Practical drying model for horizontal colloidal films in rapid evaporation processes

A practical drying model is developed for horizontal colloidal films with the vertical particle distribution in the film determined by the Peclet number (Pe). The Pe is defined as the ratio between the evaporation speed ((Formula presented.)) and the colloidal diffusion ((Formula presented.)) at the initial wet film thickness (Formula presented.) ((Formula presented.)). The model incorporates the effect of Pe on the temporal particle distribution into the collective diffusivity of particles. Two model parameters are newly adopted into the collective diffusivity, the critical volume fraction (Formula presented.) and the degree of volume exclusion (Formula presented.) to efficiently account for the out-of-equilibrium state of dispersed particles due to the fast-moving interface. The results of the proposed two-parameter model are compared to those of previous models and a recently-published lattice Boltzmann (LB) simulation. The two-parameter model is demonstrated to favorably consistent with the LB simulation for a wide range of Pe (Pe = 10 − 1500).