Stokes continuous settling

Batch-operated gravity separations avoid the complications of turbulence in continuous separators. They can be designed besed on Stokes Law for dilute dispersions, where die separation time is that for a dispersed-phase drop to go from the farthest point to the interface 6 = Hill, where 6 is separation dme, H is the height from the farthest point to die interface, and V, is the Stokes Law settling velocity. For systems where coalescence is the limiting mechanism, the ratio of die volume to cross-sectional area should be proportioanl to separation time and is the key parameter. Smell-scale batch tests can be used to confirm sizing or separation time. 

The expression given in Eq. (O) for the terminal settling velocity only applies to particles with diameters >1.5 p,m because its derivation is based on the assumption that the relative speed of the air at the surface of the particle is zero. However, as the particle becomes smaller, the air molecules appear less as a continuous fluid and more as discrete molecules separated by space through which the particles can slip. The net effect is that the particles can move faster than predicted by Eq. (O) due to this slipping between gas molecules. To correct for this effect, a correction factor must be applied to the resistance force predicted by Stokes law, Eq. (M). The correction factor, C, is a number greater than 1. Thus Eq. (M) is modified to... 

Continuous Centrifugal Sedimentation Theory The Stokes settling velocity of a spherical particle under centrifugal field is given... 

Stokes law is an analytic solution of the Navier-Stokes equation for the simplified flow case with solid particles and creeping flow. If the particles are fluid and in the absence of surface-active components, internal circulation inside the particle will reduce the drag. (Note that this is not necessarily valid for small fluid particles, but these are irrelevant in gravity separation.) The viscosity correction term for this case is given in Eq. (9). From this equation it can be seen that, for large viscosity differences between the dispersed and continuous phases, the settling will approach the Stokes velocity or 3/2 Stokes velocity (the two limiting... 

In systems with rapid coalescence the limiting parameter for separation will be the settling velocity (e.g., the droplet size distribution entering the separator). Flafskjold et al. (21) modeled the outlet oil quality from a continuous model separator by using batch data. The basis for their model was, in addition to Stokes law [Eq. (8)] and the plug-flow approximation [Eq. (11)], the water concentration in the oil outlet as a function of the concentration gradient over the oil phase ... 

In a first step the velocity pattern was calculated for different inlet heights and different throughputs. These velocity vectors are shown in Figure 5. Now for each cell the droplet diameter was calculated when the droplet starts to settle (one droplet in each cell). This point is given when the upward velocity of the continuous phase is balanced by the sinking velocity of the droplets according to Stokes law ... 

Having the droplet diameter at each cell and the time to reach this diameter, an estimation of the ovei settling time was made by use of Stokes equation and the assunq)tion of stagnant continuous phase. The results are presented in Bgure 7A. We can see that with the inlet at the tottom around 80% are settled within 15 min and 98% within one hour, respectively. The results are much worse with the inlet in the middle or the top (a,b,c,d correspond to Figure 6), because smaller drops need a longer time for settling. 

The viscosity of the oil continuous phase is extremely important in sizing a treater. Stokes law, used to determine the settling velocity of a water droplet settling through the continuous oil phase, includes the oil viscosity. As the oil viscosity increases, the settling velocity of a given droplet decreases. This requires that the treater size be increased. 

---