Coupling between the deformation of a liquid convex object and the resulting scattered acoustic field

Abstract

This paper presents a semi-analytical model for calculating the mean deformation of a cylindrical or quasi-spheroidal liquid object placed in standing acoustic waves under the near-field approach. The interaction between the waves and the object is characterized by the angular distribution of the radiation pressure Prad(θ) over the object surface. The key parameters of the model are the Helmholtz number, α, and the object shape aspect ratio, called ϵ for elliptic shapes and ϵg for arbitrary shapes. For elliptic cross-sectional rigid objects, effects are globally dominated by suction for small α or compression for large α, whatever ϵ. When suction predominates, two opposed compression maxima and two opposed suction minima are observed. When compression predominates, an interference pattern with several extrema is observed. For potentially deformable objects, a potential flattening is found whatever α, which is all the more important as ϵ decreases. A general deformation model is developed to quantify the action/reaction loop between the acoustic field and the deformable object of the aspect ratio, ϵg. The acoustic Bond number Boa and a curvature-based parameter, ϵκ, are introduced. As Boa increases, the object flattens whatever α. For small α, convex deformation is observed until a maximum Bond number is reached when ϵg = ϵκ = 0. There, an abrupt change occurs from a convex shape to a planar liquid sheet. Otherwise, a local transition from a convex to a concave shape occurs, for which ϵκ = 0, while ϵg≠0. Our model successfully predicts numerical and experimental results from the literature.