A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

Brian Moran*, Salil S. Kulkarni, Howard W. Reeves

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics.

Original languageEnglish (US)
Pages (from-to)291-300
Number of pages10
JournalInternational Journal of Fracture
Volume143
Issue number3
DOIs
StatePublished - Feb 1 2007

Keywords

  • Anti-plane crack
  • Biofilm
  • Domain integral
  • Michaelis-Menten
  • Nonlinear kinetics
  • Path-independent integral

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics

Fingerprint Dive into the research topics of 'A path-independent integral for the characterization of solute concentration and flux at biofilm detachments'. Together they form a unique fingerprint.

Cite this