On the Influence of the Surface Electric Charge on the Regularities of the Formation of Faraday Ripples on the Surface of a Low-Viscosity Liquid

Abstract

The purpose of the study is to analyze the effect of a surface electric charge on the formation conditions of the Faraday ripples on a horizontal surface of a low-viscosity liquid in a vibration field.Methods. The problem is solved analytically in the limit of small amplitude deformation of the free surface of the liquid. The final relation is derived under the condition that the dissipation is small. The liquid was considered ideally conductive with a surface-distributed electric charge. Results. A simple analytical expression is derived that quantitatively describes the effect of suppression of the Faraday ripple if the surface density of the electric charge increases. It is shown that the increase in the surface density of the electric charge significantly enlarge the threshold value of the vibration field amplitude, the excess of which leads to the formation of ripples. The threshold value of the vibration amplitude is proportional to the viscosity of the liquid and depends on its density, surface tension coefficient and the specific horizontal scale of the ripple.Conclusion. The Faraday’s ripple formed on the surface of a liquid in a vertically oscillating container is very sensitive to the value of the surface density of the electric charge. An increase of the surface charge density leads to suppression of the ripple formation. The effect can be used to prevent the appearance of parasitic convective flows that arise in liquid layers placed in vibration fields. The physical mechanism of Faraday ripple suppression is the rivalry between two qualitatively different types of flows near the liquid surface. Increasing the surface charge density changes the balance of surface forces in such a way as to promote the appearance of aperiodic motions and suppress oscillatory ones. In particular, oscillatory motions responsible for the development of Faraday instability caused by vertical vibrations of the liquid container are suppressed.