Deformation of an elastic body in low Reynolds number transport: Relevance to biofilm deformation and streamer formation

TL;DR

This study provides analytical insights into how low Reynolds number flow induces shear stress in elastic bodies, modeling biofilm deformation and streamer formation, with implications for understanding biofilm mechanics in fluid environments.

Contribution

It offers one of the first formal analyses of fluid-structure interaction related to biofilm streamer formation under low Reynolds number flow.

Findings

Shear stress distribution depends on position, Poisson ratio, and elastic rim thickness.

Flow-driven shear stress influences biofilm deformation and streamer formation.

Analytical results help interpret experimental observations of biofilm behavior.

Abstract

In this paper, we obtain analytical results for shear stress distributions inside an elastic body placed in a low Reynolds number transport. The problem definition is inspired by a recent experimental study (Valiei et al., Lab Chip, 2012, 12, 5133-5137) that reports the flow-triggered deformation of bacterial biofilms, formed on cylindrical rigid microposts, into long filamentous structures known as streamers. In our analysis, we consider an elastic body of finite thickness (forming a rim) placed over a rigid cylinder, i.e., we mimic the biofilm structure in the experiment. We consider Oseen flow solution to describe the low Reynolds transport past this cylindrical elastic structure. The stress and strain distributions inside the elastic structure are found to be functions of position, Poisson ratio, initial thickness of the elastic rim and the ratio of the flow-driven shear stress to the shear modulus of the elastic body. More importantly, these analyses, which can be deemed as one of the first formal analyses to understand the fluid-structure-interaction issues associated with the biofilm streamer formation, help us interpret several qualitative aspects associated with the streamer formation reported in different experiments.