Hydrodynamically Interacting Colloids inside a Spherical Cavity As a Model for Intracellular Transport: Hydrodynamic Entrainment and Active Motion

We study diffusion and rheology of hydrodynamically interacting particles confined by a spherical cavity via dynamic simulation, as a model for intracellular and other micro-confined biophysical transport. Previous models of 3D confined transport either focused on the motion of a single confined particle or studied collections of particles while neglecting hydrodynamic interactions. Such approximations are motivated by the challenge of modeling both far-field many-body and near-field lubrication interactions and how such interactions are influenced by the presence of a confining cavity. However, biophysical and other confined suspension systems are crowded, watery environments populated with a multitude of hydrodynamically interacting microscopic particles. In the present work, we utilize our framework for spherically confined suspensions to study the effect of 3D confinement on particle entrainment as well as on the active motion of a probe particle. Recent studies have shown that in unbound suspensions, increasing the suspension volume fraction does not lead to a change in the algebraic decay of hydrodynamic entrainment, that is, crowding does not lead to hydrodynamic screening. In contrast, studies involving a dilute system of particles near a single planar wall have observed that the presence of the boundary can lead to a change in the algebraic decay of hydrodynamic entrainment. In this work, we show how the presence of the spherical cavity impacts entrained motion in 3D confined colloidal suspensions. We calculate the hydrodynamic entrainment between particle pairs when these are immersed in an intervening medium of freely diffusing bath particles. This allows us to determine how hydrodynamic entrainment changes as a function of particle position, volume fractions, and particle-to-cavity size ratio. In addition to hydrodynamic entrainment, active motion is an important transport mechanism in many biophysical systems. We study the effect of confinement on active motion by using as a model system the motion of a single probe particle driven through the 3D confined suspension by an external force. By tracking the motion of the particle, as well as the evolution of the suspension stress rheological properties such as the micro-viscosity, osmotic pressure, and normal stresses are determined as a function of probe forcing in the linear response regime.