MATHEMATICAL-MODEL FOR CHARACTERIZATION OF BACTERIAL MIGRATION THROUGH SAND CORES

The migration of chemotactic bacteria in liquid media has previously b een characterized in terms of two fundamental transport coefficients-t he random motility coefficient and the chemotactic sensitivity coeffic ient. For modeling migration in porous media, we have shown that these coefficients which appear in macroscopic balance equations can be rep laced by effective values that reflect the impact of the porous media on the swimming behavior of individual bacteria. Explicit relationship s between values of the coefficients in porous and liquid media were d erived. This type of quantitative analysis of bacterial migration is n ecessary for predicting bacterial population distributions in subsurfa ce environments for applications such as in situ bioremediation in whi ch bacteria respond chemotactically to the pollutants that they degrad e. We analyzed bacterial penetration times through sand columns from t wo different experimental studies reported in the literature within th e context of our mathematical model to evaluate the effective transpor t coefficients. Our results indicated that the presence of the porous medium reduced the random motility of the bacterial population by a fa ctor comparable to the theoretical prediction. We were unable to deter mine the effect of the porous medium on the chemotactic sensitivity co efficient because no chemotactic response was observed in the experime ntal studies. However, the mathematical model was instrumental in deve loping a plausible explanation for why no chemotactic response was obs erved. The chemical gradients may have been too shallow over most of t he sand core to elicit a measurable response. (C) 1997 John Wiley & So ns, Inc.