Surface energy variation effect on the onset of thermocapillary instability of a thin liquid layer heated from the side

A general interfacial energy balance equation taking into account surface energy variation is derived for viscous two-layer flows. Application of this interfacial energy equation to a thin liquid layer heated from one side using a one-layer model shows that thermocapillary induced surface energy variation has a tendency to stabilize the system, resulting in an increase in the critical Marangoni number for the onset of thermocapillary instability. Thermocapillary induced surface energy variation tends to decrease the temperature of hot surface spots and increase the temperature of cold surface spots through an absorb-release mechanism. This absorb-release mechanism increases the free surface's capability to convect thermal energy from hot spots to cold spots and thus redistributes the disturbance energy evenly across the free surface. This new stabilizing effect becomes stronger at high surface temperature and at high surface dilatation rate.