Effective viscosity of a concentrated suspension of uncharged spherical soft particles

We present a theory of the effective viscosity eta(s) of a concentrated suspension of uncharged polymer-coated spherical particles, which are termed uncharged spherical soft particles, in a liquid of viscosity eta on the basis of a cell model. These particles consist of the uncharged particle core of radius a covered with an uncharged polymer layer of thickness d (a polymer-coated particle thus has an inner radius a and an outer radius b = a + d). We assume that polymer segments are regarded as resistance centers, exerting frictional forces--gamma u on the liquid flowing in the polymer layer, where u is the liquid velocity and gamma is the frictional coefficient. We derive an analytic expression for the effective viscosity eta(s) of the suspension, which depends on the radii a and b, and volume fraction phi of the spheres and a parameter lambda = (gamma/eta)(1/2). The obtained expression for eta(s) exhibits the correct limiting behaviors. That is, as phi --> 0, the obtained expression for eta(s) becomes that for a dilute suspension of uncharged soft spheres (Ohshima, Langmuir 2008, 24, 6453). As a --> 0, the obtained viscosity expression becomes that for the case of a concentrated suspension of uncharged porous spheres (Ohshima, Colloids Surf. A: Physicochem. Eng. Aspects 2009, 347, 33). In the further limit of a --> 0 and phi --> 0, the obtained viscosity expression becomes the viscosity expression derived for the case of a dilute suspension of uncharged porous spheres by Natraj and Chen (J. Colloid Interface Sci. 2002, 251, 200). As lambda --> infinity or a --> b, the obtained viscosity expression tends to Simha's result (J. Appl. Phys. 1952, 23, 1020) for a concentrated suspension of uncharged rigid spheres of radius b, while as lambda --> 0, it becomes that for uncharged rigid spheres of radius a.