Particles, Drops, and Bubbles Moving Across Sharp Interfaces and Stratified Layers

Abstract

Rigid or deformable bodies moving through continuously stratified layers or across sharp interfaces are involved in a wide variety of geophysical and engineering applications, with both miscible and immiscible fluids. In most cases, the body moves while pulling a column of fluid, in which density and possibly viscosity differ from those of the neighboring fluid. The presence of this column usually increases the fluid resistance to the relative body motion, frequently slowing down its settling or rise in a dramatic manner. This column also exhibits specific dynamics that depend on the nature of the fluids and on the various physical parameters of the system, especially the strength of the density/viscosity stratification and the relative magnitude of inertia and viscous effects. In the miscible case, as stratification increases, the wake becomes dominated by the presence of a downstream jet, which may undergo a specific instability. In immiscible fluids, the viscosity contrast combined with capillary effects may lead to strikingly different evolutions of the column, including pinch-off followed by the formation of a drop that remains attached to the body, or a massive fragmentation phenomenon. This review discusses the flow organization and its consequences on the body motion under a wide range of conditions, as well as potentialities and limitations of available models aimed at predicting the body and column dynamics.

Influence of pycnocline on settling behaviour of non-spherical particle and wake evolution

“…7), Re ul ∈ (5,9) and entrance Froude number (Eq. 11), Fr ul ∈ (0.2, 0.4) and in the previous study 25 in two-layered stratification conditions for Re ul ∈ (2,4) and Fr ul ∈ (0.2, 0.8) ( Fig. 3b in 25 ).…”

“…Particles descending through a density stratified ambient fluid are widespread in the natural environment [1][2][3] as well as in engineering processes 4 . Phenomena related to particle settling are particularly significant in natural waters where the vertical variation of temperature and/or salinity induces density gradients in the ocean, estuaries, coastal regions, lakes, and deep hypersaline anoxic basins affecting the dynamics of particles settling in a water column 2,5 .…”

“…The majority of laboratory and numerical studies have considered spherical particles to elucidate settling mechanisms in stratified systems 4 , 30 , while a large group of marine particles is far from the spherical shape; e.g., marine snow 31 , microorganisms 32 , faecal pellets 33 , bioclastic particles such as shells 34 , and microplastics 35 . Nonetheless, the studies on dynamics of non-spherical particles in the presence of background stratification are underrepresented in literature and their potential effects on micro- and macroscale processes in the environment are still unclear.…”

“…Settling dynamics of particles are coupled with the flow field and wake structure formed upstream, which has been well documented for a sphere settling in low and moderate Re number regimes in a linearly stratified fluid. A toroidal standing eddy exists behind a sphere settling in a weak stratification at moderate Re number and the vortex collapses when stratification strengthens and a jet is formed instead 4 , 16 , 17 . Moreover, a bell-shaped structure has been observed on a jet in a constant distance behind a sphere 17 .…”

Deformation of ambient chemical gradients by sinking spheres

“…A number of studies have depicted disturbance of stratification by falling spheres in order to describe increased drag (Eames & Hunt 1997;Srdić-Mitrović, Mohamed & Fernando 1999;Yick et al 2009;Zhang, Mercier & Magnaudet 2019;Magnaudet & Mercier 2020), settling speed anomalies (Abaid et al 2004;Camassa et al 2009Camassa et al , 2010Camassa et al , 2013Doostmohammadi, Dabiri & Ardekani 2014), internal wave generation (Mowbray & Rarity 1967) and buoyant jets behind the sphere (Ochoa & Van Woert 1977;Torres et al 2000;Hanazaki, Kashimoto & Okamura 2009a;Hanazaki, Konishi & Okamura 2009b;Hanazaki, Nakamura & Yoshikawa 2015). These studies indicate that perturbations of the compositional field by a sphere depend on viscosity, diffusivity and buoyancy, which we parameterize by the Reynolds number Re = Wl/ν, the Péclet number Pe = ReSc = Wl/κ and the Froude number Fr = W/Na, where W is the velocity of the sphere, l is the sphere diameter, a is the sphere radius, ν is the kinematic viscosity, κ is the diffusivity, N is the Brunt-Väisälä frequency and Sc = ν/κ is the Schmidt number.…”