Resonance frequency of different interfacial modes and steady streaming by a slug trapped at one end of a millichannel

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.