NUMERICAL MODELING OF CAPILLARY–GRAVITY WAVES USING THE PHASE FIELD METHOD

In this paper, we present a numerical model based on the widely used finite element formulation to analyze in detail the effect of surface active agents on capillary–gravity wave parameters such as phase velocity and wave amplitude. Moreover, the effect of a physicochemical parameter, which is the ratio of surface concentration to surface tension is also considered. For a number of fluid samples covering a range of concentrations from 0 to 0.01 molar, the phase speed of waves propagating on the surface of the liquid is found to decrease monotonically as the concentration of the solution considered is increased up to a limit of 0.004 molar. This is attributed to the corresponding increase in capillary number. It is shown numerically that the Marangoni effects contribute to the interfacial dynamics for fluid with physicochemical parameter value greater than 0.5. Moreover, a grid refinement study shows accuracies and convergence orders of the numerical model.