We present a method for the mixing of fluids in a quasi two-dimensional system with low Reynolds number by means of generating a vortical flow. A two-dimensional cavitation bubble is induced in liquid-expanded phase by locally heating a Langmuir monolayer at the air/liquid interface with an IR laser. The laser-induced cavitation bubble works as a microfluidic pump and generates a thermocapillary flow around the pump. As a result, the surrounding liquid-expanded phase flows in one direction. Perturbing the thermocapillary flow with solid folds that are created by compression and reexpansion of the monolayer induces the vortical flow behind the folds. Applying the equation of creeping flow, we find a torque halfway from the center causing the vortical flow. The vorticity created in this way stretches the liquid-expanded and gaseous phase in the azimuthal direction and at the same time thins both phases in the radial direction. If the vortical flow could be maintained long enough to reach a radial thinning that would allow the interdiffusion of surfactants at the surface, then this technique would open a route for the effective two-dimensional microfluidic mixing at low Reynolds numbers.