Dynamics of driven liquid films on heterogeneous surfaces

A computational study is reported of the instability and growth of fingers for liquid films driven over heterogeneous surfaces. Computations are performed using a variation of the precursor-film model, in which a disjoining pressure term is used to introduce variation in the static contact angle, which in turn models surface heterogeneity. The formulation is shown to yield results consistent with the Tanner–Hoffman–Voinov dynamic contact angle formula for sufficiently small values of the precursor film thickness. A modification of the disjoining pressure coefficient is introduced which yields correct variation of dynamic contact angle for finite values of the precursor film thickness. The fingering instability is examined both for cases with ordered strips of different static contact angle and for cases with random variation in static contact angle. Surface heterogeneity is characterized by strip width and amplitude of static contact angle variation for the case with streamwise strips and by correlation length and variance of the static contact angle variation from its mean value for the random distribution case.