Active microrheology of colloidal suspensions: Simulation and microstructural theory

Abstract

Discrete particle simulations by accelerated Stokesian dynamics (ASD) and a microstructural theory are applied to study the structure and viscosity of hard-sphere Brownian suspensions in active microrheology (MR). The work considers moderate to dense suspensions, from near to far from equilibrium conditions. The microscopic theory explicitly considers many-body hydrodynamic interactions in active MR and is compared with the results of ASD simulations, which include detailed near- and far-field hydrodynamic interactions. We consider probe and bath particles which are spherical and of the same radius a. Two conditions of moving the probe sphere are considered: These apply constant force (CF) and constant velocity (CV), which approximately model magnetic bead and optical tweezer experiments, respectively. The structure is quantified using the probability distribution of colloidal particles around the probe, Pb|p(r)=ng(r), giving the probability of finding a bath particle centered at a vector position r relative to a moving probe particle instantaneously centered at the origin; n is the bath particles number density, and is related to the suspension solid volume fraction, ϕ, by n=3ϕ/4πa3. The pair distribution function for the bath particles relative to the probe, g(r), is computed as a solution to the pair Smoluchowski equation (SE) for 0.2≤ϕ≤0.50, and a range of Péclet numbers, describing the ratio of external force on the probe to thermal forces and defined as Pef=Fexta/(kbT) and PeU=6πηUexta2/(kbT) for CF and CV conditions, respectively. Results of simulation and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large Péclet numbers, while a boundary-layer accumulation develops upstream and near the probe. The wake length saturates at Pef≫1 for CF, while it continuously grows with PeU in CV. This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion; the dispersion is a direct result of many-body nonthermal interactions. This effect is incorporated in the theory as a force-induced diffusion flux in pair SE. We also demonstrate that, despite this difference of structure in the two methods of moving the probe, the probability distribution of particles near the probe is primarily set by the Péclet number, for both CF and CV conditions, in agreement with dilute theories; as a consequence, similar values for apparent viscosity are found for the CF and CV conditions. Using the microscopic theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predicts larger distortions and Brownian viscosities in CV, by a factor of two relative to CF MR. This difference relative to dilute theory arises due to the determining role of many-body interactions associated with the underlying equilibrium structure in the semidilute to concentrated regime.