Nonlinear Marangoni instability of a liquid jet in the presence of electric field

Abstract

The work discusses the linear and nonlinear stability of cylindrical surface deformations between two incompressible fluids. The interface is carrying a uniform surface charge. The inner fluid is assumed to be a liquid jet. Both fluids are modeled as a special type of a Newtonian viscous fluid. Furthemore, the effect of surface adsorption is taken into account. Both fluids are assumed to be dielectric and the stability is discussed in the presence of a constant electric field in axial direction. The analysis is performed along the lines of a multiple scale perturbation expansion with additional slow time and space variables. The various stability criteria are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. The results show the dual role of the electric field and the negative rate of change of surface tension with the concentration of surfactant on the system stability, in both the linear and nonlinear steps. The nonlinear theory, when used to investigate the stability of liquid jet, appears accurately to predict new unstable regions. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.