Influence of Interlayer Exchanges on Vorticity-Aligned Colloidal String Assembly in a Simple Shear Flow

Hard spheres in Newtonian fluids serve as paradigms for nonNewtonian materials phenomena exhibited by colloidal suspensions. A recent experimental study (Cheng et al. Science 2011, 333, 1276) showed that upon application of shear to such a system the particles form string-like structures aligned in the vorticity direction. We explore the mechanism underlying this outof-equilibrium organization with steered transition path sampling, which allows us to bias the Brownian contribution to rotations of close pairs of particles and alter the dynamics of the suspension in a controlled fashion. Our results show a strong correlation between the string structures and the rotation dynamics. Specifically, the simulations show that accelerating the rotations of close pairs of particles, not increasing their frequency, favors the formation of the strings. This insight delineates the roles of hydrodynamics, Brownian motion, and particle packing, and, in turn, informs design strategies for controlling the assembly of large-scale particle structures. SECTION: Glasses, Colloids, Polymers, and Soft Matter C dispersions exhibit diverse mechanical and transport properties that find a wide range of applications in emerging technologies and in consumer products. These useful properties of colloidal dispersions are related to the microstructure of the dispersionthe spatial organization of the colloidal particles. For many applications, it is of great value to be able to switch between different microstructures by means of an external field, for example, a fluid flow. When a colloidal suspension is subjected to flow, the microstructure rearranges as the suspension is driven out of equilibrium. Depending on the complex interplay between hydrodynamics, Brownian motion, and particle packing, various structures can be accessed. We expect the out-ofequilibrium structure generated to depend on the direct colloid−colloid interaction (e.g., hard-sphere repulsion versus Janus sphere interaction), the particle shape, and the character of the particle surface. Understanding how these particle characteristics, and their interaction with the external field, generate particular microstructures could permit design of desired structures by manipulation of particle properties. While many experimental and theoretical efforts have attempted to investigate the intimate coupling between the flow and the flow-induced microstructure, a comprehensive understanding is still missing. A hard-sphere colloidal suspension that is confined between parallel plates and subjected to a simple shear flow captures many non-Newtonian behaviors and thus serves as a simple system for the study of these complex phenomena. (See ref 17 and references therein.) In a recent experimental analysis of such a system, Cheng et al. observed shear-dependent assembly of log-rolling colloidal strings within each layer of colloidal particles parallel to the confining plates. We studied this string structure using Stokesian dynamics simulations, and found evidence that particle exchanges between layers are important. We further proposed that one mode of particle exchange between layersthe rotation of close pairs of spheres induced by the shear flowis responsible for the observed formation of strings. However, the shear rates and the particle exchange rates in the simulations could not be varied independently to test the proposed mechanism directly. Advances in simulation algorithms now make this more detailed exploration possible. Using a recently developed method for sampling rare events, steered transition path sampling, in combination with Stokesian Dynamics simulations, we now identify the precise mechanism that leads to the string structure. We find that the time scale, rather than the number, of close-pair rotations, is the key factor in string formation. This distinction is important because different manipulations of the particle shape and packing as well as the fluid properties will favor one or the other and, in turn, different structures. We use Stokesian dynamics to simulate the dynamics of a monodisperse suspension of N = 100 hard spheres of unit Received: August 12, 2013 Accepted: September 17, 2013 Published: September 17, 2013 Letter