Resonance frequency of different interfacial modes of a slug trapped in a millichannel

Several lab-on-chip applications such as cell lysis, micromixing, and micropumping are based on flows induced by acoustically excited oscillatory bubbles. For high efficiency, such systems have to be operated at their resonant frequency. The confinement effect of the walls has a significant effect on the performance of these lab-on-chip devices. Hence, the resonant frequency is determined by the nature of confinement and its coupling with the liquid flow generated. In this work, we determine the resonant frequencies corresponding to surface modes of oscillation of a rectangular gas slug confined at one end of a milli-channel using perturbation theory. The resonant frequencies for the first four amplitude modes of a gas slug of length 1.6 mm in a channel of width 0.374 mm are 1.533, 4.161, 7.547, and 11.545 kHz, respectively. Higher interface modes are observed at higher driving frequencies. These are verified using simulations in Ansys Fluent and experimental results from a similar geometry. We show that the resonant frequency of all amplitude modes decreases as we increase the aspect ratio (length to width ratio) of the gas slug and decreases marginally with increase in viscosity of liquid for any physically realizable system. We also show that the shear stress decreases monotonically along the wall, away from the gas–liquid–solid contact line.