The unsteady axisymmetric problem of a liquid drop impacting onto a rigid vibrating substrate is studied. Initially, the drop is spherical and touches the flat substrate at a single point. Then, the substrate starts to move toward the drop and vibrate with a small amplitude and high frequency. The early stage of the impact is studied by using the potential flow theory and the Wagner approach in dimensionless variables. The effect of the substrate vibration on the drop impact is described by a single parameter. It is shown that the vibration of the substrate leads to oscillations of the pressure in the contact region. The low-pressure zone periodically appears in the wetted part of the substrate. The low-pressure zone can approach the contact line, which may lead to ventilation with separation of the liquid from the substrate. The magnitude of the low pressure grows in time. The acceleration of the contact line oscillates with time, leading to splashing of the droplet with the local increase of the thickness of the spray jet sheet at a distance from the contact line. The phase shift of the substrate vibration with respect to the impact instant is not studied. Splashing can be produced only by a forced vibration of the substrate. The impact onto an elastically supported rigid plate does not produce splashing. The obtained results and the theoretical model of the initial stage of drop impact are valid for certain ranges of parameters of the problem.

中文翻译：

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液滴在振动基板上的飞溅

研究了液滴撞击刚性振动基板的非定常轴对称问题。最初，液滴是球形的，并在一个点接触平坦的基板。然后，基板开始向液滴移动并以小幅度和高频振动。在无量纲变量中使用势流理论和瓦格纳方法研究了影响的早期阶段。基板振动对下落冲击的影响由单个参数描述。结果表明，基板的振动导致接触区压力的振荡。低压区周期性地出现在基材的润湿部分。低压区可接近接触线，这可导致液体与基材分离的通风。低压的大小随时间增长。接触线的加速度随时间振荡，导致液滴飞溅，并在距离接触线一定距离处局部增加喷射片的厚度。没有研究基板振动相对于冲击瞬间的相移。飞溅只能通过基材的强制振动产生。对弹性支撑的刚性板的冲击不会产生飞溅。获得的结果和跌落冲击初始阶段的理论模型对于问题的某些参数范围是有效的。没有研究基板振动相对于冲击瞬间的相移。飞溅只能通过基材的强制振动产生。对弹性支撑的刚性板的冲击不会产生飞溅。获得的结果和跌落冲击初始阶段的理论模型对于问题的某些参数范围是有效的。没有研究基板振动相对于冲击瞬间的相移。飞溅只能通过基材的强制振动产生。对弹性支撑的刚性板的冲击不会产生飞溅。获得的结果和跌落冲击初始阶段的理论模型对于问题的某些参数范围是有效的。