Colloidal chemotaxis and a biased random walk model with finite mean first-passage time

We introduce a power-law distance-dependent biased random walk model with a tuning parameter (sigma) in which finite mean first-passage times are realizable if sigma is less than a critical value sigma(c). We perform numerical simulations in one dimension to obtain sigma(c) approximate to 1.14. A three-dimensional variant of this model is argued to be related to the phenomenon of chemotaxis. Diffusiophoretic theory supplemented with coarse-grained simulations for colloidal chemotaxis establish the connection with the specific value of sigma = 2 as a consequence of in-built solvent diffusion. Copyright (C) EPLA, 2019