Fluid shear rates

Anodic deposition is controlled by either fluid shear (cross-flow filtration) (48), similar to gel-polarization control, or by continual anode replacement (electrodeposited paints) (46). High fluid shear rates can cause deviations from theory when E > (49). The EUF efficiency drops rapidly... 

If the blending process is between two or more fluids with relatively low viscosity such that the blending is not affected by fluid shear rates, then the difference in blend time and circulation between small and large tanks is the only factor involved. However, if the blending involves wide disparities in the density of viscosity and surface tension between the various phases, then a certain level of shear rate may be required before blending can proceed to the required degree of uniformity. 

One potential difficulty with CF-EF is the electrodeposition of the particles at the electrode away from the filtration medium. This phenomenon, if allowed to persist, will result in performance decay of CF-EF with respect to maintenance of the electric field. Several approaches such as momentaiy reverses in polarity, protection of the electrode with a porous membrane or filter medium, and/or utilization of a high fluid shear rate can minimize electrodeposition. 

For non-New tonian fluids, viscosity data are very important. Every impeller has an average fluid shear rate related to speed. For example, foi a flat blade turbine impeller, the average impeller zone fluid shear rate is 11 times the operating speed. The most exact method to obtain the viscosity is by using a standard mixing tank and impeller as a viscosimeter. By measuring the pow er response on a small scale mixer, the viscosity at shear rates similar to that in the full scale unit is obtained. 

According to Smoluchowski s theory (equation 6.53), the agglomeration rate increases proportional with the fluid shear rate 7... 

Camp and Stein (1943) originally proposed for flocculation that the mean fluid shear rate is proportional to the square root of the mean energy dissipation... 

The fluid shear stress actually brings about the mixing process, and is the multiplication of fluid shear rate and viscosity of the fluid [29]. 

Equation (15) indicates that the wall shear stress changes with position on the cell surface and at each position the stress changes with time. Figures 9 and 10 show the distributions of the fluid shear rate in the eddy and the cell surface shear stress as a function of the dimensionless radius, R, and time, yt, respectively. 

The maximum fluid shear rate in the eddy occurs at the radial position R= 1.793 [86] (Fig. 10). Thus, letting cos yt= 1.0, in Eq. (19) gives the maximum shear stress acting on the cell as ... 

If colloids are sufficiently large or the fluid shear rate high, the relative motion from velocity gradients exceeds that caused by Brownian (thermal) effects (orthokinetic agglomeration). 

Since fluid shear rates vary enormously across the radius of a capillary tube, this type of instrument is perhaps not well suited to the quantitative study of thixotropy. For this purpose, rotational instruments with a very small clearance between the cup and bob are usually excellent. They enable the determination of hysteresis loops on a shear-stress-shear-rate diagram, the shapes of which may be taken as quantitative measures of the degree of thixotropy (G3). Since the applicability of such loops to equipment design has not yet been shown, and since even their theoretical value is disputed by other rheologists (L4), they are not discussed here. These factors tend to indicate that the experimental study of flow of thixotropic materials in pipes might constitute the most direct approach to this problem, since theoretical work on thixotropy appears to be reasonably far from application. Preliminary estimates of the experimental approach may be taken from the one paper available on flow of thixotropic fluids in pipes (A4). In addition, a recent contribution by Schultz-Grunow (S6) has presented an empirical procedure for correlation of unsteady state flow phenomena in rotational viscometers which can perhaps be extended to this problem in pipe lines. 

Fluid shear rate Velocity gradient at any point in the mixing tank. 

FIGURE 10 Illustration of average velocity from the radial discharge of a radial flow impeller, showing the definition of fluid shear rate (AV/AY). 

Generally, heat transfer, blending, and solids suspension are governed primarily by the impeller s pumping capacity and not by fluid shear rates. Solid-liquid mass transfer, liquid-liquid mass transfer, and gas-liquid mass transfer have certain requirements for fluid shear in addi-... 

To further sort out the effect of mixing, it is usually desirable to vary the impeller diameter. For example, if a 100-mm impeller had been used in a 300-mm diameter tank for the original runs, and if it were thought that pumping capacity would be more helpful in fluid shear rate, a series of runs with 125- or 150-mm diameter im-... 

Recent systematic studies used steric-S-FFF with well-characterized latex beads of diameters 2-50 pm where the sedimentation force was adjusted to exactly counterbalance the lift force FL [79,301] to provide a measure of FL. This has led to a more subtle view of the hydrodynamic lift forces than expressed by Eq. (85). There are indications that the hydrodynamic lift force is presumably composed of two different contributions (a) the lift force due to the fluid inertial effect ly., which may be described by the theory of hydrodynamic lift forces [289-291], and (b) the hydrodynamic lift force by a near-wall effect ly [61,62,79,301,302]. The latter was experimentally found to be a function of particle diameter dH, the distance of the particle bottom from the wall 8, the fluid shear rate s0, and the fluid viscosity T by ... 

Actually, the fluid shear rate must be multiplied by the vis-... 

Fluid shear stress = y (fluid shear rate)... 

Mixers can be designed to Increase pumping capacity at a constant level of impeller shear rate, which would increase the total horsepower of the system, they can be designed to increase pumping capacity at the expense of fluid shear rate variables, or they can be designed to increase fluid shear rate variables at the expense of pumping capacity. 

Fluid Shear Rates, Impeller Pumping Capacity and Power Consumption... 

Fluid Shear Rates, Impeller Pumping Capacity and Power Consumption 689 h = r X (mv) [kgrti /s) (7-8)... 

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