Numerical simulation of Marangoni convection in a shallow rectangular cavity with a linear solutal boundary condition

Abstract

A series of three-dimensional numerical simulations have been carried out to examine the characteristics of Marangoni convection in a shallow rectangular cavity that is subjected to a linear solutal boundary condition. For the working fluid, two Schmidt number values (moderate and high) (Sc=10 and 100) are chosen. The computed flow velocity and concentration distributions show more unique and complex characteristics compared with those of previous studies used a constant solutal boundary condition. Results also indicate that the flow is steady at a relatively small solutal Marangoni number. The secondary vortices embedded in the liquid layer appear. Number of vortices develop greatly depends on the levels of selected solutal Marangoni and Schmidt numbers. When the solutal Marangoni number exceeds a critical value, the Marangoni flow losses its stability, and a three-dimensional oscillatory flow develops. For the oscillatory flow, compared with the case of constant boundary condition, although a backward transition from chaotic to oscillatory is observed with the use of linear boundary condition at a moderate Schmidt number, the disturbance energy of that is always weaker at the same Marangoni number levels. The evolution sequences of flow instabilities are related to the Schmidt number due to the occurrence of a secondary wave at a higher Schmidt number. In addition, the wave patterns undergo a series of evolutions, namely, expansion, separation, squeezing, and merging during propagation due to the effect of cavity boundaries. As a result, since the waves are confined within the rectangular cavity, the wave patterns of spline-like, horseshoe-like, and wedge-like develop in the domain.