Stability of a spherical drop with surfactant mass transfer

Abstract

Interphase convection and Marangoni instability have recently become the subject of active study [1–5]. The description of a number of phenomena associated with the interaction between surfactant mass transfer and capillary effects are examined at the kinetic and hydrodynamic levels, using an experimentally realizable physical model. For this model the boundary-value problem of the stability of diffusion transfer of surfactant across an initially spherical interface between two immiscible liquids in the diffusion and adsorption kinetics regimes is solved analytically. The critical values of the dimensionless parameters of the problem at which convectionless mass transfer becomes unstable with respect to monotonic disturbances are found. The drop drift effect is examined. The change in the shape of the drop and the influence of surface viscosity and diffusion effects are taken into account. The possible practical applications of the problems solved include: modeling spontaneous emulsification, cytokinesis and chemotaxis, and estimating the effect of interphase turbulence on the rate of mass transfer across media interfaces in various industrial processes.