DETERMINATION OF PARTICLE SIZE AND ELECTRIC CHARGE

Abstract: A method for the determination of particle size and electric charge or zeta potential of particles dispersed in a fluid medium. The particle size and charge are determined from measurements of (1) the phase lag between an applied alternating electric field and the resulting particle velocity, and (2) the amplitude of the particle velocity. Also disclosed is the measurement of the interaction of sound waves and electric fields in the fluid medium over a range of frequencies to obtain the particle size and zeta potential.

Description: DETERMINATION OF PARTICLE SIZE AND ELECTRIC CHARGE TECHNICAL FIELD The present invention relates to a method of a means for the determination of particle size and electr charge or zeta potential in a colloidal system. A colloid is a suspension of small particles in fluid medium (e.g. aerosols and the dispersions of solids liquids). Colloids have great scientific and industri importance. Examples include blood, paints, slurries a milk. The most significant characteristics of ma colloidal systems are the size and charge of the particle since most other properties of the system are influenced some extent by these factors. There are many areas of industry in which it necessary to be able to determine the size of particle suspended in a liquid or the electric charge on t particles. For example, in the mining industry, minera ores must be ground down until the particles are the righ size for floating, and in liquid purification processes i is important to be able to keep particle charge low in orde to encourage the coagulation of the particles into clump large enough to be filtered out. In nearly every colloidal system the particl carries an electric charge. This charge is balanced by a excess of ions of opposite charge in the suspending liquid These ions tend to cluster around the particle, forming diffuse cloud which is known as the double-layer. Th voltage difference between the particle surface and th liquid beyond the double-layer in equilibrium is referred as. the "zeta potential" denoted by ζ. The bigger t particle charge, the bigger the ζ potential. BACKGROUND ART Known methods for measuring particle size includ the use of electron microscopes. Coulter counter centrifuges and dynamic light-scattering devices. Howeve all of these known methods require the removal, a subsequent dilution of the sample prior to testing, maki such methods unsuited to on-line monitoring of particl size. Known methods for measuring particle charge a involve the measurement of the particle velocity in a electric field. In some methods, the velocity is determin by measuring the time required for the particle to pas between two points on a microscopic grid when a stea electric field is applied. In other methods, partic velocity is measured by a light-scattering technique with alternating electric field of 10 or 20 Hz. There is apparatus suitable for determining bo particle size and charge. The "Zeta Sizer" (Malve Instruments) measures the light scattered from a laser be as it passes through the suspension. In the absence of applied field, the fluctuations in the scattered lig provide information about the particle size, and if a slow varying electric field is applied the particle charge can obtained from the fluctuating light signal. All of the above methods suffer the disadvant that they require sample dilutions and most require use light-scattering instruments. Accordingly, opaque samp cannot be measured. DISCLOSURE OF THE INVENTION It is an object of the present invention provide a method of and means for the determination particle size and electric charge or zeta potential particles in a colloidal system. It is another object of the present invention provide a method of-and means for the determination particle size and electric charge or zeta potential particles in a colloidal system on-line and without samp dilution, even in opaque solutions. It is a further object of the present inventi to provide a method of and means for determination of t motion of colloidal particles in a high-frequency field, f t is by the use of high frequency measurements of partic motion that the particle size and charge can be determined These and other objects of the present inventi will be apparent from the following non-limiting disclosu of the invention. According to one aspect of the present inventi there is provided means for determining the size and char of particles dispersed in a fluid medium from the phase l an d amplitude of particle velocity in an alternating electric field. According to a further aspect of the present invention there is provided means for determining the c particle size in a fluid medium having uniform, low ζ potential from a measurement of the phase of the particle motion in a high frequency alternating electric field, and wherein the zeta-potential can be determined from the amplitude of the motion in the alternating field. ■J ^Q According to another" aspect of the invention there is provided a means for determining the particle motion in an alternating field from measurements of the interaction of sound waves in the suspension. According to a further aspect of the invention 5 there is provided means for measuring and generating the interaction of sound waves and electric fields in a suspension, comprising positioned spaced apart electrodes and pressure transducers in contact with the suspension, enabling the simultaneous measurement of electric current, 0 potential, and pressure differences in the suspension. These and other aspects of the invention will be apparent from the above, and from the following description relating to the invention. BRIEF DESCRIPTION OF THE DRAWINGS 5 The invention will be further described with reference to the drawings, in which:- Figure 1 illustrates separate graphs of applied electric field versus time and particle velocity ver time; Figure 2 ' illustrates graphic-ally determination of particle size from phase lag measurement Figure 3 illustrates graphically the subsequ determination of particle charge from amplitude measureme and Figure 4 illustrates a parallel plate cell u in obtaining measurements in some embodiments of the pres invention. MODE FOR CARRYING OUT THE INVENTION When an alternating electric field is applied a colloidal suspension it causes the particles to oscill at the frequency of the applied field in a way which depe on particle size and zeta potential. If the frequency the applied field is much lower than the optimum siz frequency (to be defined hereinafter), the particle veloc will be in phase with the applied field; i.e., when field switches direction, so too does the particle moti At higher frequencies a phase lag develops, i.e., there i time lag between the change in direction of the appl field and the subsequent change in the direction of particle motion due to the particle inertia. This illustrated in Figure 1. For a given particle, the phase lag increa with particle radius (since this increases the parti inertia) , while the velocity amplitude decreases w radius. In general these two quantities also depend on particle ζ potential. Thus by measuring phase lag and amplitude it should be possible to determine size and charge. For suspensions in which the particles have a uniform, low ζ-potential it is shown that the phase lag is independent of the magnitude of ζ . For such suspensions a measurement of phase lag can therefore be used to determine particle size, and the amplitude measurement can then be used for charge determination. Mathematical formulae relating phase lag to particle size, and amplitude to size and charge are presented for a dilute suspension of spheres with low ζ. The particle velocity can be obtained indirectly from measurements involving the interaction of electric fields and sound waves in the suspension. It can for example be obtained for the measurememt of sound waves generated by electric fields, or from the measurement of electric fields generated by sound waves in the suspension. An advantage of the present invention is that measurement can be performed on-line, as opposed to the sampling methods required of the prior art and it can be applied to opaque suspensions. The present invention can also be applied to larger particles than can the prior art light scattering techniques, which are limited to <lym range. In the case of highly charged particles, it may be necessary to reduce the charge by the addition of salt or acid/base, since the determination of size and charge is simpler for systems with low f-potential. Alternatively, high ζ systems can be siz by using a prior calibration procedure. The only theoretical studies of particle veloci that have appeared in the literature have been concerne with either a steady electric field ("Zeta Potential i Colloid Science" by R.J. Hunter, Academic Press 1981 Chapter 3) or an alternating field at frequencies which fo most suspensions are well below the optimum frequency fo size determination (Hinch E.J., et al, J. Chem. Soc. Farada Trans. 2 80 , 535 (1984)). The latter authors made n mention of the possibility of size determination from phas lag and amplitude measurement. In accordance with the present invention particl velocity has been calculated for a dilute suspension ove the frequency range which is best-suited to particle sizing that is frequencies of the order of v/a 2, where v is t hh 2 kinematic viscosity of the suspending liquid (=0.01 cm /se for water), and a is the particle radius. For an 0.1 u radius particle, this optimum frequency is 16 MHz. In thi frequency range the phase lag is a sensitive function o frequency, and for this reason it is well-suited fo determining particle sizes. As indicated above, the particle velocity can b determined by measuring the interaction of sound waves an electric fields in the suspension; it can for example b determined by measuring sound waves generated by a alternating electric field, and by measuring the electri fields generated by sound waves. Of these two effects, only the second has appeared in the scientific literature. Most of the work on this effect is restricted to electrolytes, with the most notable exception being two papers by J.A. Enderby (Proc. Roy. Soc. A 207, 329 (1951)) and J.A. Enderby and F. Booth (Proc. Phys . Soc. 65, 321 (1952)). These authors apparently had no idea that this effect was related to the particle velocity. Furthermore, there appear to be a number of errors in their work R.W. O'Brien, J. Fluid Mech. (to be published). There is no disclosure in these references of the possibility of obtaining particle size from this effect. The phenomenon of sound wave generation by an electric field is described in U.S. Patent 4,497,208. However, there is no disclosure in the above referenced patent of the link between the effect and particle velocity, or of the possibility of determining particle size from the effect. Formulae associated with particle size and charge determination There are two main aspects to this invention: (1) A method for determining particle size and charge from measurements of particle velocity in an alternating electric field (2) A method for obtaining that particle velocity from measurements of the interaction of sound waves and electric fields in the suspension. With the aid of these procedures it is possibl to determine particle size and charge from measurements o the interaction of sound waves and electric fields in an suspension. Aspect (1) of the invention will be described i the following two sections. Aspect (2) will be addressed i section 3. 1 • The velocity of an isolated sphere in an alternatin electric field. In a dilute suspension, each particle can b treated as being alone in an infinite liquid. In thi section a dilute suspension of uniform spheres will b studied. We let ξocos wt denotes the ambient electric fiel in the suspension; this is the electric field which woul apply in the absence of any particles. |E I is the amplitud of this applied field, and w/2π is the frequency. Following the standard procedure for problem involving sinusoidally varying quantities, this applie field can be rewritten as E e lwt , with the understandin ~o that the field is actually given by the real part of thi complex expression. Since colloidal particles are electricall charged, the applied field exerts an alternating force o the particles which causes them to oscillate backwards an forwards at the frequency of the applied field. Th particle velocity is denoted by V eiwt. The comple -o quantity V requires two real numbers ( and a direction ) fo its specification. The two numbers are |V | , the amplitude -o of the particle velocity, and arg V the phase lag referred —o to earlier. The quantity V is proportional to E , the -o -o strength of the applied field. For spherical particles, which on account of their symmetry move in the direction of the applied field, this proportionality relation takes the simple form v = μE_ -o (1) The phenomenon of particle motion in an electric field is called "electrophoresis" , and is termed the "electrophoretic mobility" of the particle. Like V , μ is a complex quantity. |μ | is equal to |v | for unit applied field, and arg μ is equal to the phase lag. Since μ is independent of E , it can only depend (for any given ~o frequency) on the properties of the particle and solvent; μ is the quantity which should be measured in the course of determining particle size and charge. The calculation of v is greatly complicated by the fact that the applied field distorts the double layer. As a result the double layer ions impose an electric force which retards the particle, thereby affecting both the phase lag and the amplitude of the motion. Fortunately, at the optimum sizing frequency, this double-layer distortion can be neglected in the important case of particles with low ζ potential . The range of validity of this low-ζ approximati depends on the ratio of particle radius to double-lay thickness; If that ratio is around one, the approximati should be valid for ς potentials of up to about 50mv. particle radius is much greater than double-layer thicknes the ζ potential limit will be larger; For example, if t ratio of the radius to thickness is 50, the low- approximation will work up to about lOOmv. This shoul cover most commonly occuring colloids. For the highl charged colloids it .may be necessary to add salt o acid/base to reduce the ζ potential and thereby tak advantage of the low-ζ results. For a sphere with low ;, we have shown that th electrophoretic mobility is given by the formulae I ! = 4π_ε I ζI IG| , (2) 3 arg u = (u( ζ )-i) + arg G, (3) where z (ik-κ)a + ca 3 + 2a i E 3 (-ika + <a) ^r E. (-ika + ik-κ ^ —^- E.(-ika + a) \ (4) ika 4 5 J J Here E is the exponential integral ε is the permittivity of the suspending liquid, ζ is the "zeta potential" of the particle, a quantity related to its charge (see, e.g. chapter 2 of "Zeta Potential in Colloid Science" by R.J. Hunter, Academic Press, 1981), κ ~ is the double-layer thickness (related to the electrolyte concentration; see above reference) , a is the particle radius, v '/pi is the speed at which an uncharged sphere moves when acted on by an alternating force of unit magnitude, given by v/ p , irpAJSϋ j . + |i(3 + ) + 32 (1+1) ' " ' ra / wa P is the density of the suspending liquid, v is the kinematic viscosity of the suspending liquid, and p+Δp is the particle density. Finally, the quantities kr a, b and c are defined by -3a -ika a = 2ik b - - and 2-iw' (2+ε p/ ε ) ε being the particle permittivity, and w ' = wε/K * , CO where K is electrolyte conductivity. Finally, u ( ζ ) is a function which is 0 when ζ<0, and 1 for C >0 In the case when a>>l (thin double layer), equation (4) reduces to .G = 3aV* (1-ika) (1+c) . (6) F' Since (u(ζ)-l) depends on the sign, but not on the magnitude of ζ, and G is independent of ζ, it follows from equation (3) that the phase lag arg μ is also independent of the magnitude of ζ . This property of the phase lag makes it ideal for the determination of particle size. To illustrate this point reference is made to Figure 2 wherein arg μ for the κa>>l case has been plotted as a function of the non-dimensional variable wa /v. Figure 2 was constructed using equation (6) with parameters Δp/p =1, ε /ε «= 0, and ζ>0. From this figure it can be seen that for fixed values of w and v, arg y increases monotonically with increasing particle radius, tending to a limiting value of 45° as wa /v ■ + β . With the aid of this curve it is possible t obtain a unique particle size from any measurement of arg μ ' For example a phase lag of 14 implies that wa /v«l. If th suspending liquid is water, which has a v value o 2 .01cm /sec, and if the frequency of the applied Ifield is 2 1MHz, the particle radius corresponding to wa = 1 is 0.4μm.. For a given solvent, the range of particle sizes which can be accurately measured in this way depends on th frequency of the applied field. From Figure 2 it can b shown that a one degree error in the measurement of arg u leads to a relative error of less than 6% in the assessed particle size provided Kwa 2 /v<4. Thus for any particle size , there is an optimu frequency range for size determination , given by v/a 2 <w<4v/a 2 . Although the curve in Figure 2 is only valid fo a very limited class of suspension , the notion of an optimu frequency range is likely to have universal application . The prec ise end po ints of the range may vary from on suspension to the next , but the optimum wi ll always b around v/a 1. For an 0.1 um particle in water v/a 2 corresponds to a frequency of 16MHz , whi le for a l^ 11 particle, this frequency is 160kHz. From equation (3) it can be seen that arg changes by ιr radians (corresponding to 180° in phase lag) as the ζ potential changes sign. Thus the curve of arg for ζ<0 would have the same form as Figure 2, but with arg reduced by 180°C. Since the total variation in arg u wit particle radius is only 45°, there is no possibility of positive and a negative particle yielding the same phas angle. In fact the sign of ζ can be immediatel ascertained from the quadrant in which the phase angle lies the first quadrant indicates ζ>0, while the third quadran implies ζ<0. Once the radius a and the sign of ζ have bee ascertained from the phase lag, /cf can be determined fro the measured value of I μ| • Figure 3 shows the variation o 2 the non-dimensional quantity pvjμ|/ ε |ζ| with wa /v . Once again the curve comes from equation (6), with the same parameters as in Figure 2. From the curve i can be seen that |μ| decreases monotonically with increasing frequency or particle radius. This curve can be used fo determining |'ζ|. For example, if the particle radius has been found to be 0.4 μm then from the figure pv|μ|/.t|ζ| = 0.87. If the measured |μ| is 3.5*10~ cm V s ~ - , it follows that |ζ| = 50mv (assuming p, v and ε values for water). Since the phase lag measurement indicated a positive C , it is found that ζ=50 mv Although Figures 2 and 3 were obtained with the formula (6) for the thin double layer case, the procedure herein described is valid for arbitrary double layer thickness. To summarize the main points: (1) The particle size and the sign of ζ can be obtained from phase lag measurement. (2) jζ| can then be obtained from the measured |μ j value. (3) The optimum sizing frequencies are around w=v/a . 2. Results valid for more general suspensions. The formula (1) defining the electrophoretic mobility can also be applied to a much more general class of suspensions, namely "statistically isotropic" suspensions. These are suspensions which appear to be isotropic, from the macroscopic point of view (Batchelor, G.K., J. Fluid Mech., 41, 545, (1970)). Many suspensions fall into this category, particularly if they have not been subjected to a flow and if sedimentation is not too significant. Since these isotropic suspensions may be concentrated, the particle interactions will cause the velocity to vary from one particle to the next. The quantity Y 0 which appears in equation (1) in this case is intended to represent an average of the particle velocities given by N - . K . ∑o " ∑ ^ m2 / ∑ Δm j-1 k-1 where v^e wt is t * le ve l° c i y of the centre of mass of th jth particle in the sample, and Δm i s the particle mas minus the mass of solvent displaced by the particle. The applied field E also represents an average 5 namely an average of the local electric field over representative volume of the suspension (see the previou reference) . For a dilute suspension this is equivalent t the previous definition. The notion of electrophoretic mobility i in considerably more complicated for "non-isotropic suspensions. In these suspensions the velocity v is no usually parallel to the applied field. Thus if the applie field is parallel to the x axis of some cartesian coordinat system, the particle velocity will in general have ,c components along the x,y and z axes. Since the velocity is still proportional to field strength, it is possible to define three electrophoretic mobilities, one for each component of V . Three more components are required to characterize the mobility with a field in the y direction, Q and another three for a field in the z direction, giving nine in all. It is convenient to regard these nine mobilities as the components of a single entity known as the "electrophoretic mobility sensor", denoted by K. The nine components of £. are usually set out in the 3 x 3 matrix where (i, 1 ,μ 71 ,ι_. 1 )E are the x, y and z components of Q caused by a field along the x-axis. The other two columns of the matrix give the velocity due to fields in the y and z directions respectively. In this notation, the relationship between Q and 5 for a non-isotropic suspension takes the compact form V = ιι.E -o = -o In the case of an isotropic suspension, the off-diagonal entries in the μ matrix are zero, and the diagonal entries take the common value denoted earlier by μ The above result reduces to (1) in this case. The components of μ will depend on the particle size and charge distribution. Unfortunately the exact calculation of this relationship is only feasible at present for dilute suspensions of particles of simple geometry. For the more complicated types of suspensions which are likely to be encountered in practice, there appear to be two options for obtaining approximate relations between size, charge and mobility, (a) Cell Models If the particles are not elongated or flat it should be possible to approximate them by spheres. In a cell model the effect of neigbouring particles on any given sphere is assumed to be the same as an outer spheric surface centred on that particle. The "cell" then consis of a single particle surrounded by a concentric spheric surface, with the annular region between occupied electrolyte. Such models have been successfully used in t calculation of average sedimentation velocities (see "L Reynolds Number Hydrodynamics" by Happel and H. Brenne Prentice-Hall, (1965)) and in the calculation o electrophoretic mobilities (Levine S. and Neale G., J Colloid. Interface Sci. 47, 520 (1974)) in steady electri fields, for concentrated suspensions. The boundar conditions to be applied at the outer surface of the cel depend on the problem at hand. The boundary condition suggested here are: zero total force, zero pressure, zer perturbation in ion densities, and an electric potentiona equal to -E ~o. -x, where x is the position vector measured fro the particle centre. These boundary conditions may requir some modification in the light of future experimenta studies. (k) An empirical approach If the cell model is not appropriate for th suspension of interest, an empirical approach can b adopted. In this approach, samples of the suspension ar removed and analysed after each set of mobility measurement is made. These mobility measurements should be carried ou over a range of frequencies spanning the optimum rang corresponding to the expected particle size range. Change in the particle size or ζ potential distribution can then be correlated with the form of the curves of |μ | and arg | μ.. | as a function of frequency, where the symbol μ.. denotes any measured component of the mobility tensor. For suspensions in which the ζ-potential is both uniform and small, v will be proportional to ζ . As a consequence the quantities arg u will be independent of the magnitude of ζ, as we saw in the dilute suspension of spheres in § 1. Although arg μ may depend on (ζ| for more general suspensions, it is still likely that of the two quantities | μ | and arg | μ | , the latter will be the more sensitive function of particle size. Thus in attempting to correlate mobility with particle size distribution, attention should be focussed on arg μ rather than ! f I • 3. The experimental determination of the electrophoretic mobility Turning now to the second major aspect of the invention: the means by which the electrophoretic mobility can be measured experimentally. In this section there is described a general class of devices which can be used for making these measurements, and how the mobility can be determined from the various measured quantities. The results given in this section apply to any colloid, except in those instances where statistically isotropic colloids are specifically referred to. The devices for measuring the mobility consist of a "cell" which contains the suspension, together wit various means for measuring voltage differences (or electri currents) and pressure differences across the cell, an means for generating sound waves and/or alternating electri fields in the cell. To take a simple example, the cell could consis of two parallel metal plates with the suspension filling th gap between them. Later in this section it will be show how the mobility can be determined for such a cell from th measurement of the pressure difference and open circui voltage difference generated between the plates by th vibration of one of those plates. As may be gathered from the above description the electrophoretic mobility is measured when both soun waves and electric fields are present in the suspension. I addition to its effect on particle motion, the electri field generates electric currents in the suspension. Th sound waves also generate electric currents, due to the fac that both particles and solvent carry a charge, and th particle motions in the sound wave are different from that of the liquid, owing to the particle inertia. The total current density due to the electric field and the sound waves is given by an expression of the form i - αVp + κ*E . ... ° z r o - -o (6) Here i 0 is the volume-averaged current density, a quantity which includes both free charge and electric displacement contributions (see O'Brien, R.W. , Adv. Coll. Interface Sci . , 16, 281, (1982) ) . Vp e iwt is the o macroscopic pressure gradient due to the sound waves, and α * * and are properties of the suspension, being called the "complex conductivity tensor". Equation (6) has not appeared before in the scientific literature. The quantity α ι which characterizes the current due to the sound waves, is related to the electrophoretic mobility tensor by the formula φΔp T (7) where Φ is the volume fraction of the suspension occupied by particles, and as before p is the solvent density, and • p + Δp is the suspension density:- μ T is the "transpose" of the mobility tensor, the quantity whose components are obtained by interchanging the rows and columns of the matrix. With the aid of (7) it is possible to determine u once ct is known. The devices described here determine μ by measuring α • In order to provide examples of ways is which μ can be measured using this class of device, reference is made to the parallel plate cell, illustrated in Figure 4. The separation h between the plates is assumed to be much smaller than the width and height of the plates. Sound waves are set up in the device by the forced oscillation of one of the plates. The resulting pressure difference across the plates ΔPe lwt is measured by, fo example transducers on the plates, and the open circui voltage difference Δψ e l t is also measured. In such a device the current ~ io in the suspensio is uniform. In order for such a current to flow, the plate must be linked by a wire to complete the circuit. Unde open-circuit conditions the current -io is therefore zer everywhere in the suspension. Thus equations (6) gives where, for simplicity the suspension is taken to b isotropic. Integrating this result across the plates, it i found that ΔP = K Δψ Thus if K has been determined from a conductivit measurement, α can be obtained from the measurement of Δ and Δψ . Alternatively, if the two plates are shor circuited the electric field in the suspension will be zero and (6) reduces to i 0 - α7p Q for an isotropic suspension. Integrating across the plate and using the fact that i is uniform it " is found that I h o α wt AΔP where A is the plate area, and I eiwt is the current passing between the plates. Thus by measuring the pressure difference and short-circuit current it is possible to determine without the need for a conductivity measurement. The mathematical formula for obtaining 2 for a general device is derived with the aid of the result v.± « 0, -o which holds everywhere in the suspension. Integrating equation (6) over the volume v of the suspension within the cell, and using the above identity, it is found that r x —i o .ndA * α - p ndA - K IΦndA . A A ' (8) where Z denotes the surface of v and n is the unit normal directed outwards from v. x is the position vector to the surface from an arbitrary point in the suspension, and Φe lwt is the electrical potential. From equation (8) it can be seen that components of 2 can be determined if i .n, p and ψ are known over the -o - o surface of v. in the parallel plate device referred to above, either i 0 «5 (open-circuit) or Φ (short-circuit) were set to zero , and the other two quant it ies measured . A s men t i oned i n § 2 , i t i s e nv i saged that t d ev i ces described here would make measurements over a ran of f requencies appropriate to the expected particle s i range. Previous known devices are manufactured by Mat Instruments, Warwick, R.I., U.S.A. and Pen Kern, Inc. Bedford Hills, N.Y., U.S.A. The Matec device measures soun waves generated by electric fields, and electric field generated by sound waves at about 1MHz, in a parallel plat cell. The device measures the potential, but not th pressure difference across the cell. It is therefore no suited to the direct determination of 5. The Pen-Kem instrument measures the potentia difference between two electrodes caused by the generatio of sound waves at around 200 kHz. The device also measure the pressure at a point some distance away from th electrodes. As it is not possible to directly determine th pressure difference between the electrodes from this singl pressure measurement, this device is also unsuited to th direct determination of α. Apparatus according to the present inventio measures the interaction of sound waves and electric field over a range of frequencies, and comprises means to conver the information so obtained to provide a direct measuremen of electrophoretic mobility, from which particle size an zeta potential can be inferred. Although the invention has been described above with reference to examples and to preferred embodiments, it will be appreciated that the invention may be embodied in other forms or carried out in other ways without departing from the spirit or essential characteristics thereof. The above description is therefore to be considered in all respects, illustrative and not restrictive, and all changes which come within the meaning and range of equivalency are intended to be embraced therein.

Claims: CLAIMS 1. A method for determining the size and charge particles dispersed in a fluid medium from the phase lag a amplitude of particle velocity in an alternating electr field. 2. A method for determining the particle size in fluid medium having uniform, low ζ potential from measurement of the phase of the particle motion in a hig frequency alternating electric field, and wherein th zeta-potential can be determined from the amplitude of th motion in the alternating field. 3. A method for determining the average size an charge of particles in a fluid medium by combinin measurments of the phase and amplitude of the particl motion in an electric field with an appropriate cell model. 4. A method for determining size and charge fo polydisperse suspensions by a correlation technique involving measurements of the average particle velocity ove a range of frequencies, and determining the appropriat frequency range from the expected particle size range. 5. A method for obtaining the particle velocity i an alternating electric field from measurements of th interaction of sound waves and electric fields in th suspension. 6. A method for generating and measuring th interaction of sound waves and electric fields in flui suspension comprising positioned spaced apart electrodes an pressure tranducers in contact with the suspension, enabling the simultaneous measurement of electrical potentials, currents and pressure differences in the suspension. 7. Apparatus for determining the particle size and charge of particles dispersed in a fluid medium when using a method as claimed in any one of the previous claims.

Inventors: O'BRIEN RICHARD WYNDHAM, O'BRIEN, RICHARD, WYNDHAM
Applicants: OBRIEN RICHARD WYNDHAM, O'BRIEN, RICHARD, WYNDHAM
Application year: 1987
Main classification: G01N15
IPC codes: G01N15, G01N27, G01P5, G01R29