Theory of pattern formation of metallic microparticles in poorly conducting liquids

We develop a continuum theory of self-assembly and pattern formation in metallic microparticles immersed in a poorly conducting liquid in a dc electric field. The theory is formulated in terms of conservation laws for the densities of immobile particles (precipitate) and bouncing particles (gas) coupled to the Navier-Stokes equation for the liquid. This theory successfully reproduced the correct topology of the phase diagram and primary patterns observed in the experiment [Sapozhnikov et al., Phys. Rev. Lett. 90, 114301 (2003)]: static crystals, honeycombs, dynamic pulsating rings, and rotating multipetal vortices.