Collective dynamics in particle suspensions
David Saintillan, Mechanical Science and Engineering, University of Illinois at Urbana-Champaign

Dispersions of small particles in a viscous fluid are ubiquitous in both natural and industrial processes. A major difficulty in modeling and simulating these systems arises from the slow decay of hydrodynamic disturbances at low Reynolds number, which leads to long-ranged interactions and often results in strong velocity fluctuations and large-scale correlated motions.

In this talk, I will focus on the dynamics in suspensions of self-propelled particles such as swimming microorganisms, which are characterized by unusual collective behavior. Direct particle simulations based on slender-body theory and using a fast summation algorithm have been performed, and demonstrate the existence of an orientational instability driven by hydrodynamic fluctuations. In spite of this instability, a local nematic order persists in the suspensions over short length scales and has a significant impact on the mean swimming speed. Consequences of the large-scale orientational disorder for particle diffusion are discussed and explained in the context of generalized Taylor dispersion theory. To complement the results from direct particle simulations, a kinetic theory is also developed and applied to elucidate the instabilities and pattern formation arising in these systems. Based on this model, the stability of both aligned and isotropic suspensions is investigated. In aligned suspensions, an instability is shown to always occur at finite wavelengths, in agreement with observations from the particle simulations. In isotropic suspensions, a new instability for the active particle stress is also found to exist, in which shear stresses are eigenmodes and grow exponentially at low wavenumbers.  Numerical simulations of the kinetic equations are also performed in two dimensions, and applied to study the long-time nonlinear dynamics in these systems and their relation to fluid mixing.

To conclude, I will also provide a brief overview of a few other current and future research problems, including investigations of the dynamics of gravity-driven particulate jets, the concentration instability of sedimenting spheres in viscoelastic fluids, and the nonlinear interactions of polarizable particles in electrophoresis.