Simulating Biofilm Deformation and Detachment with the Immersed Boundary Method (Communications in Computational Physics, 2018)
We apply the immersed boundary (or IB) method to simulate deformationand detachment of a periodic array of wall-bounded biofilm colonies in response to alinear shear flow. The biofilm material is represented as a network of Hookean springsthat are placed along the edges of a triangulation of the biofilm region. The interfacialshear stress, lift and drag forces acting on the biofilm colony are computed byusing fluid stress jump method developed by Williams, Fauci and Gaver [Disc. Contin.Dyn. Sys. B 11(2):519–540, 2009], with a modified version of their exclusion filter.Our detachment criterion is based on the novel concept of an averaged equivalentcontinuum stress tensor defined at each IB point in the biofilm which is then used todetermine a corresponding von Mises yield stress; wherever this yield stress exceeds agiven critical threshold the connections to that node are severed, thereby signalling theonset of a detachment event. In order to capture the deformation and detachment behaviourof a biofilm colony at different stages of growth, we consider a family of fourbiofilm shapes with varying aspect ratio. For each aspect ratio, we varied the spacingbetween colonies to investigate role of spatial clustering in offering protection againstdetachment. Our numerical simulations focus on the behaviour of weak biofilms (withrelatively low yield stress threshold) and investigate features of the fluid-structure interactionsuch as locations of maximum shear and increased drag. The most importantconclusions of this work are: (a) reducing the spacing between colonies reducesdrag by from 50 to 100% and alters the interfacial shear stress profile, suggesting thateven weak biofilms may be able to grow into tall structures because of the protectionthey gain from spatial proximity with other colonies; (b) the commonly employed detachmentstrategy in biofilm models based only on interfacial shear stress can lead toincorrect or inaccurate results when applied to the study of shear induced detachmentof weak biofilms. Our detachment strategy based on equivalent continuum stressesprovides a unified and consistent IB framework that handles both sloughing and erosion modes of biofilm detachment, and is consistent with strategies employed in manyother continuum based biofilm models.