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We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity$$\tilde {w}_b$$compared with the rise velocity in quiescent flow$$w_b$$. The decrease in mean rise velocity of bubbles$$\tilde {w}_b/w_b$$is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number$$Fr=u'/\sqrt {gd}$$, where$$u'$$is the root-mean-square velocity fluctuations,$$g$$is gravity and$$d$$is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For$$Fr > 0.5$$, we confirm the scaling$$\tilde {w}_b / w_b \propto 1 / Fr$$, as proposed previously by Ruthet al.(J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability.
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This content will become publicly available on August 25, 2026
Dynamics and clustering of sedimenting disc lattices
Uniform arrays of particles tend to cluster as they sediment in viscous fluids. Shape anisotropy of the particles enriches this dynamics by modifying the mode structure and the resulting instabilities of the array. A one-dimensional lattice of sedimenting spheroids in the Stokesian regime displays either an exponential or an algebraic rate of clustering depending on the initial lattice spacing (Chajwaet al.2020Phys.Rev.Xvol. 10, pp. 041016). This is caused by an interplay between the Crowley mechanism, which promotes clumping, and a shape-induced drift mechanism, which subdues it. We theoretically and experimentally investigate the sedimentation dynamics of one-dimensional lattices of oblate spheroids or discs and show a stark difference in clustering behaviour: the Crowley mechanism results in clumps comprising several spheroids, whereas the drift mechanism results in pairs of spheroids whose asymptotic behaviour is determined by pair–hydrodynamic interactions. We find that a Stokeslet, or point-particle, approximation is insufficient to accurately describe the instability and that the corrections provided by the first reflection are necessary for obtaining some crucial dynamical features. As opposed to a sharp boundary between exponential growth and neutral eigenvalues under the Stokeslet approximation, the first-reflection correction leads to exponential growth for all initial perturbations, but far more rapid algebraic growth than exponential growth at large dimensionless lattice spacing$$\tilde {d}$$. For discs with aspect ratio$$0.125$$, corresponding to the experimental value, the instability growth rate is found to decrease with increasing lattice spacing$$\tilde {d}$$, approximately as$$\tilde {d}^{ -4.5}$$, which is faster than the$$\tilde {d}^{-2}$$for spheres (Crowley 1971J.FluidMech.vol. 45, pp. 151–159). It is shown that the first-reflection correction has a stabilising effect for small lattice spacing and a destabilising effect for large lattice spacing. Sedimenting pairs predominantly come together to form an inverted ‘T’, or ‘$$\perp$$’, which our theory accounts for through an analysis that builds on Koch & Shaqfeh (1989J.FluidMech. vol. 209, pp. 521–542). This structure remains stable for a significant amount of time.
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- Award ID(s):
- 2319881
- PAR ID:
- 10642516
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 1017
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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