Defects of Bénard cell on a propagating front

Abstract

Bénard-Marangoni convection can be used to self-organize hexagonal convective cells, but defects easily emerge in the hexagonal pattern, which hinders its application in industry. The dynamics of front propagation and defect generation are studied in this paper. We focus especially on the onset process of a local disturbance of a hexagonal pattern, named the "nucleus." The front propagation of the nucleus has been researched through numerical simulations of a model equation and experiments. In the numerical simulations, a single nucleus can evolve into a perfect hexagon pattern under critical or subcritical conditions, and a random disturbance can generate multiple nuclei which evolve into grain boundaries. In addition, under supercritical conditions, defects also emerge as a single nucleus grows. The instability of front propagation is considered to be the mechanism for the generation of irregular patterns. The curvature effect makes the protrusion of the front have a larger velocity in supercriticality, which results in a wavy front, and defects are generated in the concave portion of the front. Also, because of the curvature effect, the front of an irregular pattern has a larger velocity than that of the regular pattern since the protrusion of the front in the irregular pattern increases the average velocity. Experiments have also been carried out by using an infrared camera to analyze front propagation. The results are qualitatively in agreement with the results of numerical simulations. Through the study of defect generation in front propagation, we put forward a method for generating a hexagon pattern which greatly reduces the number of defects.