Mass or heat transfer inside a spherical gas bubble at low to moderate Reynolds number

Mass (or heat) transfer inside a spherical gas bubble rising through a stationary liquid is investigated by direct numerical simulation. Simulations were carried out for bubble Reynolds number ranging from 0.1 to 100 and for Péclet numbers ranging from 1 to 2000. The study focuses on the effect of the bubble Reynolds number on both the interfacial transfer and the saturation time of the concentration inside the bubble. We show that the maximum velocity Umax at the bubble interface is the pertinent velocity to describe both internal and external transfers. The corresponding Sherwood (or Nusselt) numbers and the saturation time can be described by a sigmoid function depending on the Péclet number Pemax = Umaxdb/D (db and D being the bubble diameter and the corresponding diffusion coefficient).