On the Quasi-periodic Gravitational Modulation of Polymerization Front with Solid Product

Karam Allali,Mohamed Belhaq,Saadia Assiyad

doi:10.1051/matecconf/20141609001

Karam Allali, Mohamed Belhaq + Show 1 more

Open Access

https://doi.org/10.1051/matecconf/20141609001

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Abstract

The quasi-periodic gravitational modulation of polymerization front with solid product is studied in this paper. The model we consider includes the heat equation, the equation for the concentration and the Navier-Stokes equations under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled and the convective instability boundary is determined using numerical simulation. Results shown that the convective instability threshold depends strongly on the amplitudes and on the frequencies ratio.

Highlights

Frontal polymerization is the process of converting monomer to polymer via a narrow located zone, called reaction front [1]
While in [3] attention was focused on the problem of reaction front propagation in porous media with liquid reactant and liquid product considering Darcy equation, the present paper reports on the problem of polymerization front with liquid reactant and solid product considering Navier-Stokes equations
In order to study the influence of QP gravitational modulation on convective instability of polymerization front with solid product, we consider that the acceleration b acting on the fluid is given by g + b(t), where g is the gravity acceleration, b(t) = λ1 sin(σ1t) + λ2 sin(σ2t) and λ1, λ2 and σ1, σ2 are the amplitudes and the frequencies of the QP vibration, respectively

Summary

Introduction

Frontal polymerization is the process of converting monomer to polymer via a narrow located zone, called reaction front [1]. Similar study has been made for thermal instability in horizontal Newtonian magnetic liquid layer with non-magnetic rigid boundaries in the presence of a vertical magnetic field and a QP modulation [6] In these works [4, 6], the original problem is systematically reduced to a QP Mathieu equation using Galerkin method truncated to the first order. In order to study the influence of QP gravitational modulation on convective instability of polymerization front with solid product, we consider that the acceleration b acting on the fluid is given by g + b(t), where g is the gravity acceleration, b(t) = λ1 sin(σ1t) + λ2 sin(σ2t) and λ1, λ2 and σ1, σ2 are the amplitudes and the frequencies of the QP vibration, respectively.

Reaction front model

The interface problem

Numerical results

Conclusion