Conditions for Self-Organization of 45° Vortex and Phase Lag in Electric Polarization

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Abstract
When an alternating electric field of 10 kHz is applied to a suspension of micron-size polystyrene particles in an aqueous NaCl or KCl solution, four states appear: (a) homogeneous suspension, (b) pearl chains, (c) vortexlike turbulence and (d) 45° vortexes, i.e., clusters elongated at an inclination of ±45° to the electric field in which the particles are circulating. Conditions for the occurrence of the four states are determined by changing the salt concentration and the amplitude and frequency of the electric field. Experimental results confirm the hypothesis that the phase lag of particle polarization against the electric field plays an important role in producing the vortex states (c) and (d). The vortexlike turbulence (c) seems to be triggered by asymmetric boundary conditions existing in the experimental apparatus. Self-organization of the 45° vortexes (d) seems to be initiated by the formation of clusters due to particle density fluctuation.