Confined Brownian suspensions: Equilibrium diffusion, thermodynamics, and rheology

Abstract

We examine the impact of confinement on the structure, dynamics, and rheology of spherically confined macromolecular suspensions, with a focus on the role played by entropic forces, by comparing the limits of strong hydrodynamics and no hydrodynamics. We present novel measurements of the osmotic pressure, intrinsic viscosity, and long-time self-diffusivity in spherical confinement and find confinement induces strong structural correlations and restrictions on configurational entropy that drive up osmotic pressure and viscosity and drive down self-diffusion. Even in the absence of hydrodynamics, confinement produces distinct short-time and long-time self-diffusion regimes. This finding revises the previous understanding that short-time self-diffusion is a purely hydrodynamic quantity. The entropic short-time self-diffusion is proportional to an entropic mobility, a direct analog to the hydrodynamic mobility. A caging plateau following the short-time regime is stronger and more durable without hydrodynamics, and entropic drift—a gradient in volume fraction—drives particles out of their cages. The distinct long-time regime emerges when an entropic mobility gradient arising from heterogeneous distribution of particle volume drives particles out of local cages. We conclude that entropic mobility gradients produce a distinct long-time dynamical regime in confinement and that hydrodynamic interactions weaken this effect. From a statistical physics perspective, confinement restricts configurational entropy, driving up confined osmotic pressure, viscosity, and (inverse) long-time dynamics as confinement tightens. We support this claim by rescaling the volume fraction as the distance from confinement-dependent maximum packing, which collapses the data for each rheological measure onto a single curve.