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Chemotaxis in shear flow: Similarity solutions of the steady‐state chemoattractant and bacterial distributions
Author(s) -
Shim Suin,
Stone Howard A.,
Ford Roseanne M.
Publication year - 2019
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.16713
Subject(s) - chemotaxis , dimensionless quantity , steady state (chemistry) , shear (geology) , mechanics , flow (mathematics) , shear flow , chemistry , physics , materials science , receptor , biochemistry , composite material
When chemotactic bacteria are exposed to a concentration gradient of chemoattractant while flowing along a channel, the bacteria accumulate at the interface between the chemoattractant source and bacterial suspension. Assuming that the interface is no‐slip, we can apply the shear flow approximation near the no‐slip boundary and solve a steady‐state convection‐diffusion model for both chemoattractant and bacterial concentrations. We suggest similarity solutions for the two‐dimensional problem and identify a critical length scale η c for bacteria chemotaxis in a given concentration gradient. The analysis identifies three dimensionless groups representing, respectively, chemotactic sensitivity, the chemotaxis receptor constant, and the bacteria diffusion coefficient, which typically show coupled effects in experimental systems. We study the effect of the dimensionless groups separately and provide understanding of the system involving shear flow and chemotaxis.