Numerical study on the effect of gravity levels on apparent viscosity of bubbly suspensions

Based on the Couette parallel plate shear flow model, it was investigated on the effects of the gravity level and the liquid-gas viscosity ratio (λ) on the bubble deformation and the apparent viscosity of the bubbly suspension with the volume of fluid method. The results show that, for a given bubbly suspension, the effect of gravity on the bubble deformation and the relative viscosity is great when the shear action is relatively weak. However, the gravity effect can be neglected when the shear action is relatively strong. Additionally, when the gravity level and the shear action are definite, for the bubbly suspension with a small viscosity ratio (i.e., the influence of gravity is far greater than the viscous force), the relative viscosity is related to gravity because gravity has a great effect on the bubble deformation. In this situation, the bubble is stretched in the direction perpendicular to gravity, leading to the decrease of the obstruction of the bubble to the flow and the increase of the area of the free slip surface. Therefore, the relative viscosity is relatively small. On the contrary, when the viscosity ratio is large (i.e., the influence of the viscous force is much larger than that of gravity), the relative viscosity is less affected by gravity due to the weak effect of gravity on the bubble deformation. The large viscous force decreases the bubble deformation, leading to the increase of the obstruction of the bubble to the flow and the decrease of the area of the free slip surface. Thus the relative viscosity is relatively larger than that when the liquid-gas viscosity ratio is small. When the liquid-gas viscosity ratio is larger than 103, the bubble deformation is dominated by the viscous force, and the effect of gravity on the bubble deformation is negligible. Correspondingly, the effect of gravity on the relative viscosity is also negligible when λ ≥ 103.