Weakly Charged Spherical Soft Particles

When the fixed-charge density ZeN is low, it can be shown [17] that the mobility is given by 

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

Note that Eq. (21.69) can be directly derived from the condition of balance between the electric force and the drag force acting on the particle, 

Note that Eq. (21.78) corresponds to the limit of 2 — cxd, but still assumes that electrolyte ions can penetrate the polyelectrolyte layer. Therefore, the particle in this limiting case is neither a perfectly hard particle nor a perfectly soft particle. We term a particle of this type a semisoft particle. The polyelectrolyte layer coating a semisoft particle is ion permeable but there is no liquid flow inside the polyelectrolyte layer. 

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