In this paper we model the neutralization of an acid solution in which the hydrogen ions are transported according to Cattaneo's diffusion. The latter is a modification of classical Fickian diffusion in which the flux adjusts to the gradient with a positive relaxation time. Accordingly the evolution of the ions concentration is governed by the hyperbolic telegraph equation instead of the classical heat equation. We focus on the specific case of a marble slab reacting with a sulphuric acid solution and we consider a one-dimensional geometry. We show that the problem is multi-scale in time, with a reaction time scale that is larger than the diffusive time scale, so that the governing equation is reduced to the one-dimensional wave equation. The mathematical problem turns out to be a hyperbolic free boundary problem where the consumption of the slab is described by a nonlinear differential equation. Global well posedness is proved and some numerical simulations are provided.
http://hdl.handle.net/2158/1101190
Titolo: | Mathematical model for acid water neutralization with anomalous and fast diffusion |
Autori di Ateneo: | |
Autori: | CERETANI, ANDREA; BOLLATI, JULIETA; FUSI, LORENZO; ROSSO, FABIO |
Anno di registrazione: | 2018 |
Rivista: | NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS |
Volume: | 41 |
Pagina iniziale: | 509 |
Pagina finale: | 528 |
Abstract: | In this paper we model the neutralization of an acid solution in which the hydrogen ions are transported according to Cattaneo's diffusion. The latter is a modification of classical Fickian diffusion in which the flux adjusts to the gradient with a positive relaxation time. Accordingly the evolution of the ions concentration is governed by the hyperbolic telegraph equation instead of the classical heat equation. We focus on the specific case of a marble slab reacting with a sulphuric acid solution and we consider a one-dimensional geometry. We show that the problem is multi-scale in time, with a reaction time scale that is larger than the diffusive time scale, so that the governing equation is reduced to the one-dimensional wave equation. The mathematical problem turns out to be a hyperbolic free boundary problem where the consumption of the slab is described by a nonlinear differential equation. Global well posedness is proved and some numerical simulations are provided. |
Handle: | http://hdl.handle.net/2158/1101190 |
Appare nelle tipologie: | 1a - Articolo su rivista |