The rise of a deforming air bubble of fixed volume surrounded by viscoelastic liquids is investigated by an adaptive direct numerical technique coupled with the volume-of-fluid method. The effects of the Weissenberg number (characterizing the strength of elasticity in the flow) and the viscosity ratio on the three-dimensional bubble dynamics have been studied and identified in a wide range of Galilei (Ga) and Eötvös (Eo) numbers, which measure gravitational force over viscous and surface tension forces, respectively. Our results demonstrate that the deformed bubble shape is not a strong predictor of the jump in the rise velocity in different flow regimes; and we verify that in highly elastic flows, the negative wake is mainly responsible for the rising velocity jump, consistent with previous experimental findings. The viscoelasticity induces a cusp shape at large Eo, while the increase in the rising velocity diminishes with a fattened bubble shape. By probing the polymeric conformational state and stresses, it is further indicated that the strain in the fluid is associated with the shear induced by the rising bubble, which produces the release of the elastic stress, giving rise to a fluid downward motion to form the negative wake. Interestingly, we first observe that when Ga is large enough the bubble undergoes a pulsating rising velocity in highly elastic flows due to the vortex shedding in the distant wake region. Moreover, since the development of viscoelastic stresses is closely correlated with the shear-strain response, a larger polymer deformation is seen to be formed at the bubble trailing edge for modest surface tension, which affects the balance between the extensional flow and the shear stresses on the tail interface, leading to the bubble breakup to form a satellite tail.

通过自适应直接数值技术结合流体体积方法研究了固定体积的变形粘弹性液体包围的气泡的上升。在广泛的Galilei（Ga）和Eötvös（Eo）范围内，研究并确定了Weissenberg数（表征流动弹性强度）和粘度比对三维气泡动力学的影响。）数，分别测量重力对粘性力和表面张力的作用。我们的结果表明，变形的气泡形状并不是在不同流动状态下上升速度跳跃的强预测因子。并且我们验证了在高弹性流中，负尾流是速度上升的主要原因，与先前的实验结果一致。粘弹性在大Eo时引起尖头形状，而上升的速度随着发胖的气泡形状而减小。通过探测聚合物的构象状态和应力，进一步表明，流体中的应变与上升气泡引起的剪切有关，从而产生了弹性应力的释放，从而引起流体向下运动，从而形成负压。唤醒。有趣的是，我们首先看到的是，当嘎足够大的气泡由于在远处的尾流区域中的涡旋脱落而在高弹性流中经历了脉动的上升速度。此外，由于粘弹性应力的发展与剪切应变响应密切相关，因此对于适度的表面张力，在气泡尾缘处会形成较大的聚合物变形，这会影响拉伸流和剪切应力之间的平衡。尾部界面，导致气泡破裂，形成卫星尾部。