Dynamic Characteristics of Water Droplets on a Hydrophobic Membrane under External Acoustic Excitation

Acoustic excitation of water droplets on hydrophobic surfaces alters the shape of droplets and enhances their mobility while presenting potential benefits for self-cleaning operations, which become a necessity for practical applications. The present study examines the dynamic response of water droplets on a hydrophobic low-density polyethylene membrane subjected to an external acoustic excitation. Experiments were conducted to evaluate the dynamic response of the droplets via a high-speed imaging system for detailed observations. Droplet oscillations were analyzed while incorporating droplet size, surface wetting state, fluid properties, and acoustic excitation parameters. The membrane surface was hydrophobized by applying a coating of functionalized nanosilica particles, which resulted in a contact angle of ∼148° ∓ 2° with a hysteresis of about ∼2° ∓ 1°. The results reveal that substantial shape deformation and droplet break-off can occur at resonant frequencies. The droplet puddle under gravity reduces droplet natural frequency by a factor of $\sqrt{\frac{g{d}_m}{2\pi R_d^2}}$; here, d_m is the distance between the hydrophobic surface and droplet mass center and R_d is the droplet radius, which is more pronounced for larger droplets (60 μL). At resonance frequencies, oscillations alter droplet shape considerably and necking leads to break-off and formation of newborn droplets (e.g., 212.6 Hz resonance frequency for a 40 μL droplet). The break-off dynamics followed a power-law relation: $R_{nec}\left(t\right)=0.013{(t_{break-off}-t)}^{2/3}$; here, R_nec is the necking radius and t_break-off is the droplet break-off time, and a newborn droplet with radius ∼5 mm occurs at a break-off time of ∼0.0075 s for a 40 μL droplet. The findings elucidate droplet dynamics under acoustic excitations, pertinent to self-cleaning and fluidic applications, and provide insight into the droplet necking and break-off.