In a previous report where internal flows were experimentally visualized in polymer solution droplets receding on a lyophobic surface [Kaneda et al., Langmuir 2008, 24, 9102-9109], the direction of the circulation flow was found to depend on solvent and solute concentration. To identify the reason for this finding, the internal flow in the droplet is investigated numerically. A mathematical model predicts that double circulation flows initiate after a single flow develops at high Marangoni numbers, while only a single circulation flow develops at low Marangoni numbers. The dependencies of the calculated velocities on the solvent and the initial solute concentration agree qualitatively with experiment. It is concluded that the difference of the flow directions that were investigated experimentally is due to such a change in the flow structures. The effects of the contact angle and dimensions on transport phenomena in a droplet are also discussed.