Bubble oscillations in a uni-axial extensional flow

The evolution of a bubble in a uniaxial straining flow is a reduced model for bubble dynamics in more complex flows, such as turbulent flows (Rodr\'iguez-Rodr\'iguez \& al., 2006).

We use direct numerical simulations to systematically analyze the dynamics of the first bubble oscillatory modes, as a function of both the Weber number, $W_e$, (ratio of kinetic and surface tension forces) and the Reynolds number, $R_e$, (ratio of kinetic and viscous forces). We show that the temporal evolution of each mode is accurately modeled by a damped forced harmonic oscillator.

The second mode oscillates with a pulsation in $\omega_2(1 - 0.07 W_e)$, where $\omega_2$ is the pulsation in a quiescent flow. We validate the theory of Kang \& Leal (1988) which originates from a coupling between the two first modes of oscillations.

Forcing and damping constants present non trivial dependences on $W_e$ and $R_e$, which are symptomatic of complex boundary layers dynamics. Our study is a rare example where flow-interface coupling can be measured quantitatively.