Abstract
Model development and verification for mass transport to Escherichia coli cells in a turbulent flow
Saint Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota, USA
Saint Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota, USA
Theoretical studies imply that fluid motion does not significantly increase the molecular diffusive mass flux toward and away
from microscopic organisms. This study presents experimental and theoretical evidence that small-scale turbulence modulates
enhanced mass transport to Escherichia coli cells in a turbulent flow. Using the technique of inner region and outer region expansions, a model for dissolved oxygen
and glucose uptake by E. coli was developed. The mass transport to the E. coli was modeled by the Sherwood (Sh)-Péclet (Pe) number relationship with redefined characteristic length and velocity scales.
The model Sh = (1 + Pe1/2 + Pe) agreed with the laboratory measurements well. The Péclet number that quantifies the role and function of small-scale
turbulence on E. coli metabolism is defined by Pe = (
) where Ezz is the root mean square of fluid extension in the direction of local vorticity, η K is the Kolmogorov length scale, Lc is the length scale of E. coli, and D is the molecular diffusion coefficient. An alternative formulation for the redefined Pe is given by Pe = (
) where
= 0.5(
ν)1/4 is the Kolmogorov velocity averaged over the Kolmogorov length scale,
is dissipation of turbulent kinetic energy, and ν is the kinematic viscosity of fluid. The dissipation of turbulent kinetic energy was estimated directly from measured velocity
gradients and was within the reported range in engineered and natural aquatic ecosytems. The specific growth of E. coli was up to 5 times larger in a turbulent flow in comparison to the still water controls. Dissolved oxygen and glucose uptake
were enhanced with increased
in the turbulent flow.
Received 11 October 2006; accepted 4 June 2007; published 14 August 2007.
Citation: (2007), Model development and verification for mass transport to Escherichia coli cells in a turbulent flow, Water Resour. Res., 43, W08413, doi:10.1029/2006WR005613.
Cited By
