Swimming-induced non-Fickian transport of bacteria in porous media

Progress in experimental techniques and imaging methods have led to a leap in the understanding of 
microscopic transport and swimming mechanisms of motile particles in porous media. This is very different 
for the understanding and characterization of large scale transport behaviors, which result from the 
interaction of motility with flow and medium heterogeneity, and the upscaling of microscale behaviors. 
Only few works have investigated large scale dispersion of active particles in porous media, 
which mainly operate in the framework of Brownian dynamics and effective dispersion or 
are completely data driven. In this work, we use the particle tracking data of Creppy et al. [1] 
to derive the stochastic dynamics of small scale particle motion due to hydrodynamic flow variability 
and the swimming activity of bacteria. These stochastic rules are used to derive a 
continous time random walk (CTRW) based model for bacteria motion. The CTRW naturally accounts for 
persistent advective motion along streamlines [2]. In this framework, particle motility is modeled 
through a subordinated Ornstein-Uhlenbeck process that accounts for the impact of rotational diffusion on 
 particle motion in the fluid, and a compound Poisson process that accounts for the motion toward and around 
grains. The upscaled transport framework can be parameterized by the distribution of the Eulerian 
pore velocities, and the motility rules of the bacteria. The model predicts the propagators of the 
ensemble of bacteria as well as their center of mass position and dispersion for bacteria transport under different
flow rates. 

[1] A. Creppy, E. Clément, C. Douarche, M. V. D’Angelo, and H. Auradou. Effect of motility on the transport of bacteria populations through a porous medium. Phys. Rev. Fluids, 4(1), 2019.

[2] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester. Continuous time random walks for the evolution of Lagrangian velocities. Physical Review Fluids, 1(7):074004, 2016.