Including van der Waals Forces in Diffusion-Convection Equations - Modeling, Analysis, and Numerical Simulations

TL;DR

This paper introduces a model incorporating van der Waals forces into diffusion-convection equations, analyzes it through transformation to porous medium equations, and performs numerical simulations without additional regularization.

Contribution

It develops a novel approach by transforming a nonlinear diffusion-convection model with van der Waals forces into a porous medium equation, enabling new analytical and numerical insights.

Findings

Transformation to porous medium equations facilitates analysis.

Numerical simulations are performed without extra regularization.

The model provides insights into slow perikinetic coagulation.

Abstract

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.