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Mathematical Analysis and Numerical Modeling of Buoyant Flow from Solute Gradients around Growing Escherichia coli Cells.    M.R. Benoit1, E.S. Nelson2, and D.M. Klaus1. 1Aerospace Engineering Sciences Dept., Univ. of Colorado at Boulder. 2Computational Multiphysics Lab., NASA Glenn Research Center, Cleveland, OH.

   Bacteria alter their extracellular fluid environment by consuming nutrients and excreting byproducts. As bacterial cells grow, they accumulate a net gain of mass. Consequently, the extracellular fluid surrounding a cell undergoes a net loss of solute density. In the presence of gravity, buoyancy-driven convection acts on fluids of non-uniform density. If convective forces overcome viscous resistance, buoyant flow ensues.  We have observed plumes rising in the fluid above a layer of metabolically active, non-motile Escherichia coli cells. Presumably the plumes were caused by reduced fluid density from glucose consumption.  Because mass transport of nutrients and byproducts is limited to diffusion under microgravity conditions, the difference in fluid motion between 1g and microgravity is thought to contribute to changes in bacterial growth and behavior observed during spaceflight.

   Theoretical analyses were performed to further characterize convective phenomena caused by solute gradients formed around growing cells and a numerical model was developed to simulate the experimental results. The model visually illustrated how a fluid density gradient created by glucose uptake of E. coli can lead to buoyant plumes. The model output compared well with analytical calculations and empirical data. Dimensionless numbers were used to theoretically compare the buoyant force to viscous resistance over specified ranges of characteristic cell size and gravity level. The theoretical analyses also agreed well with the macroscopic laboratory results, and allowed us to predict buoyant flow thresholds at microscopic scales. This framework provides a basis for future cell biology studies by illustrating the coupling between gravity-dependent physical phenomena and cell growth and behavior.

(Supported by NASA GSRP Fellowship NGT3-52386 and BioServe Space Technologies, NASA Cooperative Agreement NCC8-242)