Interfacial dynamics driven by Marangoni stresses on a slowly moving liquid film
Differential surface tension is a common phenomenon in many chemical and biomedical processes. Localised surface tension gradients due to differential surface loading in thin films give rise to a moving shock front in the direction of higher surface tension. Existence of a background flow enhances the shock wave giving rise to wave breaking and wave separation mechanisms. The effect of a background flow field on Marangoni stress induced shock fronts were investigated in this thesis. Furthermore, a numerical procedure to find approximate solutions to the fully nonlinear flow problem that arises due to Marangoni spreading is proposed. A set of surface evolution equations that incorporates the effects of the background flow field is studied in two major respects: (i) breaking the horizontal symmetry and (ii) nonlinear accretion leading to shock front breaking or separation. The evolution of the surface is evaluated by numerical simulations for a wide range of parameter values. The investigation showed that there are two breaking mechanisms switched by the value of Peclet number. Furthermore it showed that the life time of the shock front is determined by the volumetric flow rate of the film. It is shown here that a weak Marangoni force generates a pure capillary gravity wave that propagates faster than the surfactant front. It is customary to use the lubrication approximations to simplify thin film problems. As a result, the inertial terms in flow equations and nonlinear terms in surface stress balances become excluded. To analyse the fully nonlinear flow, a finite element (FEM) analysis is proposed. The simulations shows that the lubrication theory holds globally in predicting the spreading rates but fails to do so locally until a quasi-steady state is reached. The FEM model shows the formation of two counter-rotating vortices at the beginning which diminish as time evolves. The FEM results are compared with the lubrication theory simulations. FEM model shows rapid film thinning forming extremely thin films within a short period of time. Though detailed transport mechanisms differ, both methods are in close agreement in predicting the spreading rates.