Mathematical model for acid water neutralization with anomalous and fast diffusion

CERETANI, A.N.; BOLLATI, J.; FUSI, L.; ROSSO, F.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2018 vol. 41 p. 509 - 528

1468-1218

In this paper we model the neutralization of an acid solution in which the hydrogenions are transported according to Cattaneo?s diffusion. The latter is a modificationof classical Fickian diffusion in which the flux adjusts to the gradient with a positiverelaxation time. Accordingly the evolution of the ions concentration is governed bythe hyperbolic telegraph equation instead of the classical heat equation. We focuson the specific case of a marble slab reacting with a sulphuric acid solution andwe consider a one-dimensional geometry. We show that the problem is multi-scalein time, with a reaction time scale that is larger than the diffusive time scale, sothat the governing equation is reduced to the one-dimensional wave equation. Themathematical problem turns out to be a hyperbolic free boundary problem wherethe consumption of the slab is described by a nonlinear differential equation. Globalwell posedness is proved and some numerical simulations are provided.