The passive scalar spectrum in turbulent bubble suspensions*

When bubbles rise in a liquid, due to buoyancy, they induce liquid velocity fluctuations, referred to as bubble-induced turbulence or pseudo-turbulence. These liquid fluctuations differ from the single-phase turbulent fluctuations. The turbulent kinetic energy spectrum scales with a different exponent (-3) compared to the classic Kolmogorov -5/3-spectrum of single-phase isotropic turbulence. However, while the velocity spectrum behavior has been deeply analyzed in the last years with experiments and numerical simulations, we still do not know how bubbles influence the spectrum of a passive scalar. In this work, we assess the statistics of passive scalars in bubble suspensions using fully-resolved Direct Numerical Simulations (DNS). The governing parameters are similar to heat transport in air-water systems with 2.5 mm bubbles at volume fractions of 2-5 %. From the DNS, we identify key mixing mechanisms and observe a double scaling of the scalar spectrum with a -3 power law at the scales below the bubble diameter and a classic -5/3 scaling at larger scales. We also compute the scalar spectral budget and show how the balance of the net transfer and the diffusive dissipation induces the −3 scaling at small scales (where the production is negligible).