Critical settling velocity

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. 

In situ data from the River Neckar were likewise juxtaposed to model data, assuming that the river can be represented initially as a one-dimensional system. Here again the concept of a critical settling velocity, determined by particle and flow system characteristics (leading to a transport capacity Ceq/Co), leads to a satisfactory reproduction of the observed data. 

Not only was drag reduced, but the critical settling velocity was also significantly reduced. In ordinary use, however, these systems lost their effectiveness in one or two days, and fresh solutions had to be used for maximum effectiveness. 

Using these expressions for Upzt for the intermediate region and the Newton s law range, one can etisily develop expressions for the particle size corresponding to the critical settling velocity, f/, = Vz, as well as the case of equalsettling particles. Considerable complexity, however, will be encountered in determining Upzt in concentrated suspensions. 

Once a liquid droplet is allowed to settle through a continuous vapor phase, the settling velocity depends on the particle size, resistance to settling (defined as drag), and densities on vapor and liquid phases. The critical settling velocity is defined as... 

Critical settling velocity, m/sec Terminal velocity, m/sec Volume of settling section, m ... 

Since the size range of the particles to be removed is less than the critical diameter, we are confident that the particles will follow Stokes law. Hence, the settling velocity for a 50 ft size particle is ... 

Clark, P.E. and Quadir, J.A. "Prop Transport in Hydraulic Fractures A Critical Review of Particle Settling Velocity Equations," SPE/DOE paper 9866, 1981 SPE/DOE Low Permeability Symposium, Denver, May 27-29. 

Vapor-Liquid Gravity Separator Design Fundamentals The critical factors in the performance of a horizontal separator are the vapor residence time and the settling rate of the liquid droplets. However, two other factors enter into the design—the vapor velocity must be limited to avoid liquid entrainment, and there must be sufficient freeboard within the vessel to allow for a feed distributor. For vertical separators, the design is based on a vapor velocity that must be less than the settling velocity of the smallest droplet that is to be collected, with due allowance for turbulence and maldistribution of the feed. The vapor residence time is a function of the vapor flow rate (mass), vapor density, and volume of vapor space in the separator, based on the following ... 

While there appears to be some agreement between the observed and theoretical iron oxide solids settling velocities, the observed silicon oxide values appear to be several times greater than expected. This difference in behavior of the silicon oxide and iron oxide slurries cannot be accounted for by density effects. Since the ratio of the density of iron oxide and silica is 2.ll+, the predicted VgT for an iron oxide would be 3.8 times greater than for silica, Further work is needed to determine the critical characteristics of a solid that are important in governing its settling velocity. 

If the skin friction exceeds the critical threshold for resuspension, sedimentary material is I ifted off from the bottom and is transported into the water body. Grainy particles may also be moved by the so-called bed-load transport that occurs already at a lower threshold. Deposition results from the settling of the sediment particles, if the shear stress falls below a certain limit. The critical thresholds, the settling velocities, and the erosion and deposition rates are material constants derived from experiments (Soulsby, 1997). 

If shutdown occurs while pumping a heterogeneous slurry, solids will deposit in a stationary bed along the pipe bottom. To resume the operation of the slurry pipeline, it becomes necessary to resuspend these solids to remove them from the pipe. If the fluid flow rate over the settled solids is gradually increased, a response similar to curve A of Figure 1 is obtained. With increasing shear rate, the wall shear stress decreases until a minimum is reached. The fluid velocity that corresponds to this minimum shear stress is the critical resuspension velocity, Vs (7). 

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). 

---