Ultrasonic near-field levitation allows for contactless support and transportation of an object over vibrating surface. We developed an accurate model predicting pressure distribution in the gap between the surface and levitating object. The formulation covers a wide range of the air flow regimes: from viscous squeezed flow dominating in small gap to acoustic wave propagation in larger gap. The paper explains derivation of the governing equations from the basic fluid dynamics. The nonreflective boundary conditions were developed to properly define air flow at the outlet. Comparing to direct computational fluid dynamics modeling our approach allows achieving good accuracy while keeping the computation cost low. Using the model we studied the levitation force as a function of gap distance. It was shown that there are three distinguished flow regimes: purely viscous, viscoacoustic, and acoustic. The regimes are defined by the balance of viscous and inertial forces. In the viscous regime the pressure in the gap is close to uniform while in the intermediate viscoacoustic and the acoustic regimes the pressure profile is wavy. The model was validated by a dedicated levitation experiment and compared to similar published results.
A cell membrane is a very complex medium, which is difficult to study. One of the simplest approaches is to assume it purely elastic or purely viscous. In this paper, we follow the second assumption and derive mathematical model of nearly-planar viscous plate evolving under action of applied forces. The obtained model is non-linear and covers both stretching and bending of the membrane. In contrast to analogous works on viscous sheets, we use a unique scale for velocity components and take a few first terms in asymptotic expansion. The developed approach can be used for description of the cell membrane with nanoparticles inserted.
Ultrasonic near-field levitation allows suspension of a moderately large object at a height of tens of microns above sound actuator. We developed an asymptotic approach to describe the air dynamics in the gap between an acoustic source and the levitating object. The suggested method allows computation of the lifting force. Due to resolving of both viscous and inertial effects, it remains applicable across a wide range of levitation distances. The paper explains theoretical background of the model and presents a numerical solution of the obtained equations. The results are compared to published numerical and experimental data showing very good agreement.
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