Transient enhancement of thermocapillary flow in a two-dimensional cavity by a surfactant

Abstract

In this paper, we present results of a numerical study of the effect of insoluble surfactants on thermocapillary flow in a two-dimensional slot. For surfactant-laden systems, there are pronounced nonlinearities in the surface tension dependence on both temperature and surface concentration, some of which create interesting phenomena that cannot be captured by the linear limit used in prior work. Our work focuses on two regimes of nonlinear coupling between the surface tension, surface concentration, and surface temperature. First, we address a surfactant that forms a monolayer in a single surface phase. Second, we discuss a regime in which surfactants transiently enhance thermocapillary flow, rather than oppose it. This occurs for long chain surfactants with small headgroups that form liquid-expanded (LE) and liquid-condensed (LC) phases, e.g., (insoluble) long-chain carboxylic-acids under conditions where their headgroups are not disassociated. Results indicate that a surfactant in LE/LC coexistence initially enhances thermocapillary flow in a slot, creating a surface convective flux that rapidly convects surfactant toward the cold region and depletes the warm region. However, the convection of surfactant quickly drives the surface concentration out of LE/LC coexistence and into LE (in the depleted region) and LC (in the cold region). Thereafter, the rapid initial flow is again quenched by the usual circumstance of a surfactant in a single surface phase exerting an opposing Marangoni stress that stagnates the interface. At high surface Peclet numbers, no steady-state thermocapillary flow is sustained.