Disperse systems dimensionless diameter

The parameter D is known as the axial dispersion coefficient, and the dimensionless number, Pe = uL/D, is the axial Peclet number. It is different than the Peclet number used in Section 9.1. Also, recall that the tube diameter is denoted by df. At high Reynolds numbers, D depends solely on fluctuating velocities in the axial direction. These fluctuating axial velocities cause mixing by a random process that is conceptually similar to molecular diffusion, except that the fluid elements being mixed are much larger than molecules. The same value for D is used for each component in a multicomponent system. 

Another method has been proposed by Blackwell (B16) and by Hiby and Schiimmer (H8) that avoids the necessity of measuring the complete concentration profile. A pipe with a diameter smaller than the system, thus forming an annular region, is used at the sampling point. A mixed mean sample from the annular region is now sufficient to enable one to determine the radial dispersion coefficient. From Eq. (55) this concentration will be, for an annular region of dimensionless radius a,... 

The flow regime transition in liquid-liquid flow could be explained by applying the dimensionless numbers. The flow patterns in liquid-liquid systems depend on the volume fraction of dispersed phase e ) and hydraulic diameter of the microchannel in addition to the dispersed phase Reynolds number... 

There are analogies between the minimum impeller speed Njs for solids suspension and Nmm for drop suspension. Both depend on density difference, continuous phase viscosity, and impeller diameter. However, Njs depends directly on particle size, while Nmin depends instead on interfacial tension and the other physical properties that determine drop size. Skelland and Seksaria (1978) determined the minimum speed to form a liquid-liquid dispersion from two settled (separated) phases of different density and included the sensitivity to impeller location. The vessels used were fully baffled. They determined Nmin for systems of equal volumes of light and heavy phase. Studies included use of single impellers placed midway in the dense phase (C = H/4), at the o/w interface (C = H/2) and midway in the lighter phase (C = 3H/4). They also examined the use of dual impellers located midway in both phases. Several impeller types were tested, including a propeller (Prop), a 45° pitched blade tmbine (PBT), a flat-blade turbine (FBT), and a curved-blade turbine (CBT). Their results are correlated by the following equation, which is dimensionless ... 

---