Bubble merger and scaling law of the Rayleigh-Taylor instability with surface tension

•Effects of surface tension on the growth of single and multiple bubbles in the Rayleigh-Taylor instability are studied.•The asymptotic solution for a single bubble is obtained.•Surface tension reduces the growth of a single bubble, but enhances the mixing rate of multiple bubbles at a late time.•The growth coefficient in the scaling law of the mixing zone increases with surface tension.•The discrepancy in the mixing rate between the previous experiment and numerical simulation is discussed.

We present a theoretical model to study the effects of surface tension on the growth of single and multiple bubbles in the Rayleigh-Taylor instability. The asymptotic solution for a single bubble is obtained and is expressed in terms of the Eötvös number. The bubble merger process is also demonstrated from the model. We find the contrasting effects of surface tension: it reduces the growth of a single bubble, but enhances the mixing rate of multiple bubbles at a late time. The bubble merger of Rayleigh-Taylor instability follows the same scaling law of the growth of mixing zone even when surface tension exists, but the growth coefficient in the scaling law increases with surface tension. A comparison with an experimental result is in good agreement.