Before revision:  We solve the reaction diffusion equations of a phase separating system coupled to hydrodynamic flowsand determine stability diagrams of  droplets as a function of dimensionless viscosity and reaction parameters.
After revision:  In this case chemical activity acts against surface tension and tension-induced hydrodynamic flows. By combining low Reynolds-number hydrodynamics with phase separation dynamics and chemical reaction kinetics we determine stability diagrams of droplets as a function of dimensionless viscosity and reaction parameters.