Reduced equations of motion of the interface of dielectric liquids in vertical electric and gravitational fields

摘要: The dynamics of the interface between two dielectric fluids in presence vertical electric and gravitational fields is studied theoretically. It shown that, particular case where rate change field proportional to effective acceleration, a special flow regime can be realized for which velocity potentials are linearly dependent functions. This means that there exists frame reference liquids move along lines. We derive analyze corresponding reduced equations motion liquid-liquid interface. For small density ratio, they turn into describing Laplacian growth. In spatial dimensions, we show these determine asymptotic behavior system. arbitrary ratios, growth adequately describe initial (weakly nonlinear) stage instability development. integrability makes it possible investigate evolution nonlinear waves at boundary and, particular, demonstrate tendency formation singularities (cusps).