Bubble convection within magma reservoirs

Volcanoes are gas-rich hence small bubbles slowly rise in magma reservoirs. Under certain condition of gas flux, bubble size and reservoir height, the bubble rise is no more homogeneous: the collective buoyancy of the bubbles produces instabilities and the bubble motion becomes driven by convection. If such a convection occurs, the residence time of bubbles in the reservoir is reduced and thus eruptive activity is modified. By analogy with thermal convection, we define Rayleigh ($Ra_{b}$) and Prandtl ($Pr_{b}$) numbers for bubble convection. However, the critical $Ra_{b}$ for bubble convection is hardly known from previous studies and its dependence to $Pr_{b}$ is ignored. Laboratory experiments are performed with small bubbles rising in a cylindrical tank filled with viscous oils in order to quantify bubble convection and apply it to real volcanoes. $Ra_{b}$ and $Pr_{b}$ are acurately determined from measurement, via two hydrophones, of bubble size and gas volume fraction. Bubble velocity is obtained by PIV. Experiments show two main regimes: a steady cellular regime at low Rab and a bubble plume regime when Rab is higher. The critical $Ra_{b}$ depends on the critical $Pr_{b}$ for the two transitions.