Microhydrodynamics of active colloids[HBNI Th131]

Abstract

Colloidal suspensions have been studied extensively in the past several decades. In the recent years a new class of colloids, called active colloids, have been synthesized. These active colloids are capable of producing flow, and possibly motion, in absence of external forces or torques. Thus microorganisms naturally belong to this category. In this thesis, we study the interplay of activity, fluid-mediated interactions, and external potentials in active colloidal suspensions and derive several testable predictions. We use the boundary-domain integral representation of the Stokes flow to obtain the full expression of the force per unit area on the surface of active colloids. The result is expressed as an infinite set of linear relations - generalized Stokes laws - between the tensorial spherical harmonic coefficients of the force per unit area and the boundary velocity. The generalized friction tensors give the linear relations between these coefficients. These are many-body functions of the colloidal configuration and can be obtained to any desired accuracy by solving a system of linear equations. The expression of the force per unit is then used to derive forces, torques, and thus, to obtain the Langevin description of active colloids in terms of the familiar mobility matrices and, the newly introduced, propulsion tensors. These Langevin equations have been implemented in a homegrown library to perform the numerical simulations reported in the thesis. The formalism is then applied to study various experimentally realizable settings. Our applications include the identification of the universal mechanisms of crystallization of active colloids at a plane wall. We also elucidate the role of boundaries in determining the collective behavior of active colloids. We show that the collective steady-states are characterized using the flow-induced phase separation mechanisms, which are of dynamical origin, and obtained from the balance of forces and torques. Our predictions are in excellent agreements with recent experiments on microorganisms, self-propelling droplets, and synthetic microswimmers.