Effect of combined Brinkman-Electric boundary layer on the onset of Marangoni electroconvection in a poorly conducting fluid-saturated porous layer cooled from below in the presence of an electric field

Abstract

The effect of Brinkman-electric boundary layer on the onset of electroconvection driven by the electric force and surface tension gradient, in a thin horizontal Poorly electrically conducting, fluid-saturated, sparsely packed porous layer bounded by adiabatic free boundaries is studied. The energy method combined with single term Galerkin expansion technique is shown to be convenient and useful to determine eigenvalues. The convergence of the result obtained by Galerkin technique is checked by comparing the result with those obtained using a regular perturbation technique. We found that the single-term Galerkin expansion is accurate only for small values of the combined porous and electric parameter d₁. The effect of large values of d₁ on the onset of Marangonielectroconvection is determined using the method of matched asymptotic expansion. The effect of boundary layer that exists for large values of d₁ is shown to increase the critical Marangoni number by an amount of 2d₁ compared to that for small values of d₁. The results obtained are useful in the manufacture of smart materials of nanonstructure free from impurities.