Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow

Dhanasekaran, Johnson; Roy, Anubhab; Koch, Donald L.

doi:10.1017/jfm.2020.942

Cited by 13 publications

(36 citation statements)

References 34 publications

(89 reference statements)

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“…The model fails because because higher-order corrections in a/R (lubrication forces [8]) matter at small separations. Even with lubrication forces though, the model cannot be used to compute collision efficiencies, because they are determined by the breakdown of the hydrodynamic approximation below the mean-free path [9,30].…”

Section: Resultsmentioning

confidence: 99%

“…Fig. 1(b) suggests that the separatrix explains droplet-collision outcomes, in stark contrast to the neutral case, where the breakdown of continuum hydrodynamics at small interfacial distance s = R − (a 1 + a 2 ) determines whether droplets collide [9,30]. For charged droplets, the attractive Coulomb force dominates at small s because it diverges as ∼ s −1 (log s) −2 [31], and it therefore determines collision outcomes.…”

Section: Resultsmentioning

confidence: 99%

“…How do turbulent fluctuations change the phase-space dynamics, how do they interplay with the mechanisms described above? Little is known, but recent progress was made in describing collision rates of neutral droplets in straining flow; numerical model simulations exhibit a rich variety of different dynamical behaviours, as well as intricate parameter dependencies [30]. The underlying phase-space dynamics is probably quite different from that shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

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Collisions of micron-sized, charged water droplets in still air

Magnusson,

Dubey,

Kearney

et al. 2021

Preprint

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We investigate the effect of electrical charge on collisions of hydrodynamically interacting, micronsized water droplets settling through quiescent air. The relative dynamics of charged droplets is determined by hydrodynamic interactions, particle and fluid inertia, and electrostatic forces. We analyse the resulting relative dynamics of oppositely charged droplets by determining its fixed points and their stable and unstable manifolds. The stable manifold of a saddle point forms a separatrix that separates colliding trajectories from those that do not collide. The qualitative conclusions from this theory are in excellent agreement with experiments.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Collisions of micron-sized, charged water droplets in still air

Magnusson,

Dubey,

Kearney

et al. 2021

Preprint

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“…In the overdamped limit, the relative velocities V (R) are computed using the hydrodynamic mobility tensor that relates particle velocities to the given external forces in a linear flow [7]. The elements of this tensor depend on the particle radii a 1 and a 2 , and on the particle separation R. In non-dimensional variables (R → R/a, t → ts) the equations of motion read [11]…”

Section: Modelmentioning

confidence: 99%

“…Finally consider the small non-monotonic bump in the collision rate for trajectories approaching from the upper half plane for very small Knudsen number, Kn= 10 −3 . Dhanasekaran et al [11] pointed out that the bump is due to trajectories that encircle the collision sphere and collide from below. The Knudsen number needs to be small enough for this to occur, so that grazing separatrices, such as those in Fig.…”

Section: The Grazing Bifurcationmentioning

confidence: 99%

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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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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Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow

Abstract: Abstract

Cited by 13 publications

References 34 publications

Collisions of micron-sized, charged water droplets in still air

Collisions of micron-sized, charged water droplets in still air

Bifurcations in droplet collisions

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

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