Microstructural evolution in drying colloidal films driven by evaporation and sedimentation: Lattice Boltzmann simulation and mathematical model

Abstract

Understanding the temporal evolution of particle distribution during the drying of colloidal films is essential for advancing the design and optimization of film properties. This study investigates the dynamics of colloidal particles during vertical drying using the lattice Boltzmann method. Simulation results reveal that the particle distribution during drying and the resulting film microstructure are governed by two key dimensionless numbers: the drying Péclet number (Pe) and the sedimentation Péclet number (Pe_sed). When the evaporation rate exceeds the sedimentation rate (Pe ≫ Pe_sed), particles accumulate near the air-liquid interface, ultimately forming a colloidal crystal in the top layer. Conversely, when sedimentation dominates (Pe ≪ Pe_sed), similar accumulation and crystallization occur near the bottom substrate. These findings underscore the critical influence of drying and sedimentation dynamics on the final microstructural quality of colloidal films. To complement the simulation results, a one-dimensional mathematical drying model is developed, incorporating hydrodynamic hindrance and collective diffusivity effects resulting from particle accumulation. This model demonstrates quantitative agreement with simulation results across a wide range of Pe and Pesed. Using this model, new drying regime maps are constructed in the Pe and Pe_sed spaces, delineating distinct regions dominated by evaporation, diffusion, or sedimentation.