Velocity hindered

Quite often the settling velocity is modified by the presence of a large number of particles. This hindered settling velocity is a function of soHds concentration and should be measured experimentally or estimated from Hterature correlations (1). 

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,... 

Ut = Terminal settling velocity, ft/sec Fs = CoiTection factor for hindered settling p, po = Density of water or oil, Ib/ff ... 

Normally the vortex finder should extend down into the conical portion of the cyclone. It is thought that the vortex finder plays an important role in the maintenance of a stable spiraling fluid flow in the cyclone, and this makes it more difficult for the particles to leak through the boundary layer on the roof of the lid of the cyclone to the overflow tube.- Without a vortex finder, the efficiency may be reduced by 4-5%. However, an excessive long vortex finder may hinder the high spin velocity in the fluid flow and thus reduce the efficiency of the cyclone. 

The following semi-empirical equation relates the (hindered) settling velocity of a slurry of particles to the settling velocity of a single particle, known as the Richardson and Zaki (1954) (RZ) equation. The RZ equation is also used for liquid fluidization whereby particles are supported by an up-flow of fluid. 

Examination of equation 2.43 shows that the mass flux initially increases as concentration increases but then passes through a maximum and finally declines as velocity decreases due to hindered settling (Figure 2.8). 

V,s = settling velocity for hindered uniform spherical particle, ft/s or m/s (terminal) c = volume fraction solids K = constant given by equation above Nrc = Reynolds number, Dp V,pf/ j. 

For 0.1 volume fraction solids for hindered settling velocity ... 

Overall coefficients, 332 Vertical plate coil, 331 Hindered settling velocities, 231, 236 Horsepower, centrifugal pump driver, 201 Hydraulic performance, calculations, 180-188... 

For example, for equal volumes of gas and liquid ( =0.5), Eq. (266) predicts that the Stokes velocity (which is already very small for relatively fine dispersions) should be reduced further by a factor of 38 due to hindering effects of its neighbor bubbles in the ensemble. Hence in the domain of high values and relatively fine dispersions, one can assume that the particles are completely entrained by the continuous-phase eddies, resulting in a negligible convective transfer, although this does not preclude the existence of finite relative velocities between the eddies themselves. 

Trinh et al. [399] derived a number of similar expressions for mobility and diffusion coefficients in a similar unit cell. The cases considered by Trinh et al. were (1) electrophoretic transport with the same uniform electric field in the large pore and in the constriction, (2) hindered electrophoretic transport in the pore with uniform electric fields, (3) hydrodynamic flow in the pore, where the velocity in the second pore was related to the velocity in the first pore by the overall mass continuity equation, and (4) hindered hydrodynamic flow. All of these four cases were investigated with two different boundary condi-... 

However, deep potential wells, including those on the MEP, may be avoided in the reaction mechanism. Forces exerted on the downhill slope of saddle points or ridges on the PES can impart sufficient velocity (both magnitude and direction) to steer the trajectory past a well, just as a skilled kayaker can avoid a whirlpool in the middle of a river by choosing an appropriate velocity well before the whirlpool is encountered. Multiple pathways can arise when the initial conditions upon surmounting the barrier either facilitate or hinder the avoidance of the well. The reaction OH + CH3F discussed in Section V is an example of this phenomenon. 

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