Free-surface wave damping due to viscosity and surfactants

The steady wave pattern developed on the free surface in inviscid two-dimensional fluid domain is well known. In this work, we investigate the influence of a thin film of insoluble material on an air-liquid interface on the wave characteristics. We employ a quasi-potential approximation and assume that the main flow is potential, while the effect of viscosity and surfactants enters the problem via Bernoulli equation. Thus, the problem is formulated in terms of a single potential function. The formulation presented in this work can be extended to three-dimensional problems. The wave amplitude consistent with the approximations made, may be moderate. We use our formulation to study a pressure distribution moving with a constant velocity, on a two-dimensional deep water air-liquid interface, on which there exists a monolayer film of surface active agents. The problem is solved numerically by a boundary integral equation method and numerical solutions are presented.