Fig. 5: Numerical validation of the analytical solution to Eq. (1).

a Selected snapshots of the numerically calculated ϕ_num(ξ) with initial condition c(x, 0) = δ(x − 1) and with a = 1, revealing a rapid convergence to the steady state distribution. The dashed line corresponds to the analytical form of Eq. (7a) valid at large t. b The corresponding evolution of mean area s(t), with the analytical solution at large t given by Eq. (7b) shown by the dashed line. c The mean area of the experimental samples as a function of t computed from Eq. (7b) (scattered points). The dashed line corresponds to Eq. (7b) with a(t) as given by Eq. (8). Marker colors correspond to different values of \(\tilde{{{\Delta }}}\), as indicated by the colorbar.