Fingering phenomena for driven coating films

摘要: A theoretical and numerical model is formulated to describe the instability long-time evolution of both gravity-driven surface-shear-stress-driven thin coating films. single equation, higher-order diffusive type, models flow for either problem. It derived using lubrication approximation. For partially wetting systems, effect finite contact angle incorporated in equation a particular disjoining pressure model. The base state, each case, two-dimensional steadily propagating capillary front. Slight perturbations applied along front, initiate fingering instability. Early-time results accurately reproduce wavelengths fastest growth corresponding eigenmodes as reported published linear stability analyses. As time proceeds, depending on parameter values, various patterns arise. conditions perfect with substrate downstream moving front covered precursor layer, predicted nonlinear finger agrees well experiments. ultimate pattern, this translating pattern wedge-shaped fingers. Alternatively, systems that exhibit sufficiently large static angles, long straight-sided fingers or rivulets are formed. Finally, larger at relatively low speeds, we predict flowing will become unstable break up into strings isolated droplets.