A polymer–solvent model of biofilm growth

Abstract

We provide and analyse a model for the growth of bacterial biofilms based on the concept of an extracellular polymeric substance as a polymer solution, whose viscoelastic rheology is described by the classical Flory-Huggins theory. We show that one-dimensional solutions exist, which take the form at large times of travelling waves, and we characterize their form and speed in terms of the describing parameters of the problem. Numerical solutions of the time-dependent problem converge to the travelling wave solutions.

A mathematical model of meat cooking based on polymer–solvent analogy

“…Furthermore, the model now has sufficient physics to capture the details of the underlying processes, giving better results for thin steaks, even with a one dimensional geometry. We wish to point that the model derived herein has some similarities to, and is based on the polymer-solvent models derived elsewhere in the literature in the context of biofilms; see for example, Winstanley et al [23] and Cogan and Keener [24].…”

The development of biofilm architecture

“…We will proceed with the general term θ, although, as we shall see, the precise value has little effect. 2 The factor 1 3 was incorrectly given as 1 6 in equation (2.7) of Winstanley et al [22], with largely cosmetic consequences. of no slip of EPS, no flow of water through the wall and no flux of nutrient at the wall:…”

“…We begin by recalling the polymer/solvent model presented by Winstanley et al [22]. The EPS has volume fraction φ, which is taken to include also the bacteria cells, which themselves produce the EPS.…”

“…In this paper, we elaborate on the reduction of the Winstanley et al [22] model in one lateral dimension in the simplifying regime, where EPS concentration variation through the biofilm is small. We analyse the stability of one-dimensional solutions and show that numerical solutions are consistent with the stability results.…”

“…Winstanley et al [22] started from a two-fluid model with Newtonian viscous stresses, and used estimates of model parameters to argue that the viscous stress terms are in fact negligible: at time scales larger than minutes the dominant momentum balance is between interphase drag and osmotic pressure (contrary to the assumptions of [15]). An estimate of the gradient energy parameter suggested that a sharp interface approximation is appropriate for model domains with spatial scale larger than a few micrometres.…”