Free-settling ratios

The above expression is known as the free settling ratio of the two particles (minerals) under laminar conditions. In a similar way the ratio under turbulent conditions can be obtained from Newton s law as... 

From the above two expressions for the ratio dj/d2, a general expression for the free settling ratio can be written down as... 

In real slurry reactors, where particles move at velocities much greater than the free-settling velocity and where the particles are often large, the actual Ks is much larger than K - Harriott37,38 showed that the ratio Ks/K usually falls between 1 and 4. As a first estimate, Ks may be twice Kt, which is estimated, under conditions of free flowing velocity of a particle, from Eq. (9-51). 

When a particle is at a sufficient distance from the walls of the container and from other particles so that its fall is not affected by them, the process is called free settling. Interference is less than 1% if the ratio of the particle diameter to the container diameter is less than T.200 or if the particle concentration is less than 0.2 vol % in the solution. When the particles are crowded, they settle at a lower rate and the process is called hindered settling. The separation of a dilute slurry or suspension by gravity settling into a clear fluid and a slurry of higher solids content is called sedimentation. 

Impeller diameter (ft, m) diffusivity (ft /h, mVs) mass-mean diameter (ft, m) mean particle diameter of the ith size (ft, m) particle size or diameter (ft, or m) gravitational constant (32.17 ft/sec or 9.81 m/sec ) diffusional mass transfer coefficient rate of diffusional mass transfer impeller speed (rps) number of particles in the ith size class impeller speed for just suspended state of particles (rps) impeller power (hp, W) vessel diameter (ft, m) particle-free settling velocity (ft/s, or m/s) particle-hindered settling velocity (ft/s, or m/s) mass ratio of suspended solids to liquid time 100 (kg solid/kg liquid) X100 liquid depth in vessel (ft, m)... 

For a very dilute suspension, i.e., e = 1 and (e) = 1, the settling veloeity will be equal to the free-fall veloeity. As no valid theoretieal expression for the funetion (e) is available, eommon praetiee is to rely on experimental data. Note that a unit volume of thiekened sludge eontains e volume of liquid and (1 - e) volume of solid phase, i.e., a unit volume of partieles of sludge eontains e/(l - e) volume of liquid. Denoting a as the ratio of partiele surfaee area to volume, we obtain the hydraulie radius as the ratio of this volume, e/(l - e), to the surfaee, a, when both values are related to the same volume of partieles ... 

The maximum amount of water for any class of cement is usually defined as the ratio that results in the cement particles remaining in suspension until the initial set of the slurry has taken place. If more than the maximum amount of water is used, then the cement particles will settle in such a manner that there will be pockets of free water within the set cement column. 

To sample the settling flux directly, free-floating multiple-sample programmable sediment traps (Pro-Trap) were deployed at all three fjords for about 16 h at each time (trap depth 60 m). The Pro-Trap system consists of four polyvinyl chloride (PVC) sediment tubes, each of 0.018 square meter exposed area (cylinder height of 80 cm, trap aspect ratio A 4 5.3), mounted on a stain-less-steel frame. Depth and angle sensors allowed defining the position of the traps in the water... 

Possible mechanisms of binding to the settling particles should be examined, taking into account the speciation in solution of Cu and Zn. An intriguing relationship exists between total dissolved copper, free copper ion, and copper bound in particles. The ratio of [Cu2+] to total dissolved Cu is about 10 610 As determined from the concentration in settling particles and in the water column, the distribution coefficients for Cu are Kd = 1-5 X 104 L/kg, with variations over the year. 

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