Philip L. Marston

Axial radiation force of a Bessel beam on a sphere and direction reversal of the force

An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid. The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid. The Bessel beam is characterized by the cone angle beta of its plane wave components where beta=0 gives the limiting case of an ordinary plane wave. Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation. Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam. This condition may also be helpful in the design of acoustic tweezers for biophysical applications. Other potential applications include the manipulation of objects in microgravity. Islands in the (ka, beta) parameter plane having a negative radiation force are calculated for the case of a hexane drop in water. Here k is the wave number and a is the drop radius. Low frequency approximations to the radiation force are noted for rigid, fluid, and elastic solid spheres in an inviscid fluid.

Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory

Deformations of drops and bubbles opposed by surface tension and driven by radiation stresses at the interface are calculated using spherical harmonic expansions for the radial and tangential stresses. Superimposed acoustic waves produce stresses which oscillate at the difference frequency ω of the waves in addition to static stresses. When the effects of viscosity on the acoustic waves are omitted, the tangential radiation stress vanishes; a procedure is proposed for calculating the radial stresses from the theory for ’’Acoustic Radiation Pressure on a Compressible Sphere’’ [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. The calculation of the response assumes incompressible second‐order flow and omits the body forces which are normally asociated with acoustic streaming. Resonance phase shifts and enhancements of the response should occur when ω is close to the natural oscillation frequency of a mode. Quadrupole resonance phase shifts and enhancements have been observed by the author [J. Acoust...

Scattering of a Bessel beam by a sphere

The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.

Critical angle scattering by a bubble: physical-optics approximation and observations

The intensity of light scattered by an air bubble in water is predicted by the geometric-optics calculation of Davis (1955) to have a divergent angular derivative as the critical scattering angle ϕc is approached. Effects of diffraction in the angular region near ϕc are described here. The Fraunhofer diffraction for scattering angles ϕ≤ϕc is estimated using a simplified physical-optics approximation. A ringing and decay of the far-field intensity is predicted that is formally similar to the near-field diffraction of a straight edge. Observation of millimeter radius bubbles in water with collimated monochromatic illumination confirm the existence of this ringing which has a quasi period ≃ 25 mrad. The diffraction calculation gives an approximate description of the relative ϕ of the observed maxima and minima. Fringes with a lower contrast and spacing ≃ 0.3 mrad were also observed; they appear to be caused by the interference of rays with distinct paths. Implications for the critical angle scattering of white light are discussed.

Negative axial radiation forces on solid spheres and shells in a Bessel beam

Prior computations predict that fluid spheres illuminated by an acoustic Bessel beam can be subjected to a radiation force directed opposite the direction of beam propagation. The prediction of negative acoustic radiation force is extended to the cases of a solid poly(methylmethacrylate) PMMA sphere in water and an empty aluminum spherical shell in water. Compared with the angular scattering patterns for plane wave illumination, the scattering into the back hemisphere is suppressed when the radiation force is negative. This investigation may be helpful in the development of acoustic tweezers and in the development of methods for manipulating objects during space flight.

Observations and modeling of the backscattering of short tone bursts from a spherical shell: Lamb wave echoes, glory, and axial reverberations

Tone bursts having durations of 3 or 4 cycles were incident on an air‐filled stainless steel shell in water. The resulting sequence of echoes included a specular reflection and echoes radiated by Lamb waves on the shell. Echo structure was studied for ka of 24 to 75, where a denotes the outer radius; b/a=0.838, where b denotes the inner radius. The amplitudes of Lamb wave echoes were modeled using an elastic generalization of the geometrical theory of diffraction (GTD) [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. The required Lamb wave parameters (the phase velocity cl and damping βl ) were found by the Sommerfeld–Watson method; an efficient numerical method for the computation of the required complex root νl is described. The echoes were identified by comparing arrival times with predictions; bursts reflected from a solid tungsten carbide sphere were used for a reference amplitude. Measurements with ka=24 of the largest Lamb wave echo (which was due to a flexural wave) were made at various back...

Manipulation of fluid objects with acoustic radiation pressure

Abstract: Conditions are summarized for manipulating and stabilizing fluid objects based on the acoustic radiation pressure of standing waves. Examples include (but are not limited to) liquid drops, gas bubbles in liquids, and cylindrical liquid bridges. The emphasis is on situations where the characteristic wavelength of the acoustic field is large in comparison to the relevant dimension of the fluid object. Tables are presented for ease of comparing the signs of qualitatively different radiation force parameters for a variety of fluid objects.

Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation

Understanding acoustic scattering from objects placed on the interface between two media requires incorporation of scattering off the interface. Here, this class of problems is studied in the particular context of a 61 cm long, 30.5 cm diameter solid aluminum cylinder placed on a flattened sand interface. Experimental results are presented for the monostatic scattering from this cylinder for azimuthal scattering angles from 0 degrees to 90 degrees and frequencies from 1 to 30 kHz. In addition, synthetic aperture sonar (SAS) processing is carried out. Next, details seen within these experimental results are explained using insight derived from physical acoustics. Subsequently, target strength results are compared to finite-element (FE) calculations. The simplest calculation assumes that the source and receiver are at infinity and uses the FE result for the cylinder in free space along with image cylinders for approximating the target/interface interaction. Then the effect of finite geometries and inclusion of a more complete Greens function for the target/interface interaction is examined. These first two calculations use the axial symmetry of the cylinder in carrying out the analysis. Finally, the results from a three dimensional FE analysis are presented and compared to both the experiment and the axially symmetric calculations.

Acoustic radiation force on a compressible cylinder in a standing wave

The radiation force-per-length on an infinitely long circular cylinder in an acoustic plane standing wave is expressed in terms of partial-wave scattering coefficients for the corresponding traveling wave scattering problem. This information allows a dimensionless radiation force function to be expressed using coefficients available from two-dimensional scattering theory. Four examples are given for fluid circular cylinders: A hot gas column (used to approximate a small flame), a compressible liquid bridge in a Plateau tank, a liquid bridge in air, and a cylindrical bubble of air in water. A long-wavelength approximation for the force is also examined which is analogous to one for the radiation force on compressible spheres [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. A long-wavelength approximation is also known for the monopole and dipole scattering coefficients of a compressible elliptical cylinder and the radiation force is also examined for that situation. Some of the results for the rad...

High-frequency backscattering enhancements by thick finite cylindrical shells in water at oblique incidence: Experiments, interpretation, and calculations

Impulse response backscattering measurements are presented and interpreted for the scattering of obliquely incident plane waves by air-filled finite cylindrical shells immersed in water. The measurements were carried out to determine the conditions for significant enhancements of the backscattering by thick shells at large tilt angles. The shells investigated are made of stainless steel and are slender and have thickness to radius ratios of 7.6% and 16.3%. A broadband PVDF (polyvinylidene fluoride) sheet source is used to obtain the backscattering spectral magnitude as a function of the tilt angle (measured from broadside incidence) of the cylinder. Results are plotted as a function of frequency and angle. These plots reveal large backscattering enhancements associated with elastic excitations at high tilt angles, which extend to end-on incidence in the coincidence frequency region. Similar features are present in approximate calculations for finite cylindrical shells based on full elasticity theory and t...