We studied ascending fronts of acrylamide polymerization in dimethyl sulfoxide in which the reactants in solution are converted to a gel at a higher temperature than the solution. We have calculated the stability boundary (the critical viscosity at which convection occurs) as a function of the front velocity. We found that in a two-dimensional system the presence of walls does stabilize the front compared to an infinite plane, but the shape of the boundary is not affected. Experimental fronts exhibited antisymmetric convection for low viscosities and low front velocities, as predicted by our calculations. However, the experimentally determined boundary differed significantly from the calculated ones, the experimental fronts being more stable. The shapes of the boundaries differ, and we propose this is caused by the temperature dependence of the viscosity, which is not treated in our analysis.

Abstract.The propagation of a reaction front for liquid-to-solid reaction is studied. The model includes the heat equation, an equation for the concentration of the liquid reactant, and the equations of liquid motion under the Boussinesq approximation.The linear stability of the reaction front is studied, and conditions for cellular and oscillatory instability are determined.

We study the influence of natural convection on stability of reaction fronts in liquids. In our previous article [6] we considered the case where the reactants were in a liquid phase and the product of the reaction was solid. In this paper we study the case where both of them are liquid. We carry out a linear stability analysis and show that the results are essentially different compared to the case of a solid product.

Abstract. Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on the amplitude and on the frequency of vibrations.

Abstract:In this paper we study the interaction between natural convection and heat explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. Stationary and oscillating convection regimes and oscillating heat explosion are observed. The models with quasi-stationary and unstationary Darcy equation are compared.