Liquid-Liquid Polymerization Front under Quasiperiodic Gravitational Modulation

Saadia Assiyad,Mohamed Belhaq,Karam Allali,M Belhaq

doi:10.1051/matecconf/20168307001

Saadia Assiyad, Mohamed Belhaq + Show 2 more

Open Access

https://doi.org/10.1051/matecconf/20168307001

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Abstract

The influence of quasi-periodic gravitational modulation of polymerization front with liquid monomer and liquid polymer is studied in this paper. The model considered includes the heat equation, the equation for the concentration and the Navier-Stokes equations under the Boussinesq approximation. The linear stability analysis of the problem is conducted and by using numerical simulation, the convective instability boundary is carried out. Results obtained show that the convective instability threshold depends on the amplitudes and on the frequencies ratio of the quasi-periodic gravitational modulation. Effect of Prandtl number is also examined.

Highlights

Frontal polymerization is the process of converting monomer to polymer via reaction front [1]
We study the influence of quasi-periodic (QP) gravitational modulation on the convective instability of liquid-liquid polymerization front
Other works were dedicated to analyze the effect of a periodic gravitational modulation on the convective instability with liquid-solid polymerization front in [4] and it was found that the propagation of the reaction is affected by the parameters of vibration, while the case of liquid-liquid polymerization was studied in [5] and it was concluded that, for small vibration amplitudes, the reaction front remains stable and it loses its stability for sufficiently large amplitude of vibrations

Summary

Introduction

Frontal polymerization is the process of converting monomer to polymer via reaction front [1]. Therefor, the equation of motion is considered before and after the reaction zone because, both the monomer and the polymer are liquids In this latter work, the Prandtl number is taken as a constant parameter. This paper is devoted to study the influence of QP gravitational modulation and Prandtl number on convective instability of liquid-liquid frontal polymerization. To this end, 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, respectively, the amplitudes and the frequencies of the QP vibrations.

Frontal polymerization model

The interface problem

Numerical results

Conclusion