FIG. 3.

The effective diffusivity, D_eff(L, v), as a function of the dead-end length, L, for several values of the drift velocity, v, indicated near the curves in dimensionless units. Velocity v^* is given by Eq. (4.14). Other parameters, in dimensionless units, are R = l = D₀ = D_de = 1 and a = 0.1. The curves are drawn using Eq. (4.24). Dashed straight lines show the values of the effective diffusivity in the anomalous regime, $D_{\mathit{eff}}^{\left(a\right)}\left(v\right)$, given in Eq. (4.13). Panels (a) and (b) show the same curves at different length scales. D_eff(L, v) is a non-monotonic function of L, which first decreases with L, reaches a minimum, and then increases approaching its asymptotic value $D_{\mathit{eff}}^{\left(a\right)}\left(v\right)$. As the drift velocity v decreases, the minimum becomes flatter and flatter, and D_eff(L, v) approaches D_eff(L, 0) which is a monotonically decreasing function of L.