  Active micropumping and micromixing using oscillating bubbles form the basis
for various Lab-on-chip applications. Acoustically excited oscillatory bubbles
are commonly used in active particle sorting, micropumping, micromixing,
ultrasonic imaging, cell lysis and rotation. For efficient micromixing, the
system must be operated at its resonant frequency where amplitude of
oscillation is maximum. This ensures that high-intensity cavitation
microstreaming is generated. In this work, we determine the resonant
frequencies for the different surface modes of oscillation of a rectangular gas
slug confined at one end of a millichannel using perturbation techniques and
matched asymptotic expansions. We explicitly specify the oscillation frequency
of the interface and compute the surface mode amplitudes from the interface
deformation. This oscillatory flow field at the leading order is also
determined. The effect of aspect ratio of gas slug on observable streaming is
analysed. The predictions of surface modes from perturbation theory are
validated with simulations of the system done in ANSYS Fluent.
