Robust computational algorithm for simulation of Liesegang patterns

HARISPE, DAVID; GARCÍA AGUIRRE, OCTAVIO; GERLERO, GABRIEL S.; KLER, PABLO A.

Congreso; III Brazil-Argentine Microfluidics Congress - VI Congreso de Microfluídica Argentina; 2022

Liesegang patterns are coloured bands which are formed in numerous reactions that involve theprecipitation of one compound (most frequently salt crystals) produced from the reaction oftwo specific substances under diffusion-dominated conditions. Although Liesegang and otherresearchers studied these phenomena more than a century ago, currently they are receiving arenewed and increasing interest, as far as they can serve as an alternative for the bottom-upmanufacturing of functional nano- and microstructures. Regarding the formation of Liesegangpattern, there exist few models, but the more accepted and used is the Keller–Rubinow model basedon Ostwald’s supersaturation theory. Numerical simulation of the dynamics of these processes is avery active research topic due to the discontinuous nature of the phenomena, which turns thenumerical problem into a challenging task. In fact, very recent works still discuss the ill-posedness ofsuch state-of-the-art models, i.e. as it pertains to numerical implementations of the Keller–Rubinowmodel. In this work, we propose a comprehensive numerical strategy based on original criteria foradaptive timestepping, adaptive meshing, and definition of supersaturation parameters in order toobtain a well-posed numerical formulation for the Liesegang pattern formation phenomena. Thestrategy was tested by using a case from the literature, demonstrating stability and convergencewith reasonable computational costs.