A path-independent integral for the characterization of solute concentration and flux at biofilm detachments
International Journal of Fracture
By: B. Moran, S.S. Kulkarni, and H. W. Reeves
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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. ?? Springer Science+Business Media, Inc. 2007.
Suggested Citation
Moran, B., Kulkarni, S., Reeves, H.W., 2007, A path-independent integral for the characterization of solute concentration and flux at biofilm detachments: International Journal of Fracture, v. 143, no. 3, p. 291-300, https://doi.org/10.1007/s10704-007-9067-4.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | A path-independent integral for the characterization of solute concentration and flux at biofilm detachments |
| Series title | International Journal of Fracture |
| DOI | 10.1007/s10704-007-9067-4 |
| Volume | 143 |
| Issue | 3 |
| Publication Date | April 17, 2007 |
| Year Published | 2007 |
| Language | English |
| Larger Work Type | Article |
| Larger Work Subtype | Journal Article |
| Larger Work Title | International Journal of Fracture |
| First page | 291 |
| Last page | 300 |