We investigate the evolution of convective instability in a LiBr–water binary mixture, driven by thermal and solutal Marangoni stresses, through numerical simulations. A small perturbation in absorption at the surface disturbs the equilibrium, generating surface tension gradients that drive Marangoni flows. To isolate and better understand the interplay between the Marangoni effect and absorption, we extended the previous study by investigating the LiBr–water binary system in the absence of gravity. For the first time, we observed the formation of a stable rim in an absorbing binary mixture, which underwent a slight contraction followed by rapid Marangoni spreading. This behavior shows similarities with the flow patterns seen in the “coffee-ring” and Marangoni spreading phenomena in evaporating binary mixtures. On the subsurface, convective motion breaks into several vortices, accompanied by the formation of plumes with reduced mass fraction. As the system evolves, the symmetry of the flow pattern around the cell center breaks down. The absence of buoyancy-driven forces eliminates a key counterforce to Marangoni flows, transforming the previously ordered patterns into non-periodic oscillations, followed by the development of non-stationary but regular patterns. These results complement our earlier findings [P. F. Arroiabe et al., Phys. Fluids 36, 022119 (2024)] where gravitational forces obscured these phenomena.