We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al. (2011 Proc. R. Soc. A 467, 1449–1467 (doi:10.1098/rspa.2010.0327)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.
- Received November 17, 2015.
- Accepted March 21, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.