NUMERICAL-SOLUTION OF TRANSPORT-EQUATIONS FOR BACTERIAL CHEMOTAXIS - EFFECT OF DISCRETIZATION OF DIRECTIONAL MOTION

A mathematical model proposed by Alt [J. Math. Biol., 9 (1980), pp. 14 7-177] to describe chemotactic bacterial migration is studied, and sol utions to this model are compared to solutions of a simpler model prop osed by Rivero et al. [Chemical Engineering Science, 44 (1989), pp. 28 81-2897]. It is found that a discretized version of Alt's model produc es solutions similar to the continuous model, even at very coarse disc retization. The relationship between the discretized Alt model and the model of Rivero et al. is elucidated, and it is found that a slightly modified version of the Rivero et al. model produces solutions simila r to those of the Alt model for systems with one- and two-dimensional attractant gradients, suggesting that the simple and easy-to-use River o et al. model (after slight modification) is adequate for modeling ba cterial behavior within the parameter ranges investigated. A prelimina ry investigation of the use of the lattice Boltzmann method for the st udy of bacterial migration is reported.