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.