and apparatus for optimizing the extent of dilution to be applied to a starting concentrated particle suspension, for the purpose of carrying out a relatively fast and efficient particle size analysis (PSA) of same, preferably using a single-particle sensing (SPS) technique--for example, that of single-particle optical sensing (SPOS). In particular, this new method permits fast, virtually real-time optimization of the dilution factor DF for each sample to be analyzed, thereby shortening the total time needed for dilution and subsequent analysis of the sample. An automatic dilution system based on this invention is able to optimize the dilution factor shortly after the start of injection of a concentrated sample suspension into a mixing chamber in order to arrive at an optimal, steady-state (equilibrium) particle concentration in the mixing chamber or in the fluid stream exiting therefrom, which can be analyzed immediately thereafter using an appropriate SPS-type sensor.

As indicated above, for the purpose of describing this invention it is convenient to focus on the SPOS method of particle size analysis, based on the physical principle of light extinction or light scattering or some combination thereof (as described in the Wells et al U.S. Patent application). The particle concentration in the fluid stream passing through the SPOS sensor can be expressed either as the total number of particles, or the number in a given size range, per unit volume of fluid suspension. In general it must be large enough on the one hand to dominate over spurious particle counts due to background contaminants in the diluent fluid or statistical fluctuations due to insufficient particles in a given size range, but small enough, on the other hand, to avoid significant particle coincidences--i.e. two or more particles entering the "view volume" of the SPOS sensor at approximately the same time, thereby potentially causing distortions in the resulting PSD.

It is useful to review in detail the prior art method of diluting a concentrated "sample fluid" (particle suspension) by continuously combining it in a mixing chamber with an appropriate diluent fluid. This steady-state, "mixed-flow" approach is the starting point for the present invention. The fluid contents of the mixing chamber are continuously and efficiently mixed, so that ideally the particle concentration, expressed either as the total number of particles, or the number in any given size range, per unit volume of fluid suspension, is always homogeneous throughout the mixing chamber. The "sample fluid" continuously injected into the mixing chamber is the starting concentrated suspension of particles of a given composition and particle size distribution (PSD), where the suspending fluid is typically water or some organic liquid or mixture of liquids. The second fluid continuously injected into the mixing chamber consists of relatively particle-free diluent, with which one wishes to dilute the starting sample suspension. All or part of the fluid/particle mixture exiting the mixing chamber is made to flow, at an appropriate rate, through a suitable sensor, designed to respond to individual particles in the diluted output stream, producing a signal which can be processed to obtain the PSD. A simplified diagram of the dilution scheme is shown in FIG. 1. In general one must reduce the particle concentration of the starting suspension in order to minimize the likelihood of coincidences and thereby optimize the quality of the PSA results.

Owing to conservation of fluid, the rate of flow F of the diluted particle suspension exiting the mixing chamber MC equals the sum of the two individual rates of flow, F.sub.D and F.sub.S, of diluent and concentrated particle suspension which enter the chamber through tube 12 and tube 10, respectively. Thus,

The particle suspension residing in, or exiting through port 11 from, the mixing chamber MC is less concentrated than the original particle suspension which enters mixing chamber MC through tube 10, where the extent of dilution is described by the dilution factor DF, which equals the ratio of the (volumetric) rate of flow of the output fluid F through tube 11 to the (volumetric) rate of flow of the starting concentrated particle suspension F.sub.S, provided that steady-state equilibrium conditions have been reached in the mixing chamber MC, resulting in an approximately constant particle concentration,

For many important applications involving relatively highly concentrated sample suspensions, the desired dilution factor DF will be relatively high--i.e. DF>>1--so that F.sub.D >>F.sub.S. In such cases the flow rate F of diluted particle suspension exiting the mixing chamber MC will be approximately equal to the flow rate of diluent fluid entering the mixing chamber--i.e. F.apprxeq.F.sub.D. In this case, DF.apprxeq.F.sub.D /F.sub.S.

Equation 2 above is valid provided that sufficient time has elapsed that the particle concentration in the mixing chamber has reached steady-state equilibrium. Immediately following the start of flow of the sample suspension into the mixing chamber (defined as t=0), assuming that it already contains a volume V of clean, particle-free diluent and that fresh diluent is also flowing into the mixing chamber at a steady flow rate F.sub.D, the particle concentration in the fluid stream which exits the mixing chamber, defined here as C(t), increases monotonically with time t. Assuming ideal mixing of the fluids in the mixing chamber, the output particle concentration C(t) is described by,

where C.sub.0 is the particle concentration of the starting sample suspension being injected into the mixing chamber, expressed either as the total number of particles, or the number in a given size range, per unit volume of fluid suspension. Parameter .tau. is the characteristic time constant, commonly referred to as the "decay time", or "residence time", of the chamber. Quantity .tau. characterizes the rate at which the particle concentration in the mixing chamber (and hence in the output fluid stream) approaches its final equilibrium value C.sub.0 /DF and is given by,

Here, V is the total volume of fluid (including particles) in the mixing chamber which participates in the mixing process and F is the combined rate of flow of sample suspension and diluent fluid entering the mixing chamber under steady-state conditions, given by Equation 1. The behavior of C(t) with increasing time t following the start of injection of the sample (assuming that diluent fluid is flowing) is shown in FIG. 2. In most cases of practical interest a relatively large dilution factor, DF>>1, is required. In such cases F.sub.D is much larger than F.sub.S, and hence .tau. is approximately equal to V/F.sub.D.

As indicated by Equation 3, a period of time must elapse following initial injection of the concentrated sample suspension in order for the particle concentration in the mixing chamber, and therefore in the output fluid stream exiting the mixing chamber, to reach a nearly constant, equilibrium value, given by C.sub.0 /DF. This time must exceed considerably the characteristic "residence" time .tau. of the mixing chamber, which is a measure of the average time that a newly-injected particle resides within the mixing chamber before exiting in the output fluid stream. For example, after a total elapsed time of 3.tau., assuming ideal fluid mixing, the particle concentration in the output fluid stream is given by (C.sub.0 /DF)(1-e.sup.-3)=0.95 C.sub.0 /DF--i.e. 95% of the theoretical steady-state value. Alternatively, after an elapsed time of 5.tau., the particle concentration in the output fluid equals 0.993 C.sub.0 /DF, which is less than 1% away from the final value.

The detailed "shape" of the PSD of the diluted particle suspension which exits the mixing chamber, f.sub.OUT (d) vs d, should precisely mimic the shape of the PSD of the starting sample suspension injected into the chamber, f.sub.IN (d) vs d, where d is the mean particle diameter, assuming an ideal, random mixing process. In particular, one expects,

where both f.sub.IN (d) and f.sub.OUT (d) describe the number of particles of diameter d--i.e. in a very small range of diameters,