Inverse cascade of the vortical structures near the contact line of evaporating sessile droplets

Abstract

Microscopic imaging as well as the particle image velocimetry (PIV) are carried out to evaluate the concentration, velocity and vorticity fields near the contact line of the nano-particles-laden evaporating sessile droplets. After the onset of the linear thermocapillary instabilities due to the Marangoni perturbations, the non-linear state sets in and the micro-scale jet-like vortex structures are ejected from the contact line towards the center of the droplet. Afterwards, the jet-like vortical structures expand in the spanwise directions and start to interact with the neighbouring structures. Two types of the inverse cascade mechanisms are found to occur. In the first kind, the vortices of the similar length scale merge and continuously produce larger vortices and corresponding wavelength growth. The second inverse cascade mechanism takes place due to the entrainment of the smaller vortices into the larger structures. Both inverse cascade processes are identified as the continuous feeding of the kinetic energy from the smaller scales to the larger scales. For individual micro-jets the velocity field characterizes the jet-like vortex structures ejected from the contact line towards the droplet center opposing the bulk flow from the center towards the contact line. In addition, the vorticity field overlaid by the velocity streamlines identify the sense of rotation of the low pressure zones on either side of the micro-jet as well as the high pressure stagnation point at the tip.