Microscopic Modelling of Active Bacterial Suspensions

A. Decoene; S. Martin; B. Maury

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 5, page 98-129
  • ISSN: 0973-5348

Abstract

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We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly coupling the fluid and the rigid particle problems: rigid motion is enforced by penalizing the strain rate tensor on the rigid domain, while incompressibility is treated by duality. This model allows to achieve an accurate description of fluid motion and hydrodynamic interactions in moderate to concentrated active suspensions. A mesoscopic model is also used, in which the size of the bacteria is supposed to be much smaller than the elements of fluid: the perturbation of the fluid due to propulsion and motion of the swimmers is neglected, and the fluid is only subjected to the buoyant forcing induced by the presence of the bacteria, which are denser than the fluid. Although this model does not accurately take into account hydrodynamic interactions, it is able to reproduce complex collective dynamics observed in concentrated bacterial suspensions, such as bioconvection. From a mathematical point of view, both models lead to a minimization problem which is solved with a standard Finite Element Method. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. We also reproduce chemotactic behaviour driven by oxygen: an advection-diffusion equation on the oxygen concentration is solved in the fluid domain, with a source term accounting for oxygen consumption by the bacteria. The orientations of the individual bacteria are subjected to random changes, with a frequency that depends on the surrounding oxygen concentration, in order to favor the direction of the concentration gradient.

How to cite

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Decoene, A., Martin, S., and Maury, B.. "Microscopic Modelling of Active Bacterial Suspensions." Mathematical Modelling of Natural Phenomena 6.5 (2011): 98-129. <http://eudml.org/doc/222291>.

@article{Decoene2011,
abstract = {We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly coupling the fluid and the rigid particle problems: rigid motion is enforced by penalizing the strain rate tensor on the rigid domain, while incompressibility is treated by duality. This model allows to achieve an accurate description of fluid motion and hydrodynamic interactions in moderate to concentrated active suspensions. A mesoscopic model is also used, in which the size of the bacteria is supposed to be much smaller than the elements of fluid: the perturbation of the fluid due to propulsion and motion of the swimmers is neglected, and the fluid is only subjected to the buoyant forcing induced by the presence of the bacteria, which are denser than the fluid. Although this model does not accurately take into account hydrodynamic interactions, it is able to reproduce complex collective dynamics observed in concentrated bacterial suspensions, such as bioconvection. From a mathematical point of view, both models lead to a minimization problem which is solved with a standard Finite Element Method. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. We also reproduce chemotactic behaviour driven by oxygen: an advection-diffusion equation on the oxygen concentration is solved in the fluid domain, with a source term accounting for oxygen consumption by the bacteria. The orientations of the individual bacteria are subjected to random changes, with a frequency that depends on the surrounding oxygen concentration, in order to favor the direction of the concentration gradient. },
author = {Decoene, A., Martin, S., Maury, B.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {Stokes flow; fluid-particle flows; self-propulsion; finite element method; penalty method; chemotaxis.; chemotaxis},
language = {eng},
month = {8},
number = {5},
pages = {98-129},
publisher = {EDP Sciences},
title = {Microscopic Modelling of Active Bacterial Suspensions},
url = {http://eudml.org/doc/222291},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Decoene, A.
AU - Martin, S.
AU - Maury, B.
TI - Microscopic Modelling of Active Bacterial Suspensions
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/8//
PB - EDP Sciences
VL - 6
IS - 5
SP - 98
EP - 129
AB - We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly coupling the fluid and the rigid particle problems: rigid motion is enforced by penalizing the strain rate tensor on the rigid domain, while incompressibility is treated by duality. This model allows to achieve an accurate description of fluid motion and hydrodynamic interactions in moderate to concentrated active suspensions. A mesoscopic model is also used, in which the size of the bacteria is supposed to be much smaller than the elements of fluid: the perturbation of the fluid due to propulsion and motion of the swimmers is neglected, and the fluid is only subjected to the buoyant forcing induced by the presence of the bacteria, which are denser than the fluid. Although this model does not accurately take into account hydrodynamic interactions, it is able to reproduce complex collective dynamics observed in concentrated bacterial suspensions, such as bioconvection. From a mathematical point of view, both models lead to a minimization problem which is solved with a standard Finite Element Method. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. We also reproduce chemotactic behaviour driven by oxygen: an advection-diffusion equation on the oxygen concentration is solved in the fluid domain, with a source term accounting for oxygen consumption by the bacteria. The orientations of the individual bacteria are subjected to random changes, with a frequency that depends on the surrounding oxygen concentration, in order to favor the direction of the concentration gradient.
LA - eng
KW - Stokes flow; fluid-particle flows; self-propulsion; finite element method; penalty method; chemotaxis.; chemotaxis
UR - http://eudml.org/doc/222291
ER -

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