The chemical continuous time random walk framework for upscaling transport limitations in fluid–solid reactions

Equilibrium distributions under advection–diffusion in laminar channel flow with partially absorbing boundaries

“…Surviving mass p.d.f.s p t are computed by integrating concentrations numerically over the longitudinal direction at the time of interest, using the underlying grid discretization. The breakthrough profiles p s are computed by integrating concentrations multiplied by on the first passage time picture provides good approximations and generalizes well to more complex geometries (Aquino & Le Borgne 2021a;Aquino et al 2023). This also shows that since for Da → ∞ we have α ∞ independent of the initial condition, the actual late-time tail of the first passage time distribution is independent of the initial mass distribution and is instead fully determined by the diffusion coefficient and the geometry of the problem.…”

“…The fact that the asymptotic rate is constant is consistent with the existence of a transverse equilibrium distribution. The relationship to recent descriptions in terms of first passage times (Aquino & Le Borgne 2021 a ; Aquino et al. 2023) is discussed in Appendix D.…”

“…Recently, the decay of total mass has been described in terms of first passage and return times to the reactive interface (Aquino & Le Borgne 2021a;Aquino et al 2023). In particular, for an instantaneous injection of initial mass M 0 in the 2-D channel, it is given in Laplace space by (Aquino & Le Borgne 2021a)…”

“…2023). In particular, for an instantaneous injection of initial mass in the 2-D channel, it is given in Laplace space by (Aquino & Le Borgne 2021 a ) where the tilde denotes the Laplace transform, is the Laplace variable conjugate to time, and is the survival probability, i.e. is the probability that first passage to the channel wall has not occurred by time for a given initial concentration distribution in the channel.…”

Multi-scale random walk models for reactive transport processes in fracture-matrix systems

“…Modeling reactive transport processes that occur in the natural environment is a key challenge for numerous research fields and applications. It Considering advective and diffusive mechanisms in heterogeneous geological formations amplifies the ranges of the considered scales and leads to the development of new modeling approaches and the adaptation of existing ones [e.g., 3,4,5,6].…”