Marangoni flows during drying of colloidal films

Abstract

In this study, we consider the drying of a thin film that contains a stable dispersion of colloidal particles so that a coating of these particles is formed after the liquid is driven off by evaporation. For sufficiently thin films, we show that evaporative cooling can drive a Marangoni flow that results in surface deformation of the drying film. A thin-film approximation is used to describe the velocity and temperature fields, and the particle transport equation with convective terms retained is used to describe the concentration field. A coupled finite difference/spectral element scheme is implemented numerically to solve the particle transport equation, where high accuracy is required to resolve sharp gradients within the film and to ensure particle conservation during drying. The model employed is capable of describing the evolution of film thickness and concentration field up to the time when maximum packing is nearly reached at some point in the domain. Three types of film structures are observed, all characterized by a final nonuniform thickness. In the first type, observed at low Peclet numbers, the maximum concentration is reached at the thinnest points in the film, which surround elevations with lower particle concentrations. This mode of instability suggests that dried coatings will have pronounced nonuniformities, resulting in the formation of craters or pinholes. In the second type, observed at high Peclet numbers, a closely packed skin of nonuniform thickness is formed, with low concentration fluid remaining beneath the elevations. In the final stages of drying one would expect capillary pressure to pull particles in the underlying fluid toward the skin, thus creating voids under a seemingly homogeneously applied coating. Finally, still at relatively large particle Peclet numbers and when the destabilizing Marangoni stresses are sufficiently strong, floating lumps of closely packed particles may form in the vicinity of film elevations.