Competition Between Evaporation Rate and Surface Tension Affecting Particle Deposition in a Sessile Droplet

Abstract A biharmonic stream function equation is solved analytically in axisymmetric toroidal coordinates for Stokes flow in a sessile droplet with a surface tension gradient and diffusive evaporation on the surface. Four different types of streamlines are defined and utilized to predict particle deposition either at the center or at the contact line of the droplet. The impact of UV light radius, droplet's contact angle, and humidity level on the flow pattern is investigated. When the relative humidity is high, the formation of Moffatt eddies is observed. However, the eddy size and the number of eddies decrease with an increase in UV light radius or droplet contact angle. As humidity decreases, the Moffatt eddies are restricted to a specific region, decrease in number and size, and ultimately disappear. Under lower humidity, the Marangoni flow near the contact line is dominated by capillary action. The toroidal streamlines are broken from outside and turned into transporting streamline to deposit more particles on the contact line. The region near the droplet center, where the surface tension gradient is significant, is always dominated by toroidal streamlines.