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.

中文翻译：

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重力水平对气泡悬浮液表观粘度影响的数值研究

基于库埃特平行板剪切流动模型，研究了重力水平和液-气粘度比（λ）上的气泡变形和气泡悬浮液的表观粘度随体积流体的变化而变化。结果表明，对于给定的气泡悬浮液，当剪切作用相对较弱时，重力对气泡变形和相对粘度的影响很大。但是，当剪切作用相对较强时，重力效应可以忽略。另外，当重力水平和剪切作用确定时，对于粘度比小的气泡悬浮液（即重力的影响远大于粘性力），因为重力具有很大的相对粘度，所以它与重力有关对气泡变形的影响。在这种情况下，气泡会在垂直于重力的方向上拉伸，从而减少了气泡对流动的阻碍，并增加了自由滑动表面的面积。因此，相对粘度相对较小。相反，当粘度比大时（即，粘滞力的影响远大于重力的影响），由于重力对气泡变形的影响较弱，相对粘度受重力的影响较小。大的粘性力减小了气泡的变形，从而导致气泡对流动的阻碍增加并且自由滑动表面的面积减小。因此，相对粘度比液-气粘度比小的情况下的相对粘度大。液气粘度比大于10时 相反，当粘度比大时（即，粘滞力的影响远大于重力的影响），由于重力对气泡变形的影响较弱，相对粘度受重力的影响较小。大的粘性力减小了气泡的变形，从而导致气泡对流动的阻碍增加并且自由滑动表面的面积减小。因此，相对粘度比液-气粘度比小的情况下的相对粘度大。液气粘度比大于10时 相反，当粘度比大时（即，粘滞力的影响远大于重力的影响），由于重力对气泡变形的影响较弱，相对粘度受重力的影响较小。大的粘性力减小了气泡的变形，从而导致气泡对流动的阻碍增加并且自由滑动表面的面积减小。因此，相对粘度比液-气粘度比小的情况下的相对粘度大。液气粘度比大于10时 大的粘性力减小了气泡的变形，从而导致气泡对流动的阻碍增加并且自由滑动表面的面积减小。因此，相对粘度比液-气粘度比小的情况下的相对粘度大。液气粘度比大于10时 大的粘性力减小了气泡的变形，从而导致气泡对流动的阻碍增加并且自由滑动表面的面积减小。因此，相对粘度比液-气粘度比小的情况下的相对粘度大。液气粘度比大于10时^{如图3所示}，气泡变形以粘性力为主，重力对气泡变形的影响可以忽略。相应地，重力对相对粘度的影响也可以忽略不计，当λ  ≥10 ³。