Exact solutions for the evolution of a bubble in an ideal liquid in a uniform external electric field

• Published in: Journal of experimental and theoretical physics Vol. 120; no. 1; pp. 155 - 160
• Main Authors: Zubarev, N. M., Zubareva, O. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2015; Springer
• Subjects: BUBBLES; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEFORMATION; DIELECTRIC MATERIALS; DIFFERENTIAL EQUATIONS; ELECTRIC FIELDS; Elementary Particles; EXACT SOLUTIONS; LAPLACIAN; LIQUIDS; Nonlinear; Particle and Nuclear Physics; Physics; Physics and Astronomy; POTENTIALS; Quantum Field Theory; Relativity Theory; SINGULARITY; Soft Matter Physics; Solid State Physics; Statistical; TWO-DIMENSIONAL SYSTEMS; VELOCITY; Bubble Surface; Dielectric Liquid; Dielectric Fluid; External Electric Field; Ideal Liquid
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776115010082

The dynamics of a bubble in a dielectric liquid under the influence of a uniform external electric field is considered. It is shown that in the situation where the boundary motion is determined only by electrostatic forces, the special regime of fluid motion can be realized for which the velocity and electric field potentials are linearly related. In the two-dimensional case, the corresponding equations are reduced to an equation similar in structure to the well-known Laplacian growth equation, which, in turn, can be reduced to a finite number of ordinary differential equations. This allows us to obtain exact solutions for asymmetric bubble deformations resulting in the formation of a finite-time singularity (cusp).