Solutal driven flow is studied for a binary solution submitted to solvent evaporation at the upper free surface. Evaporation induces an increase in the solute concentration close to the free surface and solutal gradients may induce a convective flow driven by buoyancy and/or surface tension. This problem is studied numerically, using several assumptions deduced from previous experiments on polymer solutions. The stability of the system is investigated as a function of the solutal Rayleigh and Marangoni numbers, the evaporative flux and the Schmidt number. The sensitivity of the thresholds to initial perturbations is analyzed. The effect of viscosity variation during drying is also investigated. At last numerical simulations are presented to study the competition between buoyancy and Marangoni effects in the nonlinear regime.