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 ${10}^4$ 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.

中文翻译：

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亲水条件下驻表面声波对界面失稳的滑移作用

在当前的工作中，我们从理论上分析了滑移现象通过沉积在亲水性基材上的毫米级水滴的表面声波对雾化的影响。首先要考虑作用在母滴自由表面上的驻表面声波进行分析。随后，将润滑理论应用于流场控制方程，从而根据声学毛细管数和Navier滑移系数推导了气液界面的演化方程。这样的方程式的数值解导致简化的液滴模型，该液滴模型描述了在滑移现象的影响下自由表面的时空变形，并且一旦获得了引起的毛细波的不稳定性长度，就预测了雾化阈值。${10}^4$ 赫兹。而且，引起液滴上的扩散现象，这与声学毛细管数的大小密切相关。在这种情况下，亲水条件下的打滑对自由表面动力学有明显影响，与无打滑情况相比，会导致更小的气溶胶特征直径。在这种情况下，本研究提供了一种解析表达式，可以根据滑移系数计算液滴直径。在此过程中，我们假定打滑现象是控制母滴变形机制以及气溶胶特征直径的一种有价值的手段。