PHYSICAL REVIEW FLUIDS 5, 013701 (2020) Quincke rotation driven flows M. Belovs and A. C¯ ebers * MMML Lab, Department of Physics, University of Latvia, Jelgavas-3, R¯ ıga, LV-1004, Latvia (Received 17 August 2019; published 2 January 2020) Flows induced by Quincke rotation in particle suspensions are considered. Nonlinear boundary problems for the suspension velocity and particle angular velocity fields in rectangular capillaries are formulated and solved for both no-slip and free boundary conditions. Linear stability analysis shows that the critical electric field strength necessary for the development of macroscopic flow is smaller than the field strength at which spontaneous Quincke rotation of a single particle occurs. This decrease is caused by hydrodynamic synchronization of the particle rotations. In the case of free boundaries interesting intermittent behavior is observed: as the parameters governing the problem pass degenerate eigenmodes revealed by the stability analysis, the nature of the induced flow changes qualitatively. DOI: 10.1103/PhysRevFluids.5.013701 I. INTRODUCTION Spontaneous rotation of dielectric particles in weakly conducting fluids was discovered by Quincke at the end of the 19th century [1]. The model of the Quincke effect in the frame of the leaky dielectric approach was developed in Ref. [2]. This model accounts for the action of antisymmetric stress and can therefore describe a wide variety of experimentally observed phenomena such as the collective motion of rolling Quincke particles [3], vortex flow in Quincke suspensions [4], and frictionless flow of the Quincke suspensions in capillaries under the action of an electric field [5]. The particle polarization equations initially derived for spherical particles were generalized to the case of ellipsoidal particles [6], leading to a description of the anomalous orientation perpendicular to the applied electric field [7,8]. It is interesting to note that including rotational inertia in the polarization model of leaky particles [2] leads to an exact derivation of the Lorentz equations and an experimental confirmation of deterministic chaos in the polarization model of leaky particles [9]. A rich class of phenomena has been observed for leaky droplets in an electric field, starting with the observation by Taylor that droplets deform into oblate shapes [10]. A substantial review of the electrohydrodynamics of droplets relevant to the Quincke effect is given in Ref. [11]. Among the different reviewed effects the equatorial streaming of the oblate droplets with the formation of sheets and their capillary breaking [12], the Quincke rotation of the droplets and formation of tilted configurations [13–15], and instabilities of particle belts leading to the formation of counter-rotating vortices on the equator of the Pickering droplets [16,17] should be mentioned. Recently, the Quincke effect in more complex situations was investigated. The Quincke particle with an attached flexible tail shows the Hopf bifurcation and self-propulsion due to the induced bending waves on the tail [18]. In Ref. [19] it is shown that a Quincke particle in the shape of a helix self-propels without the necessity for a solid wall as in the case of the Quincke rollers [3]. An algorithm for numerical simulation of the Quincke droplets based on the boundary integral equation technique is developed in Ref. [20]. * aceb@tesla.sal.lv 2469-990X/2020/5(1)/013701(10) 013701-1 ©2020 American Physical Society