Concentration Distribution of Photosensitive Liquid in a Droplet Under Ultraviolet Light

A semi-analytical solution for the concentration of photosensitive suspension is developed in a hemispherical droplet illuminated with ultraviolet (UV) laser. A biharmonic equation in stream function is analytically solved using toroidal coordinates, which is used to solve the transport equation for concentration. Flow pattern and photosensitive material concentration are affected by the peak location of the UV light intensity, which corresponds to the surface tension profile. When the laser beam is moved from the droplet center to its edge, a rotationally symmetric flow pattern changes from a single counter clockwise circulation to a circulation pair and finally to a single clockwise circulation. This modulation in the orientation of circulation modifies the concentration distribution of the photosensitive material. The distribution depends on both diffusion from the droplet surface and the Marangoni convection. The region beneath the droplet surface away from the UV light intensity peak has low concentration, while the region near the downward dividing streamline has the highest concentration. When the UV light peak reaches the droplet edge, the concentration is high everywhere in the droplet.