Cell Swelling by Osmosis: a Variational Approach

TL;DR

This paper introduces a simple mathematical model for cell swelling by osmosis, framing it as a gradient flow involving entropy and surface area, and provides solutions explaining osmosis phenomena.

Contribution

It presents a novel variational approach to model cell swelling, connecting free boundary problems with gradient flows in the Wasserstein metric.

Findings

Model captures key features of osmosis-induced cell swelling

Gradient flow framework enables solution construction

Provides insights into the nature of osmosis phenomena

Abstract

A very simple model for cell swelling by osmosis is introduced, resulting in a parabolic free boundary problem. In case of radially symmetric initial conditions, it is shown that the model can be viewed as a gradient flow involving entropy, surface area and the Wasserstein metric. This observation is used to construct solutions and explain the presence and nature of osmosis.