Shock propagation in polydisperse bubbly liquids

We investigate the shock dynamics of liquid flows containing small gas bubbles with numerical simulations based on a continuum bubbly flow model. Particular attention is devoted to the effects of distributed bubble sizes and gas-phase nonlinearity on shock dynamics. Ensemble-averaged conservation laws for polydisperse bubbly flows are closed with a Rayleigh-Plesset-type model for single bubble dynamics. Numerical simulations of one-dimensional shock propagation reveal that phase cancellations in the oscillations of different-sized bubbles can lead to an apparent damping of the averaged shock dynamics. Experimentally, we study the propagation of waves in a deformable tube filled with a bubbly liquid. The model is extended to quasi-one-dimensional cases. This leads to steady shock relations that account for the compressibility associated with tube deformation, bubbles and host liquid. A comparison between the theory and the water-hammer experiments suggests that the gas-phase nonlinearity plays an essential role in the propagation of shocks.