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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mfrac><mml:mrow><mml:mi>g</mml:mi><mml:msub><mml:mi>d</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:msubsup><mml:mi>R</mml:mi><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:msqrt></mml:math>; here, <i>d</i>_m is the distance between the hydrophobic surface and droplet mass center and <i>R</i>_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: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0.013</mml:mn><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mrow><mml:mi>b</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>k</mml:mi></mml:mrow><mml:mo>-</mml:mo><mml:mrow><mml:mi>o</mml:mi><mml:mi>f</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>; here, <i>R</i>_nec is the necking radius and <i>t</i>_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.