Approximation for Low Fixed-Charge Densities

We derive an approximate formula for the effective viscosity applicable for the case where the fixed-charge density ZeN is low. We use Eqs. (4.54)-(4.56) for the equilibrium potential i// ° r). Then, from Eq. (27.52) we obtain 

One can calculate the primary electroviscous coefficient p for a suspension of soft particles with low ZeN via Eq. (27.53). 

A simple approximate analytic expressions for L Ka, la, alb) without involving numerical integrations can be derived for the case where 

FIGURE 27.2 Function Ujca, Aa, a/b) for a suspension of soft particles as a function of Ka for alb = 0.5 and 0.9 at 2a = 50. The solid lines represent the results calculated via Eq. (27.54) and the dotted lines approximate results calculated via Eq. (27.57). The curve for alb = 1 corresponds to a suspension of spherical hard particles. Erom Ref. 26. 

For the case of particles covered with a very thin polyelectrolyte layer (a b), Eq. (27.54) becomes 

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