Scale shear rates

There is a wide variety of impellers usiu fluidfoil principles, which are used when flow from the impeller is predominant in the process requirement aud macro- or micro-scale shear rates are a subordinate issue. 

Fig. 22. Radius of drops produced by capillary breakup (solid lines) and binary breakup (dotted lines) in a hyperbolic extensional flow for different viscosity ratios (p) and scaled shear rate (p,cylo) (Janssen and Meijer, 1993). The initial amplitude of the surface disturbances is ao = 10 9 m. Note that significantly smaller drops are produced by capillary breakup for high viscosity ratios.

The RlOO (Figure 12.4) draws the most power and has the highest micro-scale shear rate. 

Recently, one of the most practical results of these studies has been the ability to design pilot plant experiments (and, in many cases, plant-scale experiments) that can establish the sensitivity of process to macro-scale mixing variables (as a function of power, pumping capacity, impeller diameter, impeller tip speeds, and macro-scale shear rates) in contrast to micro-scale mixing variables (which are relative to power per unit volume, RMS velocity fluctuations, and some estimation of the size of the micro-scale eddies). 

The shear rates are expressed in units of. The scaled shear rate, being a product of the true shear rate and the relevant relaocation time, is also referred to as Deborah-number . Instead of the ratio Tap/ro, the parameter... 

Figure 8.4 Fluctuations measured in the sheared region of the velocity profile. Scaled mean squared displacements in (a) flow direction and (b) gradient direction plotted against the scaled shear rate, (c) Velocity autocorrelation function in the flow and gradient direction. Different colours represent measurements made at different positions (shear rate) along the mean velocity profile shown in Figure 8.3c. Open symbols represent data in gradient direction while filled symbols represent data in the flow directions. Dashed lines in (a) and (b) are of slopes of 1 (i.e., diffusive motion) and dashed line in (c) is of slope 7/2 (i.e., a faster decay). (Adapted from Rycroft, C.H. et al., Phys. Rev. E, 80,031305, 2009 Orpe, A.V. et al., Europhys. Lett., 84, 64003, 2008.)...

Shear flow is characterized (in the absence of vesicles or cells) by the flow field V = jyCx, where Cx is a unit vector, compare Sect. 10.4. The control parameter of shear flow is the shear rate f, which has the dimension of an inverse time. Thus, a dimensionless, scaled shear rate y = ft can be defined, where T is a characteristic relaxation time of a vesicle. Here, t = rjoRpkBT is used, where rjo is the solvent viscosity, Rq the average radius [206]. For < 1, the internal vesicle dynamics is... 

The effect of the shear flow is to induce a tension in the membrane, which reduces the amplitude of thermal membrane undulations. This tension can be extracted directly from simulation data for the undulation spectrum. The reduction of the undulation amplimdes also implies that the fluctuations of the inclination angle 6 get reduced with increasing shear rate. The theory for quasi-circular shapes predicts a universal behavior as a function of the scaled shear rate Y A I K/ RokBT), where... 

Orthokinetic flocculation is induced by the motion of the Hquid obtained, for example, by paddle stirring or any other means that produces shear within the suspension. Orthokinetic flocculation leads to exponential growth which is a function of shear rate and particle concentration. Large-scale one-pass clarifiers used in water installations employ orthokinetic flocculators before introducing the suspension into the settling tank (see Water,... 

Maximum impeller zone shear rate will be higher in the larger tank, but the average impeller zone shear rate will be lower therefore, there will be a mu(m greater variation in shear rates in a full-scale tank than in a pilot unit. 

Since chemical reactions are on a scale much below 1 Im, and it appears that the Komolgoroff scale of isotropic turbulence turns out to be somewhere between 10 and 30 Im, other mechanisms must play a role in getting materials in and out of reaction zones and reactants in and out of those zones. One cannot really assign a shear rate magnitude to the area around a micro-scale zone, ana it is primarily an environment that particles and reactants witness in this area. 

The overall superficial fluid velocity, mentioned earlier, should be proportional to the settling velocity o the sohds if that were the main mechanism for solid suspension. If this were the case, the requirement for power if the setthng velocity were doubled should be eight times. Experimentally, it is found that the increase in power is more nearly four times, so that some effect of the shear rate in macro-scale turbulence is effec tive in providing uphft and motion in the system. 

If the process can be operated adiabaticaUy, the production capacity is scaled up as the cube of diameter since geometry shear rate, residence time, and power input per unit volume all can be held constant. 

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. 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

Important for polymer processing is the fact that when the concentration of a hard filler is increased in the composite, the unsteady flow (in the sense of large-scale distortions) of the extrudate occurs at higher shear rates (stresses) than in the case of the base polymer [200, 201,206]. Moreover, the whirling of the melt flow is even suppressed by small additions of filler [207]. 

The constant shear concept has been applied for bioreactor scale-up that utilises mycelia, where the fermentation process is shear sensitive and the broth is affected by shear rate of impeller tip velocity. For instance, in the production of novobicin, the yield of antibiotic production is dependent on impeller size and impeller tip velocity. 

Process results, 316, 323, 324 Pumping number, 400 Radial flow, 291 Reynolds number, 299, 303 Scale up, 312-318 Shear rate, 315... 

When the apparent viscosity is a function of the shear rate, the behaviour is said to he shear-dependenf, when it is a function of the duration of shearing at a particular rate, it is referred to as time-dependent. Any shear-dependent fluid must to some extent be time-dependent because, if the shear rate is suddenly changed, the apparent viscosity does not alter instantaneously, but gradually moves towards its new value. In many eases, however, the time-scale for the flow process may be sufficiently long for the effects of time-dependence to be negligible. 

Figure 3.30. Shear stress-shear rate data for Bingham-plastic and false-body fluids using linear scale axes...

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