Division of Bénard-Marangoni cells in bottom heated thin rectangular liquid layers under high supercritical number

Abstract

Though the time-dependent behavior of Bénard-Marangoni (BM) cells has been widely investigated in the past decades, most are concerned with the transformation of geometrical shape whereas few consider its division. Unlike the original incipience of the classical BM cell which comes from a static liquid layer with uniform surface temperature, the cell division occurs in a layer occupied by BM cells. The behavior of cell division is more complex than its original incipience, which is not yet understood clearly. The reason and critical conditions of the division are also unclear. The present work is aimed at these issues and a series of experiments are performed in bottom heated thin layers of silicone oil in rectangular pools. The results demonstrate that the cell division needs three conditions, i.e., an enough high supercritical number ε (= (Mav − Mac)/Mac), an enough high ratio k of local horizontal Marangoni number to local vertical Marangoni number of the cell, and five or more edges of the cell. Under enough high ε, a new cell is generated at a corner of the original cell where k is the largest among the cell corners. The percent of cell division increases with increases of ε and Pr. With increasing ε, the previous generated pentagonal cell further divides and the original cell eventually divides into three or even four cells. The threshold of the average ratio of the maximum local horizontal Marangoni number to the maximum local vertical Marangoni number for incipience of cell division is determined. The mechanisms of cell divisions are clarified and the flow field during division is provided by experiment and numerical simulation. This work helps for understanding the behavior of BM instability after generation.