Hydrodynamics settling velocity

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

It only operates in continuous mode and uses catalyst particles of a slightly larger size than in BCR an upward flow of L maintains S in suspension, but the L velocity should be slower than the S settling velocity. Stability also requires a very narrow particle size distribution. Hydrodynamics and mass transfer depend on G/L flow ratio. G velocity is usually rather slow, with bubbles rising through a continuous L phase. Heat removal is restricted to use of wall exchangers. 

Settling of a particle with radius a in a dilute suspension is hindered by the drag exerted in a dispersion medium. The resistance of the medium is proportional to the settling velocity of the particle. In a very short time, the particle reaches a constant velocity, known as the terminal velocity. The gravitational force on the particle balances the hydrodynamic resistance of the medium as given by ... 

The other one is to roughly predict the hydrodynamic behavior inside a J-type CCC device, in order to know the best combinations of some experimental conditions to obtain the highest retention of the stationary phase. For this purpose, the research worker may also use the theoretical settling velocity of a droplet of a lighter phase inside the heavier continuous liquid phase. It was demonstrated to be the better way of predicting the hydrodynamic behavior and, consequently, the best combination of experimental parameters for the highest retention of the stationary phase. 

All the above models do not consider the particle-particle interactions, although these interactions influence the settling velocity and ignore the effect of the solid phase on the hydrodynamics in the vessel. As a consequence, the practical range of application is restricted to low solids concentrations. 

The third group of terms on the right-hand side describes particle transport to the collector by gravity forces acting on the suspended particle. Hydrodynamic retardation is included. Here, Nc is a gravity number, that is, the ratio of the Stokes settling velocity of a suspended particle to the superficial or approach velocity of flow. 

Knowing t s.cr, and the actual distribution of sedimentation velocities of a suspension, one can determine the fraction of particulates with < Ws,cT- This reflects the transport capacity Ceq/Co of a system defined by hydrodynamic and particle characteristics. The actual settling velocity of the sedimenting fraction corresponds to the average of this fraction (Figure 3). 

This concept was tested on the basis of experimental data for a onedimensional system. Figure 4 shows the time-dependent decrease of the particulate concentration in an annular flume observed values and those computed according to Equation 12 show good agreement. In the experiments neither the hydrodynamic system nor the characteristics of the suspended matter were varied. One can see that the transport capacity Ceq/Co is constant (always about 50% of the initial concentration C is sedimenting) and independent of the absolute value of Co. This supports the hypothesis that there exists a critical settling velocity t s.cr, which divides the entire amount of particulates into sedimentous and nonsedimentous parts. 

Looking at the meaning of Qc in another way, if the hydrodynamic radius of an aggregate is the radius of a sphere that has the same settling velocity and drag force as the aggregate in question, then S2e can be shown to relate the radius of collision to... 

Dp, catalyst density) and the hydrodynamic parameters (gas, liquid and solid dispersion coefficients, catalyst settling velocity, gas holdup, gas-liquid interfacial area, liquid-solid mass transfer coefficient). The influence of these parameters on the catalyst concentration, reaction rate and conversion is indicated by the arrows. As the gas velocity varies with the conversion, the hydrodynamic parameters, while depending on the gas velocity, will be influenced by the conversion as well. This causes also a modification of the catalyst concentration profile in the reactor. 

It was further demonstrated that this theoretical parameter was the right one to use, as Menet et al. have carried out experiments on the evolution of the hydrodynamic behavior of the butanol-1-water system with the temperature. They showed that the observed change in behavior was explained by an increase in the y p settling velocity with the temperature, and, thus, a decrease of the settling time, explaining the hydrophobic behavior of the solvent system. 

This relationship is fundamental for the calculation of hydrodynamic properties of colloidal objects (e.g. the terminal settling velocity of small spheres). The factor 6ntja is called friction coefiicient its reciprocal is the hydrodynamic mobility fiy. ... 

Once the functional relationship between the hydrodynamic diameters and the aggregate mass is known, one can establish simple models for the average dynamic properties (e.g. for the settling velocity) of suspensions containing aggregates. However, while the aggregate mass is well defined for numeric aggregates, it is difficult to measure in real-life experiments. It is more likely that the radius of... 

As for settling of single particles in Newtonian liquids, the fundamental hydrodynamic characteristic for particle motion in non-Newtonian fluids is again the drag coefficient. Its prediction allows calculations of terminal settling velocities. Note that equation 18.10, which applies to low particle concentrations (below 0.5% by volume) in Newtonian liquids at low Reynolds numbers, can, in principle, also be used non-Newtonian fluids where viscosity // then becomes the apparent viscosity but, depending on the type of the non-Newtonian behaviour (= model), its determination may require an iterative procedure. Each model redefines the particle Reynolds number so that, for example, for a power law fluid characterized by constants n and K... 

A clear and operational boundary should be established between slurry reactors and three phase fluid beds. Particle diameter alone (e.g. d < 200 pm for slurry reactors) is not sufficient and boundaries snould be based on hydrodynamic regime, settling velocities and turbulence parameters. 

Class I Unhindered settling of discrete particles. Non-interacting particles accelerate until a terminal settling velocity is reached, where the hydrodynamic drag and... 

The important hydrodynamic variables are the relative velocity. Vs, between the solids and the liquid (also know as slip velocity) and the rate of renewal of the liquid layer near the solid surface. The relative velocity, Vg, obviously varies from point to point within the vessel, and the average value is difficult to estimate. So, in practice, the relative velocity. Vs, is assumed equal to the free settling velocity, Vt. The renewal of the boundary layer depends on the intensity of turbulence around the solid particle as well as the convective velocity distribution in the vessel. 

We make use of the fact that in the case of a settling dispersion, the hydrodynamic head decreases with time as the denser phase settles. Settling velocities and solids flux profiles may in turn be easily obtained by continuous monitoring of the resonant firequencies of a number of reeds positioned at set levels along the settling zone. 

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