Lattice-Boltzmann Modeling of Bacterial Chemotaxis in the Subsurface
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The Lattice Boltzmann method (LBM) has been widely used because it is well-suited to model flow and transport in the complex geometries that are typical for subsurface porous media. Bacterial chemotaxis enables motile bacteria to move preferably toward chemoattractants that may be contaminants in the subsurface. This microbial phenomenon provides a valuable mechanism to enhance in situ bioremediation. Therefore, we developed Lattice Boltzmann (LB) models to study bacterial chemotaxis in the subsurface. A multiple-relaxation-time (MRT) LB model was developed to study the formation and migration of traveling bacterial waves caused by chemotaxis (chemotactic waves) in the absence of bacterial growth and decay. This model was validated by comparing simulations with experiments in which the chemotactic bacteria entered a tube filled with substrate due to chemotaxis. Simulations were performed to evaluate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of such chemotactic waves. Wave formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the waves while shear flow does. Bacterial waves move both upstream and downstream when the flow velocity is small. However, the waves disappear once the velocity becomes large due to hydrodynamic dispersion. Generally waves can only be observed if the dimensionless ratio between a particularly defined coefficient, chemotactic sensitivity coefficient, and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion. Another two-relaxation-time (TRT) LB model was also introduced to simulate bacterial chemotaxis and other reactive transport. The TRT LB model can eliminate numerical diffusion by including a velocity correction term. One-dimensional solute transport with initial Gaussian and top hat distributions were investigated to evaluate the accuracy and stability of the TRT models with and without the velocity correction. The TRT model with the correction demonstrated better numerical accuracy and stability than that without the correction. When the velocity is small, the numerical diffusion can be neglected, and the TRT model without the correction attained very similar simulation results as the TRT model with the correction. However, it is necessary for the TRT model to include the velocity correction when the velocity is large. Since bacterial survival is a significant factor for contaminant remediation at contaminated sites, we studied the coupled effects of chemotaxis and growth on bacterial migration and contaminant remediation. The impacts of initial electron acceptor concentration on different bacteria and substrate systems were examined. The simulations showed that bacteria could form a growth/decay/motility wave due to a dynamic equilibrium between bacterial growth, decay and random motility, even though the bacteria perform no chemotaxis. We derived an analytical solution to estimate this growth/decay/motility wave speed. The initial electron acceptor concentration was shown to significantly affect the bacterial movement and substrate removal. The impact of chemotaxis on bacterial migration is determined by comparison of the chemotactic wave speed with the growth/decay/motility wave speed. When chemotaxis is too weak to allow for the formation of a chemotactic wave or its wave speed is less than half of the growth/decay/motility wave speed, it hardly enhances the bacterial propagation. However, chemotaxis significantly improves bacterial propagation once its wave speed exceeds the growth/decay/motility wave speed. The bacterial survival plays a crucial role in determining the efficiency of contaminant removal. If there is no growth, the traveling wave will move with a decreasing speed and finally terminates. Although chemotaxis has been widely observed to be able to improve contaminant degradation in laboratories, it is rarely reported to enhance bioremediation at field sites. We discuss this discrepancy based on our simulation findings and suggest operable measures to take advantage of chemotaxis in in situ bioremediation.