Robust computational algorithm for simulation of Liesegang patterns

DAVID G. HARISPE; OCTAVIO GARCÍA AGUIRRA; GABRIEL S. GERLERO; PABLO A. KLER

Buenos Aires

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

CNEA - CONICET - AGENCIA

Liesegang patterns are coloured bands which are formed in numerous reactions that involve the precipitation of one compound (most frequently salt crystals) produced from the reaction of two speci￿c substances under di￿usion-dominated conditions. Although Liesegang and other researchers studied these phenomena more than a century ago, currently they are receiving a renewed and increasing interest, as far as they can serve as an alternative for the bottom-up manufacturing of functional nano- and microstructures. Regarding the formation of Liesegang pattern, there exist few models, but the more accepted and used is the Keller–Rubinow model based on Ostwald’s supersaturation theory. Numerical simulation of the dynamics of these processes is a very active research topic due to the discontinuous nature of the phenomena, which turns the numerical problem into a challenging task. In fact, very recent works still discuss the ill-posedness of such state-of-the-art models, i.e. as it pertains to numerical implementations of the Keller–Rubinow model. In this work, we propose a comprehensive numerical strategy based on original criteria for adaptive timestepping, adaptive meshing, and de￿nition of supersaturation parameters in order to obtain a well-posed numerical formulation for the Liesegang pattern formation phenomena. The strategy was tested by using a case from the literature, demonstrating stability and convergence with reasonable computational costs.