(79d) Electrohydrodynamic Interactions of Colloidal Particles Under Quincke Rotation

Quincke rotation, a well-observed phenomenon in particle suspensions, denotes the spontaneous rotation of dielectric particles immersed in a slightly dielectric liquid when subjected to a high enough DC electric field. It occurs when the charge relaxation time of the particles is greater than that of the fluid medium, causing the particles to become polarized in a direction opposite to that of the electric field and therefore giving rise to an unstable equilibrium position. When slightly perturbed, the particles start to rotate, and if the applied electric field exceeds a critical value this perturbation does not decay and the particle rotation reaches a steady state with a constant angular velocity obtained by balancing the viscous torque with the electric torque due to the induced dipole. Motivated by applications in particle suspensions, where Quincke rotation can lead to a decrease in effective shear viscosity, we use a combination of numerical simulations and asymptotic theory to study the effect of electrohydrodynamic interactions between particles under Quincke rotation. We study the prototypical case of two equally sized spheres carrying no net charge and interacting with each other both electrically and hydrodynamically. We use the classic method of reflections to capture far-field interactions, and solve a coupled system of time-dependent ordinary differential equations for the dipole moments, angular velocities, and positions of the two spheres capturing interactions up to order O(R^-3) (where R is the separation distance between the sphere centers). We find that interactions between particles cause a decrease in angular velocity with respect to the single sphere case, as well as an increase in the critical electric field strength required for spontaneous rotation to occur.