Question 8.5: Anomalies in Particle Settling Provide practical examples o......
Anomalies in Particle Settling
Provide practical examples of anomalies where particles do not appear to obey Stokes’ law.
Stokes’ law assumes a particle or body is able to freely descend with an infinite dilution of the fluid within which it is suspended. This means that it is not affected by nearby objects as other particles or static surfaces. Providing that the other requirements of Stokes’ law are also met, such as a limitation on the Reynolds number, a particle that has reached its terminal velocity can be timed to descend over a fixed distance from which the viscosity of the liquid can be determined, providing the liquid is sufficiently clear to permit the visibility of the movement of the particle. An improvement on the design is to use a sinker within a transparent tube and to time the descent between two points a fixed distance apart. The tube may be open or closed, but either way, as the sinker descends there is a displacement of liquid up around the sinker through the annular gap formed between the sinker and the tube. With the sinker descending with laminar flow, the fluid in contact with the wall of the sinker is assumed to be stationary, and equally, the fluid in contact with the moving sinker has the same velocity as the sinker. Both are called the no-slip condition. The result is that as the sinker descends, it draws the liquid nearby downward, yet for the sinker within the enclosed tube, there is a flow upwards through the annulus at a rate equal to the displacement volume of the sinker descending downward. At some point across the gap between the sinker and the wall, there is a flow upward as shown in Figure 8.2. The fast descent of large particles which provides a net upflow of displaced fluid carrying smaller particles upward is the cause of sedimentary settling in which the large particles form a layer at the bottom and the finer particles eventually settle on top. This phenomenon occurs in many particle settling applications such as in the food industry in which canned foods that feature particles such as meat of various sizes in a sauce form settled layers.
