Dimensionless Parameters Define Criteria for Optimal Flow Velocity in Enhancing Chemotactic Response toward Residual Contaminants in Porous Media

Chemotactic bacteria may overcome challenges posed by nonaqueous-phase liquid (NAPL) contaminants of low solubility in groundwater and limited bioavailability in tight pores by preferentially migrating to NAPL sources. We explored the transport of chemotactic bacteria to NAPL ganglia at varying pore water velocities in a dual-permeability microfluidic device and using computer-simulated solutions of transport equations. In our experiments, bacteria exhibited a chemotactic response toward NAPL ganglia at the junctures of low- and high-permeability regions (i.e., micropockets), and the extent of retention initially increased with velocity and then decreased at the highest velocity. A dimensional analysis revealed that maximum accumulations occurred at moderate values of the Péclet number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:msub><mml:mi>d</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>χ</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:math> ∼10 in our system. We also found that accumulation dynamics in micropockets can be represented by a logistic equation incorporating convection and chemotaxis time scales <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>τ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>τ</mml:mi><mml:mi>che</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:msub><mml:mi>l</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>χ</mml:mi><mml:mi>o</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:math>, respectively. By analyzing seven literature studies on chemotaxis, we identified an exposure time scale to chemicals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>τ</mml:mi><mml:mi>exp</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:math> that was useful for evaluating the chemotaxis efficiency. Our study provided unique insights into the effect of fluid flow on chemotaxis in porous media by demonstrating that increasing the fluid velocity to some extent can promote chemotaxis. The dimensionless parameters inform the design of efficient bioremediation strategies for contaminated porous media.