Particle-laden thin film flow: An alternating direction implicit scheme and comparison between theory, numerical simulations, and experiments.

摘要

Gravity-driven thin film flows have been analyzed in terms of fourth-order lubrication models, similarity solutions, traveling wave solutions, numerical simulations, and experiments. However, in the case where particle are suspended within the fluid, studies have been largely limited to lubrication models. one-dimensional numerical simulations, and experiments. We present a numerical scheme for a lubrication model derived for particle-laden thin film flow in two dimensions with surface tension. The scheme relies on an alternating direction implicit process to handle the higher-order terms. and an iterative procedure to improve the solution at each timestep. Several aspects of the scheme are examined for a test problem, such as the timestep, runtime, and number of iterations. The results from the simulation are compared to experimental data. The simulation shows good qualitative agreement. It also suggests further lines of inquiry for the physical model. For constant-volume particle-laden thin film flow. a lubrication model with precursor and experiments are compared to a power law for the position of the front of the flow with respect to time. This power-law behavior was originally derived for clear fluid flows. In the lubrication model, the precursor has a large effect on the speed of the front. independent of the settling of the particles. Comparison between theory and experiments indicates that this scaling law persists to leading order for particle-laden thin film flows with particle settling. For gravity-driven particle-laden thin film flows on an inclined plane, three distinct regimes can be observed: particles settling to the substrate, a particle-rich ridge forming at the front of the flow, and the particles staving well-mixed. Experiments are conducted for a. variety of particle sizes and liquid viscosities. We compare experimental results with equilibrium theory that balances shear-induced migration and hindered settling. We find that the well-mixed regime is transient, with the particle size and liquid viscosity influencing its time scale.