The slow motion of a single gas bubble in a non-Newtonian fluid containing surfactants

Abstract

The drag force experienced by bubbles, rising freely in an inelastic shear-thinning fluid is calculated. In particular, the effect of contaminants is considered when the continuous phase can be represented by the power-law or the three parameter Carreau models. Two cases are examined in order to take into account the effect of surfactants: (a) interfacial mass transfer is taken into account via a perturbation around the thermodynamic equilibrium values using Gibbs elasticity, (b) a continuous distribution of impurities over the whole interface (uniform retardation) leading to Marangoni stresses. The relations obtained are based on perturbation methods around the Newtonian solution. The drag force can be evaluated via the rheological model parameters, the physical properties of the system and the concentration of impurities in the fluid. The presence of contamination was found to increase the drag resulting in a decrease of the rise velocity. Inversely, the effect of shear thinning is to decrease the drag, thus leading to a balance between both effects.