  Acoustophoresis deals with the manipulation of sub-wavelength scatterers in
an incident acoustic field. The geometric details of manipulated particles are
often neglected by replacing them with equivalent symmetric geometries such as
spheres, spheroids, cylinders or disks. It has been demonstrated that geometric
asymmetry, represented by Willis coupling terms, can strongly affect the
scattering of a small object, hence neglecting these terms may miss important
force contributions. In this work, we present a generalized formalism of
acoustic radiation force and radiation torque based on the polarizability
tensor, where Willis coupling terms are included to account for geometric
asymmetry. Following Gorkov's approach, the effects of geometric asymmetry are
explicitly formulated as additional terms in the radiation force and torque
expressions. By breaking the symmetry of a sphere along one axis using
intrusion and protrusion, we characterize the changes in the force and torque
in terms of partial components, associated with the direct and Willis Coupling
coefficients of the polarizability tensor. We investigate in detail the cases
of standing and travelling plane waves, showing how the equilibrium positions
and angles are shifted by these additional terms. We show that while the
contributions of asymmetry to the force are often negligible for small
particles, these terms greatly affect the radiation torque. Our presented
theory, providing a way of calculating radiation force and torque directly from
polarizability coefficients, shows that in general it is essential to account
for shape of objects undergoing acoustophoretic manipulation, and this may have
important implications for applications such as the manipulation of biological
cells.
