Two-dimensional modeling of the effects of insoluble surfactant on the breakup of a liquid filament

Abstract

Breakup of surfactant-laden liquid jets has received increasing consideration during the last few years because of its diverse applications, but theoretical studies have been largely restricted to evolution equations based on one-dimensional flow assumptions. Here, a fully two-dimensional finite element algorithm was used to solve the set of equations describing the dynamics of a Newtonian liquid filament covered with an insoluble surfactant in order to provide a better understanding of the underlying physical principles governing the formation of satellite drops. Results indicate that for a viscous liquid jet, formation of satellite drops between main drops is favored by the addition of surfactants. This effect is lessened, and even eliminated, by either decreasing the surfactant strength or increasing the surfactant diffusivity. On the other hand, low-viscosity liquid jets form satellite drops regardless of the presence of surfactant, but the addition of surfactant can either reduce or increase the size of the satellite formed. Reduction of the size of the satellite drop is favored by the addition of weak surfactants, a result that is in agreement with previous one-dimensional flow analyses. Conversely, addition of strong surfactants of low surface diffusivity increases the size of the satellite drop formed due to Marangoni stress-induced reversal of the capillary flow. The detailed information provided by the two-dimensional model has enabled a better understanding of the competition between viscous, inertia and capillary forces during jet breakup, and of how the competition between them changes due to the presence of the surfactant. This understanding can help in the rational design of systems such as spray, atomization, and jet printing to prevent the formation of satellite drops.