Abstract:
An improved electrical sensing zone apparatus and method for counting and measuring size of particles suspended in a diluted electrolytic solution. The apparatus includes an aperture that is optimized with the use of double or single tapered shapes that approximate a hyperboloid of one sheet. The flow rate is selectably controlled to maintain a sufficiently low Reynolds number to avoid boundary layer separation effects that cause noise and consequently low sensitivity. By measuring statistical moments within the aperture, an approximation of the distribution of particle sizes is achieved.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method and apparatus for size measurement of particles. 
   2. Description of the Related Art 
   Determining the number and size of particles suspended in a liquid solution is important for many industries. Medical applications, such as blood cell counters, have evolved from Coulter&#39;s seminal invention, U.S. Pat. No. 2,656,508 issued on Oct. 20, 1953. The preferred embodiment shown in FIGS. 1 and 6 of Coulter&#39;s patent was the beginning of what are today generically referred to as “electrical sensing zone” (ESZ) devices or methods. In an ESZ device a particle is measured by passing it through an electrical current-carrying aperture in an insulating partition between two containers, holding a conductive liquid. The motion of the particle through the aperture is caused by a pressure difference across the partition produced by a vacuum or pressure source. The presence of a particle in the aperture increases the electrical resistance of the aperture by displacing the liquid of equal volume to the particle volume. The physical chemistry of particles immersed in an electrolytic solution causes all particles (even those that are electrically conducting) to behave as if they were electrical insulators. The change in resistance may be detected as an increase in voltage across the aperture, or a decrease in current through the aperture. The change in resistance is approximately proportional to the volume of the particle. It is this approximate relationship between aperture resistance change and particle volume that gives the ESZ method good accuracy compared to several other methods of particle size measurement. On the other hand, the ESZ method has comparatively low sensitivity to submicrometer particles due to a multiplicity of noise sources in the aperture, comprising thermal noise due to aperture resistance, noise due to turbulence caused by electrical heating of the liquid in the aperture, noise due to hydrodynamic turbulence caused by flow of liquid through the aperture, noise caused by acoustic interference, noise caused by electrical interference and noise caused by mechanical vibrations. The deleterious effects of noise in the ESZ instrument are magnified by the fact that a signal pulse created by the passing of a particle through the aperture must exceed a predetermined threshold voltage in order to be detected. The threshold voltage must be set high enough so that the peaks of the noise will not falsely trigger the threshold circuit enough times to substantially interfere with the true pulses generated by the particles. The peak of the random noise is several times the root mean square (r.m.s.) level, and this requires the threshold voltage to be set a multiple number of times higher than the r.m.s. noise level. This causes a loss in sensitivity. 
   The usual aperture shape used in commercial prior art ESZ instruments is the circular cylinder. Until now, this has been considered to be the optimum aperture shape for the highest sensitivity. The circular, cylindrical, aperture shape causes pulses due to particles to have a wide variety of shapes. A pulse due to a particle passing along the axis of the aperture has a single peak. Other particle paths can have pulses with dual peaks, because at both the entrance and the exit of the aperture, the electric field intensity is higher at the edges than at the center. The variations in pulse shapes make it necessary to have a wide bandwidth pulse amplifier so that the pulses would be reproduced by the amplifier with high fidelity. The wide bandwidth increases the noise level. The thickness of the insulating partition through which the aperture is bored must be at least 30 micrometers (μm), the length-to-diameter ratio of the aperture is large, and this results in poor sensitivity. This is because the internal volume of the aperture must be small for high sensitivity, and a large thickness of the partition makes the aperture length long, which makes the aperture volume large. 
   The circular, cylindrical, aperture causes boundary-layer separation of the liquid therein. The boundary-layer separation produces noise due to turbulence. At the input of the aperture, there is a hydrodynamic constriction of the fluid flow diameter. At the output of the aperture, there is a jet oriented along the axis that is surrounded by backflow of toroidal shape. Some of the particles that have passed through the aperture are captured by the backflow and recirculate near the exit of the aperture, and this causes noise in the form of false particle pulses. 
   The measurement range, or “dynamic range” of an aperture is limited to about 20/1 in particle diameter, making the ESZ instrument useful for relatively narrow particle size distributions. 
   Most particle size analysis done with the ESZ instrument is done with apertures 30 μm in diameter, or larger. Apertures smaller in diameter have been available commercially for prior art instruments, but these smaller apertures have been little used because of their tendency to be plugged by debris. If the aperture is plugged, the instrument cannot continue to measure particles until the plug is dislodged. 
   Even if debris does not cause plugging, it can cause particles to be measured that are not part of the sample being tested. To keep debris from interfering with the sample, the sample concentration must be significantly higher than the debris concentration. But the sample concentration must be low enough to avoid multiple sample particles from being simultaneously in the aperture. This is called “coincidence.” Coincidence of particles in the aperture can cause errors in the measured particle size distribution. 
   U.S. Pat. No. 3,742,348 issued on Jun. 26, 1973 to Golibersuch, addresses the problems related to plugging by debris, coincidence, and low sensitivity to small particles, by allowing a multitude of particles to pass though the aperture simultaneously. This allows a larger diameter aperture to be used than is needed to detect single particles, thus reducing the frequency of plugging. Also, smaller particles can be detected than by a single-particle measurement. One of the disadvantages of this invention is that the circular, cylindrical, aperture requires a large length-to-diameter ratio (on the order of 20/1) in order to get a signal that can be analyzed by the signal processor proposed by the inventor. The only information it obtains is equivalent to what I call “λ 2 ” in a subsequent section of this specification, for the special case where all of the particles in the sample have equal volumes. It will be apparent that μ 2 , by itself, is not a significant amount of information about the particle size distribution. Also, assuming all of the particles to be the same size is a very unrealistic and restrictive assumption. 
   Applicant believes that the closest reference corresponds to U.S. Pat. No. 4,926,114 issued to Doutre on May 15, 1990 for an apparatus for studying particles having an aperture whose cross-sectional area changes progressively along at least part of its length. Doutre&#39;s patent discloses an apparatus and method for studying particles suspended in molten metal that includes an aperture with a current path therethrough, causing the fluid to flow through the aperture and detecting resistive pulses caused by the passage of suspended particles. An aperture with a cross-section that changes progressively along its length provides additional information about particle size. However, it differs from the present invention because it has the same sensitivity limitations of the other prior art devices since it does not keep the Reynold&#39;s number of the fluid flow within the required range to minimize or preclude boundary layer separation effects. Doutre&#39;s patent is not even concerned with these effects since it applies to molten metals. In fact, Doutre&#39;s invention is intended for use with apertures that ideally contain no more than one particle at a time. Col. 4, lines 51-53. There is not even a suggestion of using statistical moments to make inferences about the size of the particles. 
   Other patents describing the closest subject matter provide for a number of more or less complicated features that fail to solve the problem in an efficient and economical way. None of these patents suggest the novel features of the present invention. 
   SUMMARY OF THE INVENTION 
   It is one of the main objects of the present invention to provide an apparatus and method for accurately measuring particles in an electrolyte and determining the size distribution of the particles. 
   It is another object of this invention to provide such an apparatus that permits the counting and size distribution determination of particles having less than one micrometer in diameter. 
   It is still another object of the present invention to provide an apparatus and method for improving the signal-to-noise ratio. 
   Yet another object of this invention is to avoid or minimize the effects of boundary layer separation. 
   It is also another object of this invention to produce signals that can be analyzed by a signal processor to determine the lower-order statistical moments of the particle size distribution. 
   Another object of this invention is to provide an apparatus that can use larger and thus more debris resistant apertures, with substantially the same accurate results. 
   Another object of the invention is to extrapolate the particle size distribution obtained with an ESZ instrument below the threshold level. 
   It is yet another object of this invention to provide such a device that is inexpensive to manufacture and maintain while retaining its effectiveness. 
   Further objects of the invention will be brought out in the following part of the specification, wherein detailed description is for the purpose of fully disclosing the invention without placing limitations thereon. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     With the above and other related objects in view, the invention consists in the details of construction and combination of parts as will be more fully understood from the following description, when read in conjunction with the accompanying drawings in which: 
       FIG. 1  is a block diagram of the method for size measurement of particles, object of the present application. 
       FIG. 1A  is a schematic representation of one of the preferred embodiments for the improved apparatus subject of the present invention. 
       FIG. 2  is a schematic representation of a prior art electrical sensing zone (ESZ) apparatus. 
       FIG. 3  shows in solid line a typical signal pulse of a particle coaxially traveling through the aperture of an ESZ instrument, such as the one represented in  FIG. 1 . The dashed line curve represents a particle that does not travel coaxially through the aperture. 
       FIG. 4  is a representation of a double-tapered aperture. 
       FIG. 5  is a representation of a single-tapered aperture. 
       FIG. 6  is a schematic representation of a signal processor circuit to compute the lower-order statistical moments of the particle size distribution for one of the preferred embodiments. 
   

   REFERENCE NUMERALS IN DRAWINGS 
   
       
         10  present invention 
         12  tube to vacuum or pressure source 
         14  vacuum or pressure means 
         16  liquid trap 
         17  inlet of aperture 
         18  any type of aperture 
         18   a  circular, cylindrical aperture 
         18   b  double-tapered aperture 
         18   c  single-tapered aperture 
         19  tapered outlet 
         20  ESZ assembly 
         21  aqueous electrolyte solution 
         22  particle of the sample to be measured by the instrument 
         23  surface-active agent (surfactant) 
         24  partition containing the aperture 
         26  low-noise aperture voltage source 
         27  ground connection 
         28  low-noise current-limiting resistor 
         30   a  electrode in nearly closed container 
         30   b  electrode in open container 
         32  direct current (D.C.) voltage blocking capacitor 
         33  D.C. coupling voltage 
         34  low-noise preamplifier 
         36  pulse amplifier 
         40  comparator 
         42  threshold voltage reference 
         44  pulse-height analyzer 
         46  particle size distribution recorder 
         48  output of pulse amplifier 
         50  signal processor 
         50   a  half-angle, η, of double-tapered aperture 
         50   b  half-angle, η, of single-tapered aperture 
         52   a  partition thickness, double-tapered aperture 
         52   b  partition thickness, single-tapered aperture 
         54   a  aperture diameter, double-tapered aperture 
         54   b  aperture diameter, single-tapered aperture 
         56  front surface of single-tapered aperture 
         58  pulse peak 
         60  first multiplier 
         62  first multiplier output 
         63  zeroth integrator output 
         64  first integrator output 
         65  zeroth integrator 
         66  first integrator 
         68  second integrator 
         70  second integrator output 
         72  second multiplier 
         74  second multiplier output 
         76  third integrator 
         78  third integrator output 
         80  third multiplier 
         82  third multiplier output 
         84  output processor 
         86  λ 1  input 
         88  particle size distribution estimate 
         90  ν input 
         92  other inputs 
         100  output devices 
     
  
   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Referring now to the drawings, where the present invention is generally referred to with numeral  10 , it can be observed that it basically includes an electrical sensing zone (ESZ) assembly  20  and signal processor  50  and output devices  100 , as shown in  FIG. 1 . 
   ESZ assembly  20  is shown in  FIG. 2  in general terms. Assembly  20  includes electrical current-carrying aperture  18  immersed in an electrolyte with controlled concentration. In  FIG. 1A , ESZ assembly  20  is shown with current carrying aperture  18  with a tapered inlet  17  and outlet  19  immersed in an electrolyte with controlled concentration. As best seen in  FIG. 5 , in the preferred embodiment, aperture  18  has tapered outlet  19 . Inlet  17  of aperture  18  has a predetermined diameter. Aperture  18  has a length of at least 30 micrometers and it is immersed in an electrolyte solution  21  with particle  22  of at least one size. Solution  21  passes through aperture  18 . Vacuum or pressure means  14  causes solution  21  to pass through aperture  18  at selectable liquid flow rate with sufficiently low Reynolds number to preclude boundary layer separation effects inside and adjacent to aperture  18 . 
   In the embodiment represented in  FIG. 4 , aperture  18  has the double-tapered shape, which approximates a hyperboloid of one sheet. The maximum sensitivity that the invention has achieved is obtained if the angle η=60 degrees. It has been found that this shape minimizes noise and permits a more accurate measurement of the particle population and size distribution contained in the electrolyte 
   The single-tapered aperture  18   c  of  FIG. 5  performs similarly to the double-tapered aperture of  FIG. 4 , but it is easier to fabricate, and has less maximum sensitivity than the double-tapered aperture  18   b . The pulses are uniformly-shaped, as in  FIG. 2   a . The partition thickness of the single-tapered aperture  52   b  can be very large. 
   It is well known that, if Reynolds number is low, the tendency of producing boundary layer separation at the output of the aperture  18  is reduced. Using the Navier-Stokes equations, I found the maximum value of η that causes boundary layer separation for certain Reynolds numbers. For a Reynolds number (R N ) of 1, maximum η is 74.5 degrees. For R N  of 10, maximum η is 45.8 degrees. In commercial prior art ESZ instruments, R N  is in the vicinity of 500. For this R N , maximum η=5.7 degrees. R N  is reduced by reducing aperture diameter or fluid velocity. 
   A major limiting factor in the sensitivity of the ESZ instruments is that the threshold voltage  42  must be almost always above the peak of the noise voltage at the output of the pulse amplifier  36 . For this to happen, the threshold voltage  42  must be up to eight times the r.m.s. noise voltage. Such a high threshold voltage  42  means that no signals are detectable unless the signal pulse peaks are much higher than the r.m.s. noise level. 
   To detect particles  22  that would produce pulse peaks at the output of the pulse amplifier  36  below the threshold voltage  42 , many particles  22  must be passed simultaneously through the aperture  18 . To accurately detect the concentrated particles  22 , the pulse shapes produced must be uniform. To obtain uniform pulse shapes, Golibersuch used a long, narrow, circular, cylindrical, aperture  18   a . Uniform pulse shapes can be obtained, with better results, if either a double-tapered aperture  18   b  or a single-tapered aperture  18   c  is used. The diameter  54   a ,  54   b  could be in the range of 30 μm to 100 μm, but may have other sizes. The object of using an aperture  18   b ,  18   c  with concentrated particles  22  is to measure the lower-order statistical moments of the particle  22  size distribution to calculate a particle  22  size distribution obtained by single-particle  22  measurement below the threshold voltage  42 . 
   The fundamental formula I used for determining the moments of the particle size distribution using concentrated particles  22  in the aperture  18   b ,  18   c  is
 
λ n   =&lt;A   n &gt;∫ −∞   ∞′ ∫ n ( t ) dt   (Eqn 1).
 
   λ n  is measured by the system of  FIG. 6 , and is related to the n th  statistical moment of the particle size distribution. f(t) is the signal pulse of  FIG. 3   a . This pulse has nearly the same shape, regardless of the size or shape of the particle  22 . A is the pulse peak  5 S, which is proportional to the particle  22  volume. v is the number of particles  22  passing through the aperture  18   b ,  18   c  per second; so v must be found by some external instrument with more sensitivity for particle counting. Some assumption can be made that eliminates the need to measure v directly. 
   The input of the system of  FIG. 6  comes from the output of the pulse amplifier  36 , which is  48 . To find λ 1 , the D.C. coupling voltage  33  is used in place of the D.C. voltage blocking capacitor  32 . To find λ n  for n&gt;1, the D.C. voltage blocking capacitor  32  will be used in place of the D.C. coupling voltage  33 . λ 1  provides information about the first statistical moment (mean) of the particle size distribution, and is the output  63  of the zeroth integrator  65 , which gives the integral of the pulse amplifier output  48 . It is possible to obtain the information provided by λ 1  without using the zeroth integrator  65 , by finding the volumetric concentration of particles  22  in the electrolyte  21 , and finding the volumetric flow rate of the electrolytic solution  21  through the aperture  18   b ,  18   c . This gives the volumetric flow rate of particles  22  through the aperture  18   b ,  18   c . Eliminating the zeroth integrator  65  eliminates the need for D.C. coupling voltage  33 . It is desirable to use only A.C. coupling in an ESZ instrument because low frequency noise and drift are eliminated. λ 2  provides information about the second statistical moment (variance) about zero of the particle size distribution, and is the output  64  of the first integrator  66 , which gives the integral of the square of the pulse amplifier output  48 . The squaring function is provided by first multiplier  60 . The first multiplier output  62  is connected to the input of the first integrator  66 . 
   If λ 1  and λ 2  are measured, v&lt;A&gt; and v&lt;A 2 &gt;can be found because the pulse shape f(t) is known, and the integrals of Eqn 1 involving f(t) and f 2 (t) can be calculated. To find the mean and variance, it is necessary to find v. v is closely related to the particle  22  number density in the electrolytic solution  21 . If the particles  22  are very small, an ultramicroscope, or a similar instrument, would be needed to find the particle  22  number density. If the sample does not have particles less than about 30 nanometers (nm) in diameter, a conventional dark-field microscope is sensitive enough to detect the particles. 
   A kind of ultramicroscope that would eliminate the tedium of visually counting particles is called the “flow ultramicroscope.” It is an automated instrument that counts particles by detecting them as they scatter light to a photodetector while passing through an intense light beam. Light scattering does not give an accurate indication of particle size, but it can be very sensitive to the presence of a particle. Such devices are commercially available for counting particles in samples of ultrapure liquids. They can be adapted for particle number density measurements in a liquid. 
   λ 3  provides information about the third statistical moment (skew) about zero of the particle size distribution, and is the output  70  of the second integrator  68 , which provides the integral of the cube of the pulse amplifier output  48 . The cubing function is provided by the first multiplier  60  and the second multiplier  72 . The second multiplier output  74  is connected to the second integrator  68  input. 
   One way to extrapolate a particle size distribution is to assume the form of the distribution. Several kinds of distributions have been assumed in particle size analysis, but the one that has more physical justification than others is the log normal distribution. Many materials approximate a log normal distribution. 
   λ 4  provides information about the fourth statistical moment (kurtosis) about zero of the particle size distribution, and is the output  78  of the third integrator  76 , which provides the integral of the fourth power of the pulse amplifier output  48 . The fourth power function is provided by the first multiplier  60 , the second multiplier  72 , and the third multiplier  80 . The third multiplier output  82  is connected to the third integrator  76  input. 
     FIG. 6  does not show how to obtain λ 5 , but it is obvious from examining  FIG. 6  how to obtain any value of λ n . 
   The integral of the signal is proportional to the mean of the particle size distribution curve. The integral of the square of the signal is related to the variance of the particle size distribution curve. The integral of the third power of the signal is related to the skew of the particle size distribution curve. The integral of the fourth power of the signal is related to the kurtosis or peakedness of the particle size distribution curve. 
   Higher powers of the signal do not have specific names but are also relevant. They are more difficult to compute. For the purposes of the present invention, however, it has been found that computing these first four statistical moments, namely, the mean, the variance, the skew and kurtosis of the particle size distribution curve, provides the necessary information to accurately estimate the shape of the particle distribution. 
   The integrator outputs  63 ,  64 ,  70 , and  78  are applied to an output processor  84  that gives a particle size distribution estimate  88 . If λ 1  is not obtained from the zeroth integrator output  63 , it is applied to the output processor  84  at λ 1  input  86 . If v is not calculated by assuming the form of the particle size distribution, it is applied to the output processor  84  at v input  90 . 
   It is possible to find the parameters of a log normal distribution by only knowing λ 1  and the particle size distribution above the threshold voltage  42  obtained by using the ESZ instrument for single-particle  22  measurement. From λ 1  one can calculate the total volume of the sample. From the particle size distribution above the volume representing the threshold voltage  42 , combined with the total volume of the sample, we can compute the cumulative particle size distribution. 
   The foregoing description conveys the best understanding of the objectives and advantages of the present invention. Different embodiments may be made of the inventive concept of this invention. It is to be understood that all matter disclosed herein is to be interpreted merely as illustrative, and not in a limiting sense.