The effect of convection on a propagating front with a liquid product: Comparison of theory and experiments

Abstract

This work is devoted to the investigation of propagating polymerization fronts converting a liquid monomer into a liquid polymer. We consider a simplified mathematical model which consists of the heat equation and equation for the depth of conversion for one-step chemical reaction and of the Navier-Stokes equations under the Boussinesq approximation. We fulfill the linear stability analysis of the stationary propagating front and find conditions of convective and thermal instabilities. We show that convection can occur not only for ascending fronts but also for descending fronts. Though in the latter case the exothermic chemical reaction heats the cold monomer from above, the instability appears and can be explained by the interaction of chemical reaction with hydrodynamics. Hydrodynamics changes also conditions of the thermal instability. The front propagating upwards becomes less stable than without convection, the front propagating downwards more stable. The theoretical results are compared with experiments. The experimentally measured stability boundary for polymerization of benzyl acrylate in dimethyl formamide is well approximated by the theoretical stability boundary. (c) 1998 American Institute of Physics.

Frontal Polymerization

“…McCaughey et al tested the analysis of Garbey et al and found the same bifurcation sequence of antisymmetric to axisymmetric convection in ascending fronts [83] as seen with the liquid/solid case.…”

Free‐Radical Frontal Copolymerization: The Dependence of the Front Velocity on the Monomer Feed Composition and Reactivity Ratios

“…[19] A great deal of attention has also been devoted to the instability of polymerization fronts. The studies focused on linear stability analyses, [20,21] convective instabilities, [22,23] and nonlinear dynamics of polymerization waves. [24][25][26][27] Mathematical models of frontal free-radical polymerization were proposed.…”

Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. I. Linear stability analysis

“…The opposite is the case for other families of reactions 14 such as the chlorite-tetrathionate ͑CT͒, [15][16][17][18][19][20][21][22][23] nitric acid-iron͑II͒, [24][25][26] reactions, or polymerization fronts. 50,51 Here, in isothermal conditions, the reaction products are denser and so a downward propagating front will be buoyantly unstable featuring density fingering while the upward moving front remains stable. An alternative way for reaction-diffusion fronts to become unstable is through the diffusion coefficients of the substrate and autocatalyst being sufficiently different.…”