Electrophoretic mobility of soft particles

GENERAL THEORY OF ELECTROPHORETIC MOBILITY OF SOFT PARTICLES 435... 

Equation (22.23) is the required approximate expression for the electrophoretic mobility of soft particles in concentrated suspensions when the condition [22.22] (which holds for most cases) is satisfied. In the limit 0 0, Eq. (22.23) tends to Eq. (21.51) for the dilute case. For low potentials, Eq. (22.23) reduces to... 

The dynamic electrophoretic mobility of colloidal particles in an applied oscillating electric field plays an essential role in analyzing the results of electroacoustic measurements of colloidal dispersions, that is, colloid vibration potential (CVP) and electrokinetic sonic amplitude (ESA) measurements [1-20]. This is because CVP and ESA are proportional to the dynamic electrophoretic mobility of colloidal particles. In this chapter, we develop a theory of the dynamic electrophoretic mobility of soft particles in dilute suspensions [21]. 

Ohshima, H., Electrophoretic mobility of soft particles, J. Colloid Interface ScL, 163, 474, 1994. Ohshima, H., Electrophoretic mobility of soft particles, Adv. Colloid Interface ScL, 62, 443, 1995. Ohshima, H., Electrophoretic mobility of soft particles. Colloids Surf. A Physicochem. Eng. Aspects, 103, 249, 1995. 

Equation (21.62) shows that as k co, p tends to a nonzero limiting value p°°. This is a characteristic of the electrokinetic behavior of soft particles, in contrast to the case of the electrophoretic mobility of hard particles, which should reduces to zero due to the shielding effects, since the mobility expressions for rigid particles (Chapter 3) do not have p°°. The term p°° can be interpreted as resulting from the balance between the electric force acting on the fixed charges ZeN)E and the frictional force yu, namely. 

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

ANALYTIC APPROXIMATIONS FOR THE ELECTROPHORETIC MOBILITY OF SPHERICAL SOFT PARTICLES... 

Consider various limiting behaviors of the electrophoretic mobility fi of soft particles. 

As in the case of electrophoresis of hard cylindrical particles, the electrophoretic mobility of a soft cylinder depends on the orientation of the particle [44, 47]. 

SOFT PARTICLE ANALYSIS OF THE ELECTROPHORETIC MOBILITY OF BIOLOGICAL CELLS AND THEIR MODEL PARTICLES... 

The sign reversal takes place also in the electrophoretic mobility of a non-uniformly charged soft particles, as shown in this section. We treat a large soft particle. The x-axis is taken to be perpendicular to the soft surface with its origin at the front edge of the surface layer (Fig. 21.8). The soft surface consists of the outer layer —d < x < 0) and the inner layer (x < —d), where the inner layer is sufficiently thick so that the inner layer can be considered practically to be infinitely thick. The liquid flow m(x) and equilibrium electric potential i//(x) satisfy the following planar Navier-Stokes equations and the Poisson-Boltzmann equations [39] ... 

The electrophoretic mobility of spherical soft particles in a concentrated suspension is defined by = UIE. It must be mentioned here that the electrophoretic mobility fx in this chapter is defined with respect to the externally applied electric field E so that the boundary condition (22.8) has been employed following Levine and Neale [5]. There is another way of defining the electrophoretic mobility in the concentrated case, where the mobility /i is defined as /i = U/ E), (E) being the magnitude of the average electric field (E) within the suspension [8, 19-21]. It follows from the continuity condition of electric current that K E) = K°°E, where K and K°° are, respectively, the electric conductivity of the suspension and that of the electrolyte solution in the absence of the particles. Thus, jx and ix are related to each other by = K /K°°. For the dilute case, there is no difference between jx and jx. ... 

By evaluating h(r) at r = c, we obtain the following general expression for the electrophoretic mobility fx of soft particles in a concentrated suspension [1,3] ... 

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