Slippage effect on interfacial destabilization driven by standing surface acoustic waves under hydrophilic conditions

In the present work, we theoretically analyze the influence of the slippage phenomenon on the atomization via surface acoustic waves of a millimeter-order water drop deposited over a hydrophilic substrate. The analysis is conducted by considering, in the first place, a standing surface acoustic wave acting at the free surface of the parent drop. Subsequently, the lubrication theory is applied to the flow field governing equations to derive an evolution equation of the air-liquid interface in terms of the acoustic capillary number and the Navier-slip coefficient. Such an equation's numerical solution leads to a simplified drop model, depicting the spatiotemporal deformation of the free surface under the influence of slippage phenomenon and predicts the atomization threshold once the instability length at the induced capillary waves is achieved. Our numerical simulations show that the high-frequency acoustic excitation under consideration leads to the development of a standing wave at the free surface, which oscillates at a viscous-capillary resonance frequency on order 104 Hz. Moreover, a spreading phenomenon on the fluid drop is induced, strongly linked to the magnitude of the acoustic capillary number. In this scenario, the slippage under hydrophilic conditions has a noticeable impact on the free surface dynamics, causing smaller aerosol characteristic diameters in comparison with the no-slip case. In this context, the present study provides an analytical expression that calculates the droplet diameter in terms of the slip coefficient. In the process, we postulate the slippage phenomenon as a valuable means to control the parent drop's deformation mechanism and, therefore, the aerosol characteristic diameter.