# Simulation of self-propelled chemotactic bacteria in a stokes flow*

A. Decoene; A. Lorz; S. Martin; B. Maury; M. Tang

ESAIM: Proceedings (2010)

- Volume: 30, page 104-123
- ISSN: 1270-900X

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topDecoene, A., et al. Bresch, D., et al, eds. " Simulation of self-propelled chemotactic bacteria in a stokes flow*." ESAIM: Proceedings 30 (2010): 104-123. <http://eudml.org/doc/251246>.

@article{Decoene2010,

abstract = {We prescrit a method to simulate the motion of self-propelled rigid particles in a
twodimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion
is modelled as a point force associated to each particle, placed at a certain distance
from its gravity centre. The method for solving the fluid flow and the motion of the
bacteria is based on a variational formulation on the whole domain, including fluid and
particles: rigid motion is enforced by penalizing the strain rate tensor on the rigid
domain, while incompressibility is treated by duality. This leads to a minimisation
problem over unconstrained functional spaces which cari lie easily implemented from any
finite element Stokes solver. In order to ensure robustness, a projection algorithm is
used to deal with contacts between particles. The particles are meant to represent
bacteria of the Escherichia coli type, which interact with their chemical
environment through consumption of nutrients and orientation in some favorable direction.
Our mode’ takes into account the interaction with 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. In addition, self-propulsion is deactivated for
those particles which cannot consume enough oxygen. Finally, the mode’ includes random
changes in the orientation of the individual bacteria, with a frequency that depends on
the surrounding oxygen concentration, in order to favor the direction of the concentration
gradient and thus to reproduce chemotactic behaviour. Numerical simulations implemented
with FreeFem++ are presented.},

author = {Decoene, A., Lorz, A., Martin, S., Maury, B., Tang, M.},

editor = {Bresch, D., Calvez, V., Grenier, E., Vigneaux, P., Gerbeau, J-F.},

journal = {ESAIM: Proceedings},

language = {eng},

month = {12},

pages = {104-123},

publisher = {EDP Sciences},

title = { Simulation of self-propelled chemotactic bacteria in a stokes flow*},

url = {http://eudml.org/doc/251246},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Decoene, A.

AU - Lorz, A.

AU - Martin, S.

AU - Maury, B.

AU - Tang, M.

AU - Bresch, D.

AU - Calvez, V.

AU - Grenier, E.

AU - Vigneaux, P.

AU - Gerbeau, J-F.

TI - Simulation of self-propelled chemotactic bacteria in a stokes flow*

JO - ESAIM: Proceedings

DA - 2010/12//

PB - EDP Sciences

VL - 30

SP - 104

EP - 123

AB - We prescrit a method to simulate the motion of self-propelled rigid particles in a
twodimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion
is modelled as a point force associated to each particle, placed at a certain distance
from its gravity centre. The method for solving the fluid flow and the motion of the
bacteria is based on a variational formulation on the whole domain, including fluid and
particles: rigid motion is enforced by penalizing the strain rate tensor on the rigid
domain, while incompressibility is treated by duality. This leads to a minimisation
problem over unconstrained functional spaces which cari lie easily implemented from any
finite element Stokes solver. In order to ensure robustness, a projection algorithm is
used to deal with contacts between particles. The particles are meant to represent
bacteria of the Escherichia coli type, which interact with their chemical
environment through consumption of nutrients and orientation in some favorable direction.
Our mode’ takes into account the interaction with 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. In addition, self-propulsion is deactivated for
those particles which cannot consume enough oxygen. Finally, the mode’ includes random
changes in the orientation of the individual bacteria, with a frequency that depends on
the surrounding oxygen concentration, in order to favor the direction of the concentration
gradient and thus to reproduce chemotactic behaviour. Numerical simulations implemented
with FreeFem++ are presented.

LA - eng

UR - http://eudml.org/doc/251246

ER -

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