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Abstract

We develop a theoretical model of anomalous transport with polymerization-reaction dynamics. We are motivated by the experimental problem of actin polymerization occurring in a microfluidic device with a comb-like geometry. Depending on the concentration of reagents, two limiting regimes for the propagation of reaction are recovered: the failure of the reaction front propagation and a finite speed of the reaction front corresponding to the Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) at the long time asymptotic regime. To predict the relevance of these regimes we obtain an explicit expression for the transient time as a function of geometry and parameters of the experimental setup. Explicit analytical expressions of the reaction front velocity are obtained as functions of the experimental setup. (C) 2016 Elsevier Ltd. All rights reserved.