  We present a semi-analytical theory for the acoustic fields and
particle-trapping forces in a viscous fluid inside a capillary tube with
arbitrary cross section and ultrasound actuation at the walls. We find that the
acoustic fields vary axially on a length scale proportional to the square root
of the quality factor of the two-dimensional (2D) cross-section resonance mode.
This axial variation is determined analytically based on the numerical solution
to the eigenvalue problem in the 2D cross section. The analysis is developed in
two steps: First, we generalize a recently published expression for the 2D
standing-wave resonance modes in a rectangular cross section to arbitrary
shapes, including the viscous boundary layer. Second, based on these 2D modes,
we derive analytical expressions in three dimensions for the acoustic pressure,
the acoustic radiation and trapping force, as well as the acoustic energy flux
density. We validate the theory by comparison to three-dimensional numerical
simulations.
