Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

Abstract

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.

Rheology of polymer solutions using colloidal-probe atomic force microscopy

“…The viscosity measured did not depend on the velocity, and the changes in the effective viscosity extended to large (at least 20-nanoparticle diameters) separation distances. These results are consistent with the predictions of Bhattacharya and Blawzdziewicz [9].…”

“…When mesoscopic constituents are present (consider large molecular weight polymers in a liquid or colloids or nanoparticles in solution that introduce a characteristic size), if the gap used approaches a few characteristic sizes, the local concentration of the constituents may vary with solicitation. Recent calculations and observations have highlighted the fact that local concentrations of nanoparticles in small gaps may be much smaller than the bulk concentration, for example [9,10]. The role of confinement on the behavior of fluids is, therefore, essential not only for probing their properties at scales comparable to their constituents' dimensions but also for a better understanding of the results of different recent techniques.…”

“…On the other hand, Bhattacharya and Blawzdziewicz [9] have carried out a theoretical analysis of the hydrodynamic force exerted on a colloidal particle approaching a solid surface in a dilute solution of smaller, nonadsorbing, spherical particles. The authors found that as the particle-flat surface gap width diminished, the viscosity in the gap region varied.…”

An analysis of the far-field response to external forcing of a suspension in the Stokes flow in a parallel-wall channel

“…25.͒ As discussed in Ref. ͑12a͒ and ͑12b͒ using asymptotic farfield expressions for Green's functions T and Q.…”

Nonlinear dynamics of spherical particles in Poiseuille flow under creeping-flow condition

“…[4][5][6][7] An essential aspect for understanding these devices is the flow induced cross-streamline migration of suspended objects in confined geometries. Hydrodynamic coupling under confinement with and without imposed flow has been discussed close to a planar wall, [8][9][10] close to a planar fluid-fluid interface, 11 between two planar walls, 12 or in a spherical cell. 13 From a fundamental point of view cross-streamline migration gives rise to interesting dynamical patterns in particulate flow.…”