Electrohydrodynamic interaction of spherical particles under Quincke rotation
Debasish Das (University of Illinois), David Saintillan (University of Illinois at Urbana-Champaign)
Electrohydrodynamics and electrokinetics of fluid systems
Mon 2:40 - 4:00
Barus-Holley 161
Quincke rotation denotes the spontaneous rotation of dielectric particles suspended in a dielectric liquid of higher conductivity when placed in a sufficiently strong DC electric field. This phenomenon has interesting applications in the rheology of these suspensions under shear flow, whose effective viscosity can be controlled and reduced by application of an external field. It is observed that particle-particle interactions are likely significant in concentrated suspensions. Motivated by this observation, we extend the classic description of Quincke rotation based on Taylor-Melcher leaky dielectric model to account for pair electrohydrodynamic interactions between two identical spheres using the method of reflections. A coupled system of evolution equations for the dipole moments and angular velocities of the spheres is derived that accounts for electrohydrodynamic interactions up to order O(R^{-5}), where R is the separation distance between the spheres. A linear stability analysis of this system shows that interactions modify the value of the critical electric field for the onset of Quincke rotation: both electric and hydrodynamic interactions can either stabilize or destabilize the system depending on the orientation of the spheres. We also analyze the dynamics in the nonlinear regime by performing numerical simulations of the governing equations. In the case of a pair of spheres that are fixed in space, we find that particle rotations always synchronize in magnitude at long times, though the directions of rotation of the spheres need not be the same. The steady-state angular velocity magnitude depends on the configuration of the spheres and electric field strength and agrees very well with an asymptotic estimate derived for co-rotating spheres. In the case of freely-suspended spheres, a number of distinct behaviors are observed depending on the initial relative configuration of the spheres and on any infinitesimal initial perturbation introduced in the system.