Leveling of thixotropic liquids

In this paper the effect of thixotropy in the hydrodynamic behavior of thin films is studied. The simple problem of leveling on a horizontal substrate is considered. The rheological properties of the material are assumed to evolve over time due purely to changes in its internal structure. These changes are modeled in terms of a single structural variable. Neither elastic nor yielding effects are taken into account. More specifically, two distinct rheological models are considered: the simple model proposed by Moore and the more complex model proposed by Baravanian et al. These models exhibit a large range of variation for the liquid viscosity across the film thickness. After deriving the hydrodynamic equations governing leveling flows with the standard assumptions required by the lubrication approximation and running time-dependent numerical simulations, the nonlinear leveling history of the liquid can be predicted as a function of the initial microstructural state, rheological parameters, and initial disturbance of the liquid free surface. The main effort of this work is devoted to devising approximation schemes which lead to significant simplifications of the governing equations and their numerical computations. By approximating the inverse of viscosity as a monotonic function between its substrate and free-surface values, excellent agreement is found for the film amplitude, irrespective of the values of the rheological parameters of both models. Finally, a linear analysis yields a generalization of the Orchard’s law of leveling for Newtonian liquids to take into account the effect of thixotropy.