Thermocapillary control of rupture in thin viscous fluid sheets

We consider the evolution of a thin viscous fluid sheet subject to thermocapillary effects. Using a lubrication approximation we find, for symmetric interfacial deflections, coupled evolution equations for the interfacial profile, the streamwise component of the fluid velocity and the temperature variation along the surface. Initial temperature profiles change the initial flow field through Marangoni-induced shear stresses. These changes then lead to preferred conditions for rupture prescribed by the initial temperature distribution. We show that the time to rupture may be minimized by varying the phase difference between the initial velocity profile and the initial temperature profile. For sufficiently large temperature differences, the phase difference between the initial velocity and temperature profiles determines the rupture location.