(459d) Influence of An Insoluble Surfactant Monolayer On the Stability of a Liquid Film Flowing Over a Locally Heated Substrate

The influence of an insoluble surfactant monolayer on the stability of a liquid film flowing under the influence of gravity down a locally heated surface is studied using a long-wave, lubrication analysis.  A thermocapillary flow at the upstream edge of a rectangular heater aligned perpendicular to the flow opposes the bulk flow, thereby decreasing the fluid velocity and inducing a pronounced fluid ridge.  A rivulet instability occurs above a threshold value of a Marangoni parameter, M = M_c, that characterizes the variation in the surface tension with temperature.  An oscillatory, thermocapillary instability also occurs for sufficiently strong heat transfer from the liquid to the surrounding gas that is characterized by a Biot number.  Even for M<M_c the thermocapillary flow causes flow reversal and a region of recirculation near the upstream edge of the heater, accompanied by a stagnation point at the free surface where adsorbed species accumulate.  In the presence of an insoluble surfactant, significant surfactant accumulation in this region partially immobilizes the interface, eliminates the stagnation point, and greatly reduces the amplitude of the fluid ridge.  A linear stability analysis reveals that a constant upstream supply of surfactant even at a small concentration suppresses the rivulet instability because of the partial leveling of the fluid ridge and the corresponding effect on the velocity profile.  For very large values of the Marangoni parameter and the Biot number, however, the oscillatory thermocapillary mode of the instability can occur at modest surfactant concentrations.  Predictions based on a model assuming a linear variation of the surface tension with the surfactant concentration are found to be in good agreement with calculations using a nonlinear equation of state despite the large accumulation of surfactant near the heater.