Three-dimensional double-diffusive Marangoni convection in a cubic cavity is studied in the present paper. Both the temperature and solute concentration gradients are applied horizontally. Direct numerical simulations are carried out for surface-tension Reynolds number $10\le \text{Re}\le 500$, surface-tension ratio $-2\le R_{\sigma }\le 1$, and Lewis number $1<\text{Le}\le 200$. Symmetry-breaking pitchfork bifurcation is observed, which does not exist in the pure thermocapillary case, and the flow field is essentially three dimensional. The evolution of the flow structure, as well as the dependence of the heat and mass transfer rates on the different parameters, is investigated systematically. The simulations are performed until the temporal chaotic flow regime is reached and an atypical bifurcation sequence is identified. Namely, as the thermal forcing of the system increases, the flow can undergo a reverse transition from a temporal chaotic to a steady state. Multiple solution branches exist in some parameter ranges, and these are depicted in terms of the heat and mass transfer rates. Corresponding two-dimensional simulations are also performed to clearly illustrate the deviations from the three-dimensional model. The onset of oscillatory flow from the quiescent equilibrium state is also considered. The present work intends to initiate the study of double-diffusive Marangoni convection in three-dimensional confined cavities with horizontal temperature and concentration gradients.

• Received 3 August 2010

DOI:https://doi.org/10.1103/PhysRevE.82.066305