Role of charge diffusion in finite-amplitude electroconvection

The interplay of charge diffusion, a hitherto neglected phenomenon, and Coulomb repulsion in the finite-amplitude electroconvection of a layer of insulating liquid subjected to weak unipolar injection is discussed. Analytical considerations and numerical simulations show that there exists a fundamental nondimensional parameter that relates the strength of the Coulomb repulsion to the diffusion coefficient. Unless this parameter is much larger than 1, diffusion must be included. A projection of the two-dimensional charge conservation equation into a one-dimensional space allows us to obtain good estimates of the charge-density distribution for any value of this parameter.