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Register a new userCluster formation and self-assembly in stratified fluids: a novel mechanism for particulate aggregation
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Added by
Richard M. McLaughlin
Publication date
2019
fields
Physics
and research's language is
English
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An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Some examples include: sedimenting marine snow particles in lakes and oceans (central to carbon sequestration), dense microplastics in the oceans (which impact ocean ecology and the food chain), and even iron snow on Mercury (conjectured as its magnetic field source). These fluid systems all have stable density stratification, which is known to trap particulates through upper lightweight fluid coating the sinking particles, thus providing transient buoyancy. The current understanding of aggregation of such trapped matter involves collisions (due to Brownian motion, shear, and differential settling) and adhesion. Here, we observe and rationalize a new fundamental effective attractive mechanism by which particles suspended within stratification may self-assemble and form large aggregates without need for short range binding effects. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and aggregate geometry, which produces toroidal flows. We show that these toroidal flows yield attractive horizontal forces between particles. We observe that many particles demonstrate a collective motion revealing a system which self-assembles, appearing to solve jigsaw-like puzzles on its way to organizing into a disc-like shape, with the effective force increasing as the collective disc radius grows. Control experiments with two objects isolate the individual dynamics, which are quantitatively predicted through numerical integration of the underlying equations of motion. This new mechanism may be an important process in formation of marine snow aggregates and distribution of phytoplankton in lakes and oceans. Further, it potentially provides a new mechanism for general sorting and packing of layered material.
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The interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and lower plates. Lack of conservation occurs even though in this configuration only vertical external forces act on the system. This apparent paradox was seemingly first noticed by Benjamin (J. Fluid Mech., vol. 165, 1986, pp. 445-474) in his classification of the invariants by symmetry groups with the Hamiltonian structure of the Euler equations in two dimensional settings, but it appears to have been largely ignored since. By working directly with the motion equations, the paradox is shown here to be a consequence of the rigid lid constraint coupling through incompressibility with the infinite inertia of the far ends of the channel, assumed to be at rest in hydrostatic equilibrium. Accordingly, when inertia is removed by eliminating the stratification, or, remarkably, by using the Boussinesq approximation of uniform density for the inertia terms, horizontal momentum conservation is recovered. This interplay between constraints,action at a distance by incompressibility, and inertia is illustrated by layer-averaged exact results, two-layer long-wave models, and direct numerical simulations of the incompressible Euler equations with smooth stratification.
Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a Carreau non-Newtonian fluid. The exact solution is used to study the effect of the rheology of the shear-thinning liquid on two-phase flow characteristics considering both gas/liquid and liquid/liquid systems. Concurrent and counter-current inclined systems are investigated, including the mapping of multiple solution boundaries. Aspects relevant to practical applications are discussed, such as the insitu hold-up, or lubrication effects achieved by adding a less viscous phase. A characteristic of this family of systems is that, even if the liquid has a complex rheology (Carreau fluid), the two-phase stratified flow can behave like the liquid is Newtonian for a wide range of operational conditions. The capability of the two-fluid model to yield satisfactory predictions in the presence of shear-thinning liquids is tested, and an algorithm is proposed to a priori predict if the Newtonian (zero shear rate viscosity) behaviour arises for a given operational conditions in order to avoid large errors in the predictions of flow characteristics when the power-law is considered for modelling the shear-thinning behaviour. Two-fluid model closures implied by the exact solution and the effect of a turbulent gas layer are also addressed.
The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the zonal potential vorticity gradient. This equation is applied to the problem of planetary wave modulational instability, where it is used to predict a fastest growing mode of finite wavenumber. A wave-mean flow numerical model is used to test the analytical predictions, and an intuitive explanation of modulational instability and jet asymmetry is given via the motion of planetary wavepackets in phase space.
Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shear-thinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the rheology of a shear-thinning fluid, owing to its capability to describe properly the constant viscosity limits (Newtonian behavior) at low and high shear rates. The results are presented in the form of stability boundaries on flow pattern maps (with the phases superficial velocities as coordinates) for several practically important gas-liquid and liquid-liquid systems. The stability maps are accompanied by spatial profiles of the critical perturbations, along with the distributions of the effective and tangent viscosities in the non-Newtonian layer, to show the influence of the complex rheological behavior of shear-thinning liquids on the mechanisms responsible for triggering instability. Due to the complexity of the considered problem, a working methodology is proposed to alleviate the search for the stability boundary. Implementation of the proposed methodology helps to reveal that in many cases the investigation of the simpler Newtonian problem is sufficient for the prediction of the exact (non-Newtonian) stability boundary of smooth stratified flow (i.e., in case of horizontal gas-liquid flow). Therefore, the knowledge gained from the stability analysis of Newtonian fluids is applicable to those (usually highly viscous) non-Newtonian systems. Since the stability of stratified flow involving highly viscous Newtonian liquids has not been researched in the literature, interesting findings on the viscosity effects are also obtained.
Ruelle predicted that the maximal amplification of perturbations in homogeneous isotropic turbulence is exponential $e^{sigma sqrt{Re} t}$ (where $sigma sqrt{Re}$ is the maximal Liapunov exponent). In our earlier works, we predicted that the maximal amplification of perturbations in fully developed turbulence is faster than exponential $e^{sigma sqrt{Re} sqrt{t} +sigma_1 t}$. That is, we predicted superfast initial amplification of perturbations. Built upon our earlier numerical verification of our prediction, here we conduct a large numerical verification with resolution up to $2048^3$ and Reynolds number up to $6210$. Our direct numerical simulation here confirms our analytical prediction. Our numerical simulation also demonstrates that such superfast amplification of perturbations leads to superfast nonlinear saturation. We conclude that such superfast amplification and superfast nonlinear saturation of ever existing perturbations serve as the mechanism for the generation, development and persistence of fully developed turbulence.
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