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

  • Authors:

  • R. Parashar;J. H. Cushman

  • Affiliations:

  • Department of Civil Engineering, Purdue University, West Lafayette, IN 47907, USA;Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, USA and Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

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, @a@?(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.