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.
Cite this article
Martijn Zaal, Cell swelling by osmosis: A variational approach. Interfaces Free Bound. 14 (2012), no. 4, pp. 487–520