History effects in the sedimentation of light aerosols in turbulence: The case of marine snow

Guseva, Ksenia; Daitche, Anton; Feudel, Ulrike; Tél, Tamás

doi:10.1103/physrevfluids.1.074203

Cited by 22 publications

(23 citation statements)

References 55 publications

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“…• Planktons: Planktons in the ocean come in various sizes and different density ratios. The effect of turbulence on clustering (Guseva et al 2016) is poorly understood and we believe Basset history, given its non-trivial dynamics, might play a role in its settling. A plankton of size a ∼ 100µm has a terminal velocity of U t ∼ 0.1mm/s when ∆ρ/ρ ∼ 0.1 (where ∆ρ is the difference between particle density and fluid density and ρ being density of water).…”

Section: Explicit Solution For Particular Flowsmentioning

confidence: 97%

Accurate solution method for the Maxey–Riley equation, and the effects of Basset history

2019

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The Maxey-Riley equation has been extensively used by the fluid dynamics community to study the dynamics of small inertial particles in fluid flow. However, most often, the Basset history force in this equation is neglected. Analytical solutions have almost never been attempted because of the difficulty in handling an integro-differential equation of this type. Including the Basset force in numerical solutions of particulate flows involves storage requirements which rapidly increase in time. Thus the significance of the Basset history force in the dynamics has not been understood. In this paper, we show that the Maxey-Riley equation in its entirety can be exactly mapped as a forced, time-dependent Robin boundary condition of the one-dimensional diffusion equation, and solved using the Unified Transform Method.We obtain the exact solution for a general homogeneous time-dependent flow field, and apply it to a range of physically relevant situations. In a particle coming to a halt in a quiescent environment, the Basset history force speeds up the decay as stretchedexponential at short time while slowing it down to a power-law relaxation, ∼ t −3/2 , at long time. A particle settling under gravity is shown to relax even more slowly to its terminal velocity (∼ t −1/2 ), whereas this relaxation would be expected to take place exponentially fast if the history term were to be neglected. An important mechanism for the growth of rain drops is by the gravitational settling of larger drops through an environment of smaller droplets, and repeatedly colliding and coalescing with them. Using our solution we estimate that the rate of growth rate of a rain drop can be gross overestimated when history effects are not accounted. We solve exactly for particle motion in a plane Couette flow and show that the location (and final velocity) to which a particle relaxes is different from that due to Stokes drag alone.For a general flow, our approach makes possible a numerical scheme for arbitrary but smooth flows without increasing memory demands and with spectral accuracy. We use our numerical scheme to solve an example spatially varying flow of inertial particles in the vicinity of a point vortex. We show that the critical radius for caustics formation shrinks slightly due to history effects.Our scheme opens up a method for future studies to include the Basset history term in their calculations to spectral accuracy, without astronomical storage costs. Moreover our results indicate that the Basset history can affect dynamics significantly.

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Section: Explicit Solution For Particular Flowsmentioning

confidence: 97%

Accurate solution method for the Maxey–Riley equation, and the effects of Basset history

2019

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“…The description (4) would be applicable in other circumstances beyond the ones described above, but, of course, there would be situations -for example, coastal wave-breaking turbulence environments, industrial flows, or (other) cases in which St is not small enough -in which inertial terms will have central importance, with effects that have been studied in recent works [13][14][15][16][17][18] .…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…Such an equation of motion, if the fluid flow is incompressible, preserves phase-space volume (note that the phase space coincides here with the configuration space). Thus, inertial effects, which have been typically identified as the main causes for particle clustering (also called preferential concentration) in other situations [13][14][15][16][17][18] , cannot explain inhomogeneities in mesoscale oceanic sedimentation. Then the question is which the mechanisms are that lead to sedimentation inhomogeneities in the absence of particle inertia.…”

Section: Introductionmentioning

confidence: 99%

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

Drótos

Monroy

Hernández-Garcı́a

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform within a finite support in an incompressible flow, advection in the flow will give rise to inhomogeneities in the observed density. In this paper we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting towards a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet. a) gabor@ifisc.uib-csic.es 1 Sedimentation of small particles in complex flows is an outstanding problem in science and technology. In particular, the sinking of biogenic particles from the marine surface to the bottom is a fundamental process of the biological carbon pump, playing a key role in the global carbon cycle. A complete understanding of this problem is still lacking. It has been recently shown that despite fluid incompressibility, sedimenting particles moving as noninertial particles in the ocean on large scales show density inhomogeneities when accumulated on some bottom surface. Here, we analytically derive the relation between the geometry of the flow and the emerging distribution for an initially homogeneous sheet of particles. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out conditions under which an extreme form of inhomogeneity, caustics, can develop.

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“…droplets in clouds (Shaw 2003;Grabowski & Wang 2013), marine snow (Kiorboe 1997;Guseva et al 2016) and sediment transport (Papanicolaou et al 2008). For these problems, it is important to quantify the settling speed of the particles as they fall through the turbulent flow, since this determines the vertical mass flux of the particles.…”

mentioning

confidence: 99%

Multiscale preferential sweeping of particles settling in turbulence

Tom

Bragg

2019

J. Fluid Mech.

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In a seminal article, Maxey (1987, J. Fluid Mech., 174:441-465) presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent Direct Numerical Simulation (DNS) results in Ireland et al. (2016b, J. Fluid Mech., 796:659-711) show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, there are several outstanding questions concerning the role of different turbulent flow scales on the enhanced settling, and the role of the Taylor Reynolds number R λ . The analysis of Maxey does not explain these issues, partly since it was restricted to particle Stokes numbers St ≪ 1. To address these issues, we have developed a new theoretical result, valid for arbitrary St, that reveals the multiscale nature of the mechanism generating the enhanced settling speeds. In particular, it shows how the range of scales at which the preferential sweeping mechanism operates depends on St. This analysis is complemented by results from DNS where we examine the role of different flow scales on the particle settling speeds by coarse-graining the underlying flow. The results show how the flow scales that contribute to the enhanced settling depend on St, and that contrary to previous claims, there can be no single turbulent velocity scale that characterizes the enhanced settling speed. The results explain the dependence of the particle settling speeds on R λ , and show how the saturation of this dependence at sufficiently large R λ depends upon St.The results also show that as the Stokes settling velocity of the particles is increased, the flow scales of the turbulence responsible for enhancing the particle settling speed become larger. Finally, we explored the multiscale nature of the preferential sweeping mechanism by considering how particles preferentially sample the fluid velocity gradients coarsegrained at various scales. The results show that while rapidly settling particles do not preferentially sample the fluid velocity gradients, they do preferentially sample the fluid velocity gradients coarse-grained at scales outside of the dissipation range. This explains the findings of Ireland et al., and further illustrates the truly multiscale nature of the mechanism generating enhanced particle settling speeds in turbulence.

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History effects in the sedimentation of light aerosols in turbulence: The case of marine snow

Cited by 22 publications

References 55 publications

Accurate solution method for the Maxey–Riley equation, and the effects of Basset history

Accurate solution method for the Maxey–Riley equation, and the effects of Basset history

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

Multiscale preferential sweeping of particles settling in turbulence

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