Including van der Waals Forces in Diffusion-Convection Equations - Modeling, Analysis, and Numerical Simulations
This work provides a new modeling framework for including van der Waals forces in diffusion-convection processes, relevant for colloid and aerosol science.
The paper models van der Waals forces within diffusion-convection equations, transforming the model to a porous medium equation to leverage existing analytical results. Numerical simulations are performed without regularization, demonstrating the model's applicability to slow perikinetic coagulation.
This paper presents a model of van der Waals forces in the framework of diffusion-convection equations. The model consists of a nonlinear and degenerated diffusion-convection equation, which furthermore can be considered as a model for slow perikinetic coagulation. For the analytical investigation, we transform the model to a porous medium equation, which provides us access to the comprehensive analytical results for porous medium equations. Additionally, this transformation reveals a new application for porous medium equations. Eventually, we present numerical simulations of the model by solving the porous medium equation. We note that we solve the porous medium equation without any further regularization, which is often applied in this context.