Sedimentation turbulent flow

Those particles with sizes d > d" at a given set of conditions (v, p, Pp, and a ) will settle only in the turbulent flow regime. For particles with sizes d < d, d" will settle only when the flow around the object is in the transitional regime. Recall that the transitional zone occurs in the Reynolds number range of 0.2 to 500. The sedimentation numbers corresponding to this zone are 3.6 < S, < 82,500 and 0.0022 < S2 < 1,515. 

Chapter 3 Diffusion Coefficients. This chapter demonstrates how to estimate the diffusion coefficients of dilute chemical concentrations in water and air. The chapter is important any time that diffusion cannot be ignored in an application of chemical transport and fate. Some of these cases would be in laminar flows, in sediment, in groundwater transport, and close to an interface in turbulent flows. 

In Chapter 21 on box models no distinction was made between a compound being present as a dissolved species or sorbed to solid surfaces (e.g., suspended particles, sediment-water interface). In Boxes 18.5 and 19.1, and also in Illustrative Example 19.6, we learned that several of the transport and transformation processes may selectively act on either the dissolved or the sorbed form of a constituent. For instance, a molecule sitting on the surface of a sedimentaiy particle at the lake bottom does not feel the effect of turbulent flow in the lake water, while the dissolved chemical species is passively moved around by the currents. In contrast, a molecule sorbed to a suspended particle (e.g., an algal cell) can sink through the water column because of gravity, unlike its dissolved counterpart. 

Particle-laden multiphase flows, usually turbulent, cover a wide range of applications, such as pollution control, sediment transport, combustion processes, erosion effects in gas turbines, and so on. One of the most important aspects of particle-laden turbulent flows is the mutual interactions between particles and turbulence. PIV techniques, as a powerful tool other than numerical simulation method and theoretical analysis, have been applied to this research field of particle-laden multiphase flows. Note that, dispersed-phase particles in particle-laden... 

Review of the theory of turbulent flow and its relation to sediment-transportation." Trans. Am. Geophys. Union, Hydrology Sec., 14th ann. meeting, pp. 487-491. 

The thin, clay and iron-rich red layer caps a transition to a calmer water depositional environment. The red layer is predominantly composed of quiet water clay laminae, but at least five separate episodes of turbulent flow introduced clay rip-up clasts into the system. The red layer marks the last occurrence of remobilized clay clasts. These were in turn covered by laminae deposited during the quieter phase of flow. The high iron and kaolinite clay contents suggest an influx of weathered soil sediment. The iron enriched caps on fining upward laminae implies that an extraordinary amount of iron was allowed to settle or precipitate out in quiet water. 

These redox cells can operate on a number of scales that depend on the length of the diffusion path from the point that the oxidised form becomes reduced to the point where it reduces another sediment constituent. In some pelagic cores these diffusion paths can be observed in linear portions of the pore-water profiles (e.g. Sawlan Murray, 1983). Here the sedimentation rate and the carbon burial rate are sufficiently low, relative to diffusion, to extend the processes of early diagenesis over tens of metres into the sediment. In coastal environments the sedimentation rate and the concentration and reactivity of the organic matter is often high, which results in a much more complex pattern. In this case, the distances between the cells are much shorter, since by definition the adjustment must occur more rapidly. Like laminar and turbulent flow, there may come a point where the flow of electrons downwards is better dispersed through eddies , which in this case are transitory micro-environments with small-scale three dimensional diffusion, rather than more stable... 

Sutherland, A. J. (1967). Proposed mechanism for sediment entrainment by turbulent flows. J. Geophys. Res. 72, 6183-6194. 

Sedimentation analysis can be successfully used in systems containing particles with radii in the range between 1 and 100 pm. When larger particles settle in a low viscosity medium, such as water, one has to account for the deviations from the Stokes equation due to turbulent flow of medium around the particles, and introduce correction factors accounting for the acceleration of particles at the beginning of sedimentation. Sedimentation of particles with sizes on the order of fractions of a micron and those of smaller sizes is influenced by the diffusion phenomena to a significant extent (see Chapter V,... 

The transition from a turbulent flow regime with advective and eddy transport to a small scale dominated by viscosity and diffusional transport is apparent when an impermeable solid-water interface such as the sediment surface is approached (Fig. 5.4). According to the classical eddy diffusion theory, the vertical component of the eddy diffusivity, E, decreases as a solid interface is approached according to E = A v where A is... 

In this context the number of particles depositing for given hydraulic conditions (C — Ceq) must be determined. This means that the characteristics of the particulates must be correlated to local parameters describing the turbulent flow field. This leads to a critical sedimentation velocity i s.cr for a particle. It is derived on the basis of an energy balance the potential energy loss attributable to settling in a non-turbulent system must equal the turbulent kinetic energy that must be imparted on the particle in a turbulent flow system to prevent sedimentation (29). 

Suspensions consist of relatively large particles in a liquid. The particles eventually settle unless disturbed by shaking or turbulent flow. Suspensions can be important in biology because the large particles sometimes scatter or reflect light necessary for aquatic species, or they may form a sediment when they settle that can either entrap smaller individuals or choke filtration mechanisms. Suspensions can sometimes be stabilized by detergents that attach the particles to water or by the formation of a gel structure. 

The use of turbulent emulsion flow regime to facilitate integration of drops is justifled by the substantial increase of collision frequency that is achieved in a turbulent flow as compared to the collision frequency during the sedimentation of drops in a quiescent liquid or in a laminar flow. Particles suspended in the liquid are entrained by turbulent pulsations and move chaotically inside the volume in a pattern similar to Brownian motion. Therefore this pulsation motion of particles can be characterized by the effective factor of turbulent diffusion Dj, and the problem reduces to the determination of collision frequency of particles in the framework of the diffusion problem, as it was first done by Smoluchowsld for Brownian motion [18]. A similar approach was first proposed and realized in [19] for the problem of coagulation of non-interacting particles. The result was that the obtained frequency of collisions turned out to be much greater than the frequency found in experiments on turbulent flow of emulsion in pipes and agitators [20, 21]. 

At J —> 0, the expression for h of a drop with mobile surface has an integrable singularity. So, in a laminar flow, particularly, in the process of gravitational sedimentation, a contact between drops is possible even in the absence of molecular forces. In a turbulent flow, the turbulent diffusion factor is Dj 1/H, therefore in the absence of molecular forces, any contact between drops with fully mobile surfaces is also impossible. 

Compare the characteristic time of drop integration in a turbulent flow Tl"" with the characteristic time of gravitational sedimentation of the emulsion (the electric field is present in both cases) ... 

The mechanism of drop coagulation depends on the conditions of mixture flow. In laminar flow, the coagulation is caused by the approach of drops due to different velocities of their motion or in the non-uniform field of velocities of an external medium, or on sedimentation in the gravity field. In a turbulent flow, the approach of drops occurs due to chaotic turbulent pulsations. In comparison with the laminar flow, the number of collisions of drops in unit time increases. Any, even insignificant, mixing of the flow increases the collision frequency. 

Separate from particle/droplet size and the Knudsen number, there is another reason that aerosol sedimentation does not always follow Stokes law. As the flow regime goes from laminar flow (viscous dominated Reynolds number, Af u < 1) to turbulent flow (inertia dominated Reynolds number, Nr > 1000), things change (see Section 6.1 and Equation 6.6 for more on the Reynolds number). 

Figure 2.24 Illustration of flow regimes in aerosol sedimentation, as the flow regime goes from laminar flow (viscous dominated Reynolds number, Nf, < 1) to turbulent flow (inertia...

The chapter by Urdahl, Wayth, Fordedal, Williams, and Bailey begins by discussing droplet break-up processes under both laminar and turbulent flow conditions and in electrostatic fields. The authors then discuss the droplet coalescence process under normal Brownian motion, under gravity sedimentation, and in laminar shear, including turbulent collisions as well as collisions due to electrostatic forces. The remainder of the chapter is devoted to electrostatic-induced separation of the water-in-oil emulsions and emerging technologies. 

In pipes at higher Reynolds numbers, ranging from 2000 to 25 000, and therefore in turbulent flow, Doll has demonstrated the mixing and flocculation conditions in laboratory systems. These employed silica particle suspensions, flocculated with three different cationic polymers, and the turbulent root mean square velocity gradient (G) characterized the influence of flow rate on reaction rate. In West Berlin, a practical pipe flocculator has been used prior to the entry of treated waste water into a sedimentation tank, based on the concepts set out in section 4.10.3, with the pipe set out in a snake-like pattern on the ground surface. 

Hsu, S. T., A. V. Beken, E. Landweber, and J. F. Kennedy. 1971. The distribution of suspended sediment in turbulent flows in circular pipes. Paper presented at the American Institute of Chemical Engeering Conference on Solids Transport in Slurries, Atlantic City, NJ. 

Collision of colloids can be effected by Brownian motion, by velocity gradients resulting from laminar and turbulent flow and so by differential movement in the sedimentation of such particulates. If coagulation is used as technical process for the improvement of solid separation through aggregation, then velocity gradient induced collisions predominate. 

---