Vibration-Enhanced Droplet Motion Modes: Simulations of Rocking, Ratcheting, Ratcheting With Breakup, and Ejection

Power plant water usage is a coupling of the energy-water nexus; this research investigates water droplet motion, with implications for water recovery in cooling towers. Simulations of a 2.6 mm-diameter droplet motion on a hydrophobic, vertical surface were conducted in XFLOW using the lattice Boltzmann method (LBM). Results were compared to two experimental cases; in the first case, experimental and simulated droplets experienced 30 Hz vibrations (i.e., +/- 0.1mm x-direction amplitude, +/- 0.2mm y-direction amplitude) and the droplet ratcheted down the surface. In the second case, 100 Hz vibrations (i.e., +/- 0.8mm x-direction amplitude, +/- 0.2mm y-direction amplitude) caused droplet ejection. Simulations were then conducted for a wide range of frequencies (i.e., 10-100 Hz) and amplitudes (i.e., +/- 0.018-50 mm), resulting in maximum accelerations of 0.197-1970 m/s(2). Under low maximum accelerations (e.g., <7 m/s(2)), droplets rocked upward and downward in rocking mode, but did not overcome the contact angle hysteresis and, therefore, did not move. As acceleration increased, droplets overcame the contact angle hysteresis and entered ratcheting mode. For vibrations that prompted droplet motion, droplet velocities varied between 10-1000 mm/s. At capillary numbers above approximately 0.0044 and Weber numbers above 3.6, liquid breakup was observed in ratcheting droplets (e.g., the formation of smaller child droplets from the parent droplet). It was noted that both x- and y-direction vibrations were required for droplet ejection.