Active microrheology of colloidal suspensions: Simulation and microstructural theory

Abstract

SynopsisDiscrete particle simulations by Accelerated Stokesian Dynamics (ASD) and a microstructural theory are applied to study structure and the 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 the 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, P b|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 particle 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 P e f = F ext a/(k b T ) and P e U = 6πηU ext a 2 /(k b T ) 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. The wake length saturates 1 arXiv:1509.07082v1 [cond-mat.soft] 23 Sep 2015at P e f ≫ 1 for CF while it continuously grows 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 hydrodynamic interactions. This effect is incorporated in the theory as a force-induced hydrodynamic diffusion flux in the 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 predict larger distortions and Brownian viscosities in CV, by a factor of two relative to CF microrheology. This difference relative to dilute theory arises due to the determining role of many-body interactions associated with the underlying equi...

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

“…Moreover, living systems typically operate far from equilibrium -due to internally generated forces being much larger than thermal forces -and constitutive relationship is required to extract rheological behavior based on, for example, the trajectories of probe particles. Finding microscopic constitutive relations is difficult even for the simplest of out-of-equilibrium complex fluids, a hard-sphere colloidal suspension, due to the complex and nonlinear relations between rheological properties and microstructural dynamics [NM15].…”

Universal Long Ranged Correlations in Driven Binary Mixtures

“…Previous studies suggest that these correlations may be long-ranged. Indeed, when only a small fraction of the particles is biased, the correlation between them and the unbiased particles follows the distribution of the density of particles in the wake of a single intruder moving in a quiescent bath, which is relevant for microrheology [17][18][19][20]. This distribution has been computed for different models: Brownian dilute hard spheres [21], dense soft spheres [22] or hard core particles on a lattice [23].…”

Rheology evolution of a geopolymer precursor aqueous suspension during aging

“…Understanding the rheology of concentrated suspensions is still an active field of research, both through simulation 5,6 and | 1803…”