Acoustic Radiation Force and Torque on a Solid Elliptic Cylinder

Abstract

Exact expressions for the acoustic radiation torque and force components experienced by elastic cylinders of elliptic cross-section immersed in ideal fluids and placed in a progressive or standing wave field is developed. The classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop analytical expressions in the form of infinite series involving Mathieu and modified Mathieu functions. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding with distinct wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. Numerical calculations of the radiation force and torque function amplitudes are performed in a wide range of frequencies and cross-sectional eccentricities for a stainless steel cylinder submerged in water. Particular attention is paid to assessment of the effects of cross-sectional ellipticity as well as incident field asymmetry on the acoustic radiation force/torque acting on the elliptical cylinder. Limiting case involving an elastic circular or elliptic cylinder in an ideal fluid is considered and fair agreements with well-known solutions are established.

Calculation of Acoustic Radiation Force and Moment in Microfluidic Devices

“…for standing wave (14) (a) (b) 3 shows that the finite element results for very small rigid oblate ellipsoids with zero incidence angle, α=0°, compared well with the results of Marston's formula. This verified the accuracy of the finite element model, and it can be used for different incidence angles and aspect ratios.…”

“…He assumed that the length of the cylinder is infinite. He also confirmed that the calculation of acoustic radiation moment yields zero moment for circular cylinders 14 .…”

“…They used far field integration to avoid the viscous boundary layer around the spheres 8 . Many researchers have used the multipole expansion method in calculating the acoustic radiation force [1][2][3][4][5][6][7][8][14][15][16][17][18][19][20][21][22][23][24][25][26] . The results of their studies corroborate that only the first two terms, monopole and dipole, of the infinite series of multipole expansion are adequate for calculating the force and moment acting on very small spheres and spheroids.…”

“…In the literature review, there are few studies about acoustic radiation moment [13][14] . It is obvious that the radiation moment depends highly on the geometry of the objects.…”

Optical radiation force (per–length) on an electrically conducting elliptical cylinder having a smooth or ribbed surface

“…The aim of this work is therefore directed toward developing a semi-analytical formalism based on the partial wave series expansion method in cylindrical coordinates [10] without any approximations. Another method may consider a wave-basis using infinite series expansions in elliptical Mathieu functions [15][16][17][18][19][20][21], however, the generation and computation of the elliptical functions may not be a straightforward task in numerical implementation.…”