Some recent achievements in microfabrication have demonstrated ultrasound-actuated artificial micro-swimmers for medical applications. However, the theoretical model of actuation and swimming is still lacking. Here we report a theoretical study of an acoustically actuated sperm-like artificial micro-swimmer which consists of a rigid head and a flexible flagellum. We provide the quantitative relation between head oscillation amplitude and acoustic pressure and frequency, and the theoretical account of how the flagellum is whipped, which brings about propulsion. The resistive force theory is employed in our model to relate the dynamic response of a flagellum and the motility of the swimmer. In order to make our theoretical model applicable in a realistic design of sperm-like micro-swimmer, we have involved the inertia term and material damping in the governing equation and considered the variable cross-section of a flagellum. The numerical results reveal that the micro-swimmer actuated by ultrasound can achieve a perceptible velocity, especially at resonance. Influences of non-dimensional parameters, such as the resonance index, sperm number, and material damping coefficient, are discussed and a comparison with experimental results demonstrates the validity of the proposed model.

中文翻译：

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声学驱动的人工微游泳器的建模。

在微细加工方面的一些最新成就已经证明了用于医疗应用的超声驱动的人造微细水洗器。但是，仍然缺乏驱动和游泳的理论模型。在这里，我们报告了一种由声学驱动的像精子一样的人工微游泳器的理论研究，该人工微游泳器由刚性头部和柔性鞭毛组成。我们提供了头部振动幅度与声压和频率之间的定量关系，以及鞭毛如何鞭打的理论说明，鞭毛会产生推动力。在我们的模型中采用了阻力理论，将鞭毛的动态响应与游泳者的运动联系起来。为了使我们的理论模型适用于逼真的精子状微游泳器设计，我们将惯性项和材料阻尼包含在控制方程中，并考虑了鞭毛的可变横截面。数值结果表明，超声驱动的微游泳器可以达到可感知的速度，特别是在共振时。讨论了共振系数，精子数和材料阻尼系数等无量纲参数的影响，并与实验结果进行比较，证明了该模型的有效性。