Viscous drag increases from moisture exchange with an ascending bubble

The terminal velocity of a bubble in a viscous fluid, where inertial forces are negligible compared to viscous forces, has been well studied. For interfaces free of surface-active species such as surfactants or contaminants, the ascent velocity is described by the Hadamard-Rybczynski equation; otherwise, it follows the slower Stokes velocity. However, in our observations of bubble dynamics in corn syrup, a common fluid of high viscosity (9 Pa s), bubbles ascend slower than the Stokes equations predict, with the viscous drag coefficient being approximately 23% higher than the Stokes value. To explain this surprising behavior, computations were undertaken to solve the creeping-flow equations for a spherical bubble in a Newtonian fluid with a viscosity that depends on the concentration of a molecular tracer, such as water, subject to advection and diffusion. Numerical simulations investigated various bubble behaviors. The simulations demonstrated that a bubble depletes water in its vicinity, locally increasing the viscosity, which in turn decreases the terminal velocity. Conversely, increasing the water concentration around the bubble decreases the local viscosity, causing the bubble to ascend faster than predicted by the Hadamard-Rybczynski equation. In these two cases, the viscous drag coefficient transitions from a diffusive to an advective regime with increasing Peclet number. At low Péclet numbers, the viscous drag is constant and outside of the range constrained by Hadamard-Rybczynski (2/3) and Stokes (1) values. At high Péclet number, the viscous drag coefficient tends to the range 2/3-1. The Péclet number at this transition is influenced by the specific viscosity-concentration dependence and tracer solubility. These results enhance our understanding of bubble dynamics and coalescence in viscous fluids, crucial for various processes ranging from industrial foaming to volcanic eruptions