title: Link between alginate reaction front propagation and general reaction diffusion theory.
abstract: We provide a common theoretical framework reuniting specific models for the Ca(2+)-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differential equations that are traditionally solved numerically: the Mikkelsen-Elgsaeter model. Applying the traveling-wave hypothesis as a major simplification, we obtain an analytical solution. The solution indicates that the fundamental properties of the alginate reaction front are governed by a single dimensionless parameter λ. For small λ values, a large depletion zone accompanies the reaction front. For large λ values, the alginate reacts before having the time to diffuse significantly. We show that the λ parameter is of general importance beyond the alginate model system, as it can be used to classify known solutions for second-order reaction diffusion schemes, along with the novel solution presented here. For experimental validation, we develop a microchip model system, in which the alginate gel formation can be carried out in a highly controlled, essentially 1D environment. The use of a filter barrier enables us to rapidly renew the CaCl(2) solution, while maintaining flow speeds lower than 1 μm/s for the alginate compartment. This allows one to impose an exactly known bulk CaCl(2) concentration and diffusion resistance. This experimental model system, taken together with the theoretical development, enables the determination of the entire set of physicochemical parameters governing the alginate reaction front in a single experiment.
authors.affiliation: LMIS4, EPFL, 1015 Lausanne, Switzerland. thomas.braschler@gmail.com
authors.forename: Thomas
authors.initials: T
authors.lastname: Braschler
authors.forename: Ana
authors.initials: A
authors.lastname: Valero
authors.forename: Ludovica
authors.initials: L
authors.lastname: Colella
authors.forename: Kristopher
authors.initials: K
authors.lastname: Pataky
authors.forename: Jürgen
authors.initials: J
authors.lastname: Brugger
authors.forename: Philippe
authors.initials: P
authors.lastname: Renaud
mesh_terms: D000464:Alginates / Q000737:chemistry*; D002118:Calcium / Q000737:chemistry; D004058:Diffusion; D005782:Gels; D020723:Glucuronic Acid / Q000737:chemistry; D006603:Hexuronic Acids / Q000737:chemistry; D007700:Kinetics; D008956:Models, Chemical; D015203:Reproducibility of Results; D013050:Spectrometry, Fluorescence
chemical_list: D000464:Alginates; D005782:Gels; D006603:Hexuronic Acids; D020723:Glucuronic Acid; D002118:Calcium