Hydrodynamic interactions and extreme particle clustering in turbulence

Bragg, Andrew D.; Hammond, Adam; Dhariwal, Rohit; Meng, Hui

doi:10.1017/jfm.2021.1099

Cited by 16 publications

(63 citation statements)

References 37 publications

(158 reference statements)

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“…This might lead to interesting bifurcations similar to those seen in impacting systems [20]. We note also that Bragg et al [33] observed pairs of spheres that stuck together. These could be the result of inelastic collisions, corresponding to a third qualitatively different collision outcome.…”

Section: Discussionsupporting

confidence: 66%

“…In particular it remains to be seen to which extent the spatial clustering is weakened when the flow becomes time dependent. We note that recent experimental studies [33,36] of colliding particle in turbulence show strong spatial clustering at small separations. Whether or not the clustering mechanism described above can offer an explanation of these observations, depends on whether it survives averaging over different steady linear flows, and to which extent it is weakened by stochastic driving in a time-dependent flow.…”

Section: Discussionmentioning

confidence: 58%

“…Moreover, it is unclear to which extent spatial clustering survives in this case. If it does, it could be a mechanism for the extreme spatial clustering observed in recent experiments [33,36], which remains unexplained.…”

Section: Discussionmentioning

confidence: 96%

“…In our case, the collision dynamics stops at the boundary at R = 2 because we imposed that the droplets coalesce. Recent experiments [33] considered the collision dynamics of glass spheres in turbulence. Glass spheres may roll along the collision sphere at R = 2, leading to new bifurcations [34].…”

Section: Discussionmentioning

confidence: 99%

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Bifurcations in droplet collisions

Dubey,

Gustavsson,

Bewley

et al. 2022

Preprint

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Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of in a steady straining flow show that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity, and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains non-zero in the limit Kn → 0, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a non-dimensional measure of the mean free path of air). Second, the non-monotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called 'closed trajectories' appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel.

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Section: Discussionsupporting

confidence: 66%

Section: Discussionmentioning

confidence: 58%

Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

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Bifurcations in droplet collisions

Dubey,

Gustavsson,

Bewley

et al. 2022

Preprint

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“…One approach to incorporate HI is to modify our descriptions of the relative velocities and radial distributions to account for HI [e.g. 8,10]. For the purposes of this paper, we instead consider drawing values for the relative velocities and radial distributions from the relatively mature theories for noninteracting inertial particles in turbulence, and to modify the corresponding collision-rate prediction with a multiplicative collision efficiency that incorporates a physical understanding of the mechanisms by which HI reduces coalescence rates [e.g.…”

mentioning

confidence: 99%

Relative accelerations characterize the hydrodynamic interaction of cloud droplets

Kearney¹,

Bewley²

2022

Preprint

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Water droplets coalesce into larger ones in atmospheric clouds to form rain. But droplets on collision courses do not always coalesce due to the cushioning effects of the air between them. The extent to which these so-called hydrodynamic interactions reduce coalescence rates is embodied in the collision efficiency, which is often small and is not generally known. In order to characterize the mechanisms that determine the collision efficiency, we exploited new time-resolved three-dimensional droplet tracking techniques to measure the positions of cloud droplet pairs settling through quiescent air. We did so with an unprecedented precision that enabled us to calculate the relative positions, velocities, and accelerations of the droplets at droplet surface-to-surface separations as small as about one-tenth of a droplet diameter. We show that relative accelerations clearly distinguish coalescing from non-coalescing droplet trajectories, the former being associated with relative accelerations that exceeded a threshold value. We outline how relative accelerations relate to hydrodynamic interactions, and present scaling arguments that predict the threshold relative acceleration. We speculate that the relative acceleration distribution of droplets in turbulent clouds can parameterize the collision efficiency, and that this distribution together with the well-known relative position and velocity distributions can generate a physical description of both the collision and coalescence rates of cloud droplets. I. INTRODUCTIONIn warm atmospheric clouds, liquid water droplets are set onto collision courses by mechanisms that include differential sedimentation and turbulence [1][2][3]. The rate at which this happens can be explained by the way turbulence generates droplet relative position and velocity distributions [4,5]. In order for droplets on collision courses to coalescence into one larger droplet, however, they need to squeeze out the air between them, a process that couples the motions of droplets relative to one another through hydrodynamic interaction (HI) [e.g. 6, 7]. These interactions cause droplets to decelerate, which modifies the probability distributions of droplet relative positions and velocities in a way as yet unknown [e.g. 8-10]. The effect is most pronounced precisely where these distributions need to be evaluated, which is at the moment of contact between two droplets.Theoretical and empirical descriptions of the relative velocity distributions [e.g. 11-13] and radial distribution functions [e.g. 14-16] exist for droplets that are separated widely enough that they do not

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Collision Statistics of Droplets in Turbulence Considering Lubrication Interactions, Mobility of Interfaces, and Non-continuum Molecular Effects

Ababaei

Michel

Rosa

2023

Flow Turbulence Combust

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Collision statistics of same-size aerodynamically interacting droplets in homogeneous isotropic turbulence is examined via hybrid direct numerical simulations combined with Lagrangian particle tracking under a point-particle assumption and a one-way momentum coupling. The simulations are performed both in the absence and presence of gravity for various droplet Stokes numbers (0.1–2) over a wide range of liquid water contents (LWCs = 1–30 $$\text {g/m}^3$$ g/m 3 ). Also, the effects of using different representations of the lubrication forces, i.e. a continuum and a non-continuum one, have been investigated. The results have highlighted the importance of considering the aerodynamic interaction, especially in the presence of gravity for the systems that have high LWCs. Likewise, taking the lubrication force into account shows a notable change in statistics, but a non-continuum representation yields results that are close to the continuum one. In addition, the impact of modeling droplets as fluid drops instead of rigid particles has been examined. Obtaining quite close statistics under both cases demonstrates that a rigid particle assumption for water droplets in air is sufficiently accurate owing to the high water-to-air viscosity ratio. Moreover, the collision efficiency is shown to be in the range 60–100% in the absence of gravity, which approaches 100% as the LWC is enlarged. In the presence of gravity, however, the efficiency grows, with both the Stokes number and the LWC, to values as high as 300%. Finally, for settling droplet systems, the enhancement factor due to turbulence is quantified, exhibiting a growth with the LWC and a reduction with the Stokes number.

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Hydrodynamic interactions and extreme particle clustering in turbulence

Cited by 16 publications

References 37 publications

Bifurcations in droplet collisions

Bifurcations in droplet collisions

Relative accelerations characterize the hydrodynamic interaction of cloud droplets

Collision Statistics of Droplets in Turbulence Considering Lubrication Interactions, Mobility of Interfaces, and Non-continuum Molecular Effects

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