Collective behavior of colloidal suspensions under electric fields and confinement

Electrokinetic phenomena have been widely used in microfluidic devices as a means of manipulating fluids and particles. As a main area of interest in the present study, particle dynamics driven by electrokinetic phenomena in Stokes flow are investigated using theory and numerical simulations. In particular, we focus on the dynamics and collective behavior of colloidal suspensions of spherical particles under electric fields and confinement. We first analyze the nonlinear dynamics of non-colloidal, uncharged ideally polarizable spheres freely suspended in a viscous electrolyte in a uniform electric field. Specifically, we investigate two nonlinear electrokinetic effects, dielectrophoresis and induced-charge electrophoresis. While these phenomena yield no net motion in the case of a single uncharged sphere, they can drive relative motions by symmetry breaking when several particles are present. We perform large-scale simulations of such suspensions with periodic boundary conditions using an efficient simulation method. While the dynamics under dielectrophoresis alone are shown to be characterized by particle chaining along the field direction, chaining is not found to occur when induced-charge electrophoresis occurs as well, which instead causes transient particle pairings and results in a non-uniform microstructure with large number density fluctuations. We also present results on hydrodynamic dispersion and velocity fluctuations, and their dependence on volume fraction is discussed. We then pay attention to two special cases. First, colloidal suspensions of spheres undergoing dielectrophoresis alone in a uniform AC electric field under confinement are considered to investigate the long-time dynamics and pattern formation. Building on a previously developed algorithm with Brownian motion and steric interactions with rigid walls, we can probe a large range of time scales for the pattern formation in these suspensions. The rapid chain formation that occurs in the field direction as a result of dipolar interactions is found to be followed by a slow coarsening process by which chains coalesce into hexagonal sheets and eventually rearrange to form mesoscale cellular structures. Secondly, we investigate the effects of surface contamination, modeled as a thin dielectric coating, on the dynamics in suspensions of ideally polarizable spheres in an applied electric field using large-scale simulations. As surface contamination becomes significant, a transition from diffusive dynamics to sub-diffusive dynamics with local aggregation and chaining is shown to arise. This effect has a strong impact on the suspension microstructure as well as on particle velocities, which are strongly reduced for contaminated particles. As an application of these studies, we investigate electrophoretic deposition, a multiphysics phenomenon, as a method for the assembly of colloidal suspensions. Although the basic mechanisms in electrophoretic deposition are well-known and have been studied extensively, a detailed, quantitative model for the dynamics and kinetics is lacking, and is needed to optimize the deposition process. To this end, we develop a detailed model, and we implement a simulation method that captures the dynamics during the electrophoretic deposition process, with the aim of predicting deposit microstructures and assessing the precise influence of various parameters. We first present simulation results with uniform electrodes, where various analyses of the deposit microstructure are conducted. We then present results on the use of patterned electrodes for the manufacturing of more complex deposits. In addition, the simulation results presented are also directly compared to experimental observations for the validation of the models as well as for their improvement. Finally, we propose an efficient method for the calculation of hydrodynamic interactions between two parallel planar walls in Stokes flow. In this method, the problem is split into two parts. The first part corresponds to finding a periodic solution in the absence of the walls, for which efficient algorithms are applicable. The second part, called the auxiliary problem, aims to find an auxiliary solution to account for correction to the periodic solution for the two planar walls, when appropriate wall-boundary conditions are enforced at the walls. In particular, it is found that analytic solutions to the auxiliary problem can be obtained using a spectral method. This method will find a wide range of applications in the modeling of suspensions in confined geometries