Colloid vibration potential in a suspension of soft particles

We develop a theory of the vibration potential produced in a dilute suspension of soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution when a sound wave (i.e., an oscillating pressure gradient field) is applied to the suspension. The total vibration potential (TVP) consists of two components. One is the colloid vibration potential (CVP) and the other is the ion vibration potential (IVP). The obtained CVP expression covers two extreme cases, that is, the CVP in a suspension of hard particles (in the absence of the polyelectrolyte layer) and that in a suspension of spherical polyelectrolytes (in the absence of the particle core). A simple analytic expression for CVP, which is proportional to the dynamic electrophoretic mobility of a soft particle, is given. It is shown that the CVP of a suspension of a soft particle depends on the density of the volume charge distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, on the thickness of the polyelectrolyte layer, and on the frequency of the applied oscillating pressure gradient field.