Acoustic radiation force on a spherical contrast agent shell near a vessel porous wall--theory

Analytical solution for acoustic radiation force on a sphere near a planar boundary

Acoustic radiation force on a sphere in an inviscid fluid near a planar boundary, which may be rigid or pressure release, is calculated using spherical wave functions to expand the total pressure field. The condition at the boundary is satisfied with the addition of a reflected wave and an image sphere. The total pressure field, which is exact in the linear approximation, is composed of the incident field, the reflected field, and the scattered fields due to the physical sphere and the image sphere. The expansion coefficients for the pressure field are used to evaluate the acoustic radiation force on the sphere using a known analytical expression obtained from integration of the radiation stress tensor. Calculations illustrate the influence of multiple scattering effects on the radiation force acting on the sphere. The model applies to compressible and elastic spheres and for any incident field structure. An approximation is introduced that extends the analytical model to other types of interfaces, including a fluid-fluid interface. The analytical model is validated by comparisons with an independent finite element model.

Acoustic radiation force on a rigid cylinder between two impedance boundaries in a viscous fluid

Acoustofluidic technology combines acoustic and microfluidic technologies to realize particle manipulation in microchannels driven by acoustic waves, and the acoustic radiation force (ARF) with boundaries is important for particle manipulation in an acoustofluidic device. In the work reported here, the ARF on a free cylinder immersed in a viscous fluid with an incident plane wave between two impedance boundaries is derived analytically and calculated numerically. The influence of multiple scattering between the particle and the impedance boundaries is described by means of image theory, the finite-series method, and the translational addition theorem, and multiple scattering is included partly in image theory. The ARF on a free rigid cylinder in a viscous fluid is analyzed by numerical calculation, with consideration given to the effects of the distances from cylinder edge to boundaries, fluid viscosity, cylinder size, and boundary reflectivity. The results show that the interaction between the two boundaries and the cylinder makes the ARF change more violently with different frequencies, while increasing the viscosity can reduce the amplitude of the ARF in boundary space. This study provides a theoretical basis for particle manipulation by the ARF in acoustofluidics.

Interaction between particles and bubbles driven by ultrasound: Acoustic radiation force on an elastic particle immersed in the ideal fluid near a bubble

A theoretical model is proposed to investigate the acoustic radiation force on the elastic particle for coupled particle-bubble system. Based on the sound scattering theory, an analytical expression of the force function is obtained for the particle in plane wave sound field. Numerical simulations are presented for elastic particle of stainless steel, steel or brass. The results reveal that the presence of bubbles can affect the feature of radiation force curves of particles. The force curve fluctuates, and negative force emerges in the small kR₁ region for certain distance between the bubble and particle. There are more sharp peaks and dips in the curves because of the resonance of the elasticity of the system and the resonant peaks of the acoustic radiation force transfer to low frequencies when the size of elastic particle is increased. The approximate positive flat region is shortened because of the presence of bubble, which may help to optimize the size ranges of particle for acoustic screening. This study provides for improvement of the acoustic manipulation theoretical model.

Acoustic radiation force on a fluid cylindrical particle immersed in water near an impedance boundary

This work presents a theoretical model to calculate the acoustic radiation force of a fluid cylindrical particle immersed in water near a boundary. A solution of the acoustic radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface area, is derived for a cylinder near a boundary in normal incident plane wave by applying the translation addition theorem of cylindrical function. The effects of impedance boundary on acoustic radiation force of a fluid oleic acid cylinder and a mixture fluid cylinder immersed in water are analyzed with particular emphasis on the radius of fluid cylinder and the distance from its center to the impedance boundary. The results reveal that the existence of particle trapping behavior depends on the choice of the nondimensional frequency ka as well as the offset distance from the impedance boundary. This study provides a theoretical basis for acoustic manipulation, which may be of benefit to the improvement and development of the acoustic control technology.

Physical constraints on the non-dimensional absorption coefficients of compressional and shear waves for viscoelastic cylinders

BACKGROUND

Normalized absorption coefficients for the longitudinal and shear waves in viscoelastic (polymer-type) materials, extracted from non-fictional experimental data showed anomalous effects, such as the generation of a negative radiation force (NRF) in plane progressive waves, negative energy absorption and extinction efficiencies and a scattering enhancement, not in agreement with energy conservation.

OBJECTIVE

The objective of this work is directed towards analyzing those anomalies from the standpoint of energy conservation. Physical conditions which demonstrate that the ratio of the normalized absorption coefficients cannot be of arbitrary value but depends on the ratio of the square of the compressional and shear wave speeds, are established and discussed.

METHOD

The necessary physical condition for the validity of the linear viscoelastic (VE) model for any passive (i.e. that does not generate energy) polymeric cylinder with an ultrasonic absorption of hysteresis-type submerged in a non-viscous fluid requires that the absorption efficiency be positive (Q_abs>0) since there are no active radiating sources inside the core material. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce anomalous/unphysical NRF, negative absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency using plane progressive waves, not in agreement with energy conservation.

RESULTS

Based on the partial wave series expansion method in cylindrical coordinates, numerical results for the radiation force, extinction, absorption and scattering energy efficiencies assuming plane progressive wave incidence are performed for three VE polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient, the dimensionless size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the partial-wave mode number n. Physical and mathematical conditions are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. the 2D case) in terms of the sound velocities in the VE material. The physical condition for the spherical 3D case is also noted.

CONCLUSION

For passive materials, the physical conditions must be always satisfied to allow accurate computations of the acoustic radiation force, torque, and energy absorption, extinction and scattering efficiencies for VE cylinders having a hysteresis type of absorption (such as polymers and plastics), and submerged in a non-viscous fluid. The physical conditions must be always satisfied regardless of the shape of the incident field. They also serve to validate and verify experimental data for VE materials and test the accuracy of related numerical computations.

Computing the acoustic radiation force exerted on a sphere using the translational addition theorem

In this paper, the translational addition theorem for spherical functions is employed to calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere arbitrarily suspended in an inviscid fluid. The procedure is also based on the partial-wave expansion method, which depends on the beam-shape and scattering coefficients. Given a set of beam-shape coefficients (BSCs) for an acoustic beam relative to a reference frame, the translational addition theorem can be used to obtain the BSCs relative to the sphere positioned anywhere in the medium. The scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. The method based on the addition theorem is particularly useful to avoid quadrature schemes to obtain the BSCs. We use it to compute the acoustic radiation force exerted by a spherically focused beam (in the paraxial approximation) on a silicone-oil droplet (compressible fluid sphere). The analysis is carried out in the Rayleigh (i.e., the particle diameter is much smaller than the wavelength) and Mie (i.e., the particle diameter is of the order of the wavelength or larger) scattering regimes. The obtained results show that the paraxial focused beam can only trap particles in the Rayleigh scattering regime.

Generalized theory of resonance scattering (GTRS) using the translational addition theorem for spherical wave functions

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent.

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.

Indentation of poroviscoelastic vocal fold tissue using an atomic force microscope

The elastic properties of the vocal folds (VFs) vary as a function of depth relative to the epithelial surface. The poroelastic anisotropic properties of porcine VFs, at various depths, were measured using atomic force microscopy (AFM)-based indentation. The minimum tip diameter to effectively capture the local properties was found to be 25µm, based on nonlinear laser scanning microscopy data and image analysis. The effects of AFM tip dimensions and AFM cantilever stiffness were systematically investigated. The indentation tests were performed along the sagittal and coronal planes for an evaluation of the VF anisotropy. Hertzian contact theory was used along with the governing equations of linear poroelasticity to calculate the diffusivity coefficient of the tissue from AFM indentation creep testing. The permeability coefficient of the porcine VF was found to be 1.80±0.32×10(-15)m(4)/Ns.