Dispersion of motile bacteria in a porous medium: Experimental data and theory

The sound understanding and quantification of the transport and dispersion
mechanisms of bacteria in porous media is of central concern in applications
such as bioremediation and biomineralization. Recent experimental and numerical
studies indicate that motility plays a key role for the fate of bacteria.
Data from microfluidic experiments in model porous media consisting of randomly
placed pillars show that non-motile bacteria have compact displacement
distributions, while the distribution of motile bacteria are characterized by
strong peak retention and forward tailing. Detailed analysis of bacteria
trajectories reveals two key attributes: 1. The emergence of a motility-induced
trapping and retention process due to active motion from the stream toward the
solid grain. 2. Increase or decrease of dispersion due to the transfer between
pore channels and grains, depending on the flow rate. We develop a physical model
based ona continuous time random walk (CTRW) approach. Bacteria dispersion due to
hydrodynamic flow fluctuations is quantified by a Markov model for the equidistantly
sampled particle speeds. The impact of motility is modeled by a two-rate trapping
process that accounts for the motion toward and active trapping at the grains.
The theoretical model captures the displacement distributions of both non-motile
and motile bacteria. It provides explicit analytical expressions for the motility-induced
hydrodynamic dispersion coefficients in terms of the trapping and release rates,
which characterize the bacteria motility. The experimental data shows that these
motility parameters are flow-rate dependent, which manifest in a reduction of
dispersion compared to the non-motile bacteria at low flow rates, and an increase
at high flow rates. The model reproduces the experimental observations and allows to
predict bacteria dispersion at the continuum scale.