On the absence of collective motion in a bulk suspension of spontaneously rotating dielectric particles

A suspension of dielectric particles rotating spontaneously when subjected to a DC electric field in two dimensions next to a no-slip electrode has proven to be an ideal model for active matter [Bricard et al., Nature, 2013, 503, 95–98]. In this system, an electrohydrodynamic (EHD) instability called Quincke rotation was exploited to create self-propelling particles which aligned with each other due to EHD interactions, giving rise to collective motion on large length scales. It is natural to question whether a suspension of such particles in three dimensions will also display collective motion and spontaneously flow like bacterial suspensions do. Using molecular dynamics type simulations, we show that dielectrophoretic forces responsible for chaining in the direction of the applied electric field in conventional electrorheological fluids and the counter-rotation of neighboring particles in these chains prevent collective motion in suspensions undergoing spontaneous particle rotations. Our simulations discover that the fundamental microstructural unit of a suspension under Quincke rotation is a pair of counter-rotating spheres aligned in the direction of the electric field. We perform a linear stability analysis that explains this observation.