Thermosolutocapillary convection within a rectangular cavity with dynamic free surface is numerically investigated in the absence of gravitational effects. Both the temperature and solute concentration gradients are applied horizontally. The free surface deformation is captured by the level set method. Two cases of the ratio of thermal to solutal Marangoni number Rσ < −1 and Rσ = −1 are considered. For Rσ< −1, the free surface bulges out near the left wall and bulges in near the right wall; with the increase of Marangoni number, the free surface deformation decreases and with the increase of capillary number and aspect ratio, it increases. For Rσ= −1, the free surface bulges out near the left and right walls and bulges in at the central zone; with the increase of Marangoni number, the free surface deformation mode is changed and with the increase of capillary number and aspect ratio, the free surface deformation increases.

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