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A phenomenological model is proposed to describe the deformation and orientation dynamics of finite-sized bubbles in both quiescent and turbulent aqueous media. This model extends and generalizes a previous work that is limited to only the viscous deformation of neutrally buoyant droplets, conducted by Maffettone & Minale ( J. Non-Newtonian Fluid Mech. , vol. 78, 1998, pp. 227–241), into a high Reynolds number regime where the bubble deformation is dominated by flow inertia. By deliberately dividing flow inertia into contributions from the slip velocity and velocity gradients, a new formulation for bubble deformation is constructed and validated against two experiments designed to capture the deformation and orientation dynamics of bubbles simultaneously with two types of surrounding flows. The relative importance of each deformation mechanism is measured by its respective dimensionless coefficient, which can be isolated and evaluated independently through several experimental constraints without multi-variable fitting, and the results agree with the model predictions well. The acquired coefficients imply that bubbles reorient through body rotation as they rise in water at rest but through deformation along a different direction in turbulence. Finally, we provide suggestions on how to implement the proposed framework for characterizing the dynamics of deformable bubbles/drops in simulations. 

We present simultaneous three-dimensional measurements of deformable finite-sized bubbles and surrounding turbulent flows. The orientations of bubbles are linked to two key mechanisms that drive bubble deformation: the turbulent strain rate and slip velocity between the two phases. The strongest preferential alignment is between the bubbles and slip velocity, indicating the latter plays a dominant role. We also compared our experimental results with the deformation of ideal material elements with no slip velocity or surface tension. Without these, material elements show highly different orientations, further confirming the importance of the slip velocity in the bubble orientation. In addition to deformation, when bubbles begin to break, their relative orientations change significantly. Although the alignment of the severely deformed bubbles with the eigenvectors of the turbulent strain rate becomes much stronger, the bubble semi-major axis becomes aligned with (rather than perpendicular to) the slip velocity through an almost $90^{\circ }$ turn. This puzzling orientation change occurs because the slip velocity contains the contributions from both the bubble and the background flow. As the bubble experiences strong deformation, the rapid elongation of its semi-major axis leads to a large bubble velocity, which dominates the slip velocity and forces its alignment with the bubble's semi-major axis. The slip velocity thereby switches from a driving mechanism to a driven result as bubbles approach breakup. The results highlight the complex coupling between the bubble orientation and the surrounding flow, which should be included when modelling the bubble deformation and breakup in turbulence. 

We present an experimental investigation of the acceleration statistics and the added mass tensor of deformable gas bubbles in turbulence. By simultaneously tracking both bubbles and their surrounding flow in three dimensions, we find two independent ways of estimating the bubble acceleration: either directly measured from three-dimensional bubble trajectories or indirectly calculated from the bubble's equation of motion. When such an equation is projected onto the bubble frame, the added-mass coefficient becomes a diagonal tensor with three elements being linked to the standard deviation of bubble acceleration along three bubble principal axes. This constraint aids in experimentally determining the added mass coefficient tensor. The obtained trend of $C_A$ seems to agree with Lamb's potential flow solutions for spheroids, suggesting that the added-mass force on deformable bubbles can be modelled using spheroids with the same geometry and orientation. In addition, the probability density function of the relative orientation between the semi-major axis of deformed bubbles and the slip acceleration in turbulence is shown. A surprising finding is that the bubble orientation, indicated by the bubble's major axis, is not random in turbulence but rather is preferentially aligned with the slip acceleration. The degree of this alignment increases as bubbles deform more. Because accelerating along the major axis of a more deformed bubble entails reduced added mass, the acceleration standard deviation of deformable bubbles increases as a function of the bubble aspect ratio.