Propagating transitions of electroconvection

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Abstract
In a thin dielectric liquid layer, electroconvection can be generated by means of charge injection to the liquid under a vertical electric field. When a parameter which gives the critical condition of the onset of convection is rapidly increased up to some value across the critical point, a propagating transition of the system from the quiescent state to the convecting state is expected to appear. We have tried to show such propagating transitions in two different models. One for a bipolar-injection type with free-free boundaries was analyzed with use of the amplitude-equation approach of Newell and Whitehead, and the other for a unipolar-injection type with rigid-rigid boundaries was numerically analyzed. Both cases have shown propagating transitions of convecting state with definite velocities.