Soft particles, mobility expression

This section deals with a general theory of electrophoresis of soft particles and approximate analytic expressions for the mobility of soft particles [30-51]. This theory unites the electrophoresis theories of hard particles [1-29] and of polyelec-trolytes [52], since a soft particle tends to a hard particle in the absence of the polymer layer and to a polyelectrolyte in the absence of the particle. 

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... 

Equation (21.63) covers a plate-like soft particle. Indeed, in the limiting case of oo, the general mobility expression (Eq. (21.41)) reduces to... 

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. 

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] ... 

Equation (25.45) is the required expression for the dynamic mobility of a soft particle, applicable for most practical cases. When co 0 fi 2, y 0, and F 0), Eq. (25.45) tends to Eq. (21.51) for the static case. When the polyelectrolyte layer... 

For a spherical soft particle, an approximate expression for p(co) for the dynamic electrophoretic mobility is given by Eq. (25.45), which is a good approximation when the following conditions are satisfied ... 

VIII. GENERAL MOBILITY EXPRESSION FOR SOFT PARTICLES... 

Ohshima [42-45] presented a theory for electrophoresis of a soft particle. The general mobility expression of a soft particle that consists of the hard particle core of radius a covered with a layer of polyelectrolytes of thickness d (=b — a) and moves in an electrolyte solution of viscosity tj is given... 

For cylindrical soft particles, Ohshima [49,50] derived the following mobility expressions ... 

Ohshima, H., On the general expression for the electrophoretic mobility of a soft particle, J. Colloid Interface ScL, 228, 190, 2000. 

For such hydrodynamicaUy soft particles having an impermeable core of radius a and a permeable coating of thickness d, quantitative theories have been developed, mainly by Ohshima. Here, we present the main features of a simple version. Under conditions of ka 1, Krf 1, and when pg, is constant throughout the permeable layer, Ohshima derived the following expression for the electrophoretic mobility ... 

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