Sedimentation particle Reynolds number

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Thus, for any voidage the drag force on a sedimenting particle can be calculated, and the corresponding velocity required to produce this force on a particle at the same voidage in the model is obtained from the experimental results. All the experiments were carried out at particle Reynolds number greater than 500, and under these conditions the observed sedimentation velocity is given by equations 5.76 and 5.84 as ... 

The particle Reynolds number, given by dvpc/t]c, must be smaller than about 0.1, since otherwise turbulence will develop in the wake of the sedimenting particle, decreasing its velocity. Putting v = vs, it turns out that for an oil drop in water, the critical particle size is 140 pm. 

In dilute sedimentation the particle Reynolds numbers are usually low (< 1.0) and in this case the CovRe relation bip can be described sinq>]. Stokes solved the Navier-Stokes equation, which describes the bdiaviour of an infinitesimal elemwt of an incompressible fluid e q>eriencing only gravity as a body force, by assuming the inertia term to be negligible and produced ... 

For non-flocculated systems Richardson and Zaki [1954] were able to draw an analogy between sedimentation and fluidisation and diowed that the settling rate is linked to the terminal settling velocity of the particles by the voidage or volumetric concentration of the solids, raised to a power that is a function of the particle Reynolds number. These relationships are described by the equation ... 

Verifying the applicability of the chosen sedimentation region, by calculating the particle Reynolds number ... 

This expression represents the first form of the general dimensionless equation of sedimentation theory. As the desired value is the velocity of the particle, equation 64 is solved for the Reynolds number ... 

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. 

Da (Dl IDA)m is the Stokes diameter, equal to the diameter of sphere, which in a laminar region (low Reynolds number Re < 0.2), sediments with the same velocity as the considered particle. 

Richardson and Mijkle 63 1 have shown that, at high concentrations, the results of sedimentation and fluidisation experiments can be represented in a manner similar to that used by Carman" 4 1 for fixed beds, discussed in Chapter 4. Using the interstitial velocity and a linear dimension given by the reciprocal of the surface of particles per unit volume of fluid, the Reynolds number is defined as ... 

Because equation 4.18 is applicable to low Reynolds numbers at which the flow is streamline, it appears that the flow of fluid at high concentrations of particles in a sedimenting or fluidised system is also streamline. The resistance to flow in the latter case appears to be about 30 per cent lower, presumably because the particles are free to move relative to one another. 

In order to achieve simultaneous suspension of solid particles and dispersion of gas, it is necessary to define the state when the gas phase is well dispersed. Nienow (1975) defined this to be coincident with the minimum in Power number, Ne, against the aeration number, 1VA, relationship (see Fig. 12 [Sicardi et al., 1981]). While Chapman et al. (1981) accept this definition, their study also showed that there is some critical particle density (relative to the liquid density) above which particle suspension governs the power necessary to achieve a well-mixed system and below which gas dispersion governs the power requirements. Thus, aeration at the critical stirrer speed for complete suspension of solid particles in nonaerated systems causes partial sedimentation of relatively heavy particles and aids suspension of relatively light particles. Furthermore, there may be a similar (but weaker) effect with particle size. Wiedmann et al. (1980), on the other hand, define the complete state of suspension to be the one where the maximum in the Ne-Ren diagram occurs for a constant gas Reynolds number. 

We can use the same record of the trajectory of a particle to determine at the same time its hydrodynamic radius and its density. For sedimentation at low Reynolds number, the average vertical velocity is given by the balance between the body force and the friction force ... 

Using the linear relation between drag coefficient and Reynolds number, a pure laminar flow pattern of the sedimentating particles is implied. For spherical particles, flow is considered as laminar for Reynolds number smaller than 0.1. For Reynolds numbers up to 1, the linear relation with drag coefficient is generally accepted. Several investigators accepted the linear relation as far... 

Sedimentation in liquids During gravitational sedimentation particles dispersed in a liquid settle with a velocity that is a function of their size. For a single, spherical particle in an infinite body of liquid the Stokes law is valid at low settling velocity (Reynolds number <0.2) ... 

Problem 7-24. Sedimentation of a Colloidal Aggregate. Colloidal particles often aggregate because of London-van der Waals or other attractive interparticle forces unless measures are taken to stabilize them. The aggregation kinetics are such that the aggregate formed has a fractal dimension Df, which is often less than the spatial dimension. The fractal dimension measures the amount of mass in a sphere of radius R, i.e., mass R D<. For a fractal aggregate composed of Aprimary particles of radius Op with mass mp, estimate the sedimentation velocity of the aggregate when the Reynolds number for the motion is small. What is the appropriate Reynolds number ... 

In Chapters 3 and 4 we analyze mass and heat transfer in plane channels, tubes, and fluid films. We consider the mass and heat exchange between particles, drops, or bubbles and uniform or shear flows at various Peclet and Reynolds numbers. The results presented are of great importance in obtaining scientifically justified methods for a number of technological processes such as dissolution, drying, adsorption, aerosol and colloid sedimentation, heterogeneous catalytic reactions, absorption, extraction, and rectification. 

A noticeable deviation of sedimentation potentials from Smoluchowski s formula takes place at large siuface concentration variation along the bubble surface. Before considering experimental data, it has to be pointed out that the validity of Smoluchowski s formula for the description of the Dorn effect at large Peclet numbers applies only to solid spherical particles. In particular, the correctness of conclusions of some papers (Dukhin, 1964 Dukhin Buikov, 1965 Derjaguin Dukhin, 1967, 1971) is experimentally confirmed by Usui et al. (1980). Sedimentation potential for four sizes of glass balls appears to be the same. Since the radii of the particles under consideration are approximately 50, 150, 250, and 350 pm, the absence of any effect of Peclet and Reynolds numbers on the sedimentation potential could be demonstrated. 

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