Scaling the fractional advective-dispersive equation for numerical evaluation of microbial dynamics in confined geometries with sticky boundaries

Journal Article · Fri Jun 20 04:00:00 EDT 2008 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2008.03.021· OSTI ID:21159396

Parashar, R ^[1]; Cushman, J H ^[2]

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1. Department of Civil Engineering, Purdue University, West Lafayette, IN 47907 (United States)
2. Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907 (United States)

Microbial motility is often characterized by 'run and tumble' behavior which consists of bacteria making sequences of runs followed by tumbles (random changes in direction). As a superset of Brownian motion, Levy motion seems to describe such a motility pattern. The Eulerian (Fokker-Planck) equation describing these motions is similar to the classical advection-diffusion equation except that the order of highest derivative is fractional, {alpha} element of (0, 2]. The Lagrangian equation, driven by a Levy measure with drift, is stochastic and employed to numerically explore the dynamics of microbes in a flow cell with sticky boundaries. The Eulerian equation is used to non-dimensionalize parameters. The amount of sorbed time on the boundaries is modeled as a random variable that can vary over a wide range of values. Salient features of first passage time are studied with respect to scaled parameters.

• OSTI ID: 21159396
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 13 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADVECTION
BACTERIA
BROWNIAN MOVEMENT
DIFFUSION EQUATIONS
EVALUATION
FOKKER-PLANCK EQUATION
GEOMETRY
LAGRANGIAN FUNCTION
RANDOMNESS
STOCHASTIC PROCESSES