Maximum shear rate

Obviously shear rate in different parts of a mixing tank are different, and therefore there are several definitions of shear rate (/) for average shear rate in the impeller region, oc V, the proportionaUty constant varies between 8 and 14 for all impeller types (2) maximum shear rate, oc tip speed (%NU), occurs near the blade tip (3) average shear rate in the entire tank is an order of magnitude less than case / and (4) minimum shear rate is about 25% of case 3. 

The maximum shear rate (at the plate rim) is given by equation 32, where is the radius of the plate and h the distance between the two plates. 

The Nametre Rotary B rotational viscometer measures torque in terms of the current needed to drive the d-c motor at a given speed while a material is under test. The standard sensors are coaxial cylinders or Brookfield disk-type spindles, but a cone—plate system is also available. The viscosity range for the coaxial cylinder sensors is 5 to 5 x 1(T mPa-s, and the maximum shear rate is 200. ... 

Maximum shear rate, average shear rate and mixing time, impeller tip velocity, NDt. 

The streamlines of this flow are shown by Peters and Smith (12). In this case, the effective thickness of this layer appears to be about equal to the gap with the wall, indicating a pressure flow about equal to the drag flow. It can be calculated that this would increase the maximum shear rate on the fluid passing under the agitator blade by a factor of seven. 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

The power of this technique is two-fold. Firstly, the viscosity can be measured over a wide range of shear rates. At the tube center, symmetry considerations require that the velocity gradient be zero and hence the shear rate. The shear rate increases as r increases until a maximum is reached at the tube wall. On a theoretical basis alone, the viscosity variation with shear rate can be determined from very low shear rates, theoretically zero, to a maximum shear rate at the wall, yw. The corresponding variation in the viscosity was described above for the power-law model, where it was shown that over the tube radius, the viscosity can vary by several orders of magnitude. The wall shear rate can be found using the Weissen-berg-Rabinowitsch equation ... 

The shear rates in the heat exchanger are believed to have been much higher than the maximum shear rates obtained in the viscometer hence constancy of the differential viscosities at these higher shear rates is indicated. They should not, however, be considered equal to the apparent viscosities at infinite shear rate, as they were termed by Miller, as no data are available to support such a statement. 

At a low shear rates equal to 0.015 s 1, which is usually used to measure the induction period, 8=0.01. Fig. 2.32 shows that x =1 i.e., we have measured the "static" limit of the induction period. The maximum shear rate used in the experimental investigations was equal to 15 s. The value 8 corresponding to this shear rate was 10.8 and (according to Fig. 2.32) in this case, x =0.2 i.e., we can expect a 5-fold decrease in the induction period to only 0.8 min. Although it is only an approximation, rather than an exact calculation, this 5-fold decrease in the induction period in comparison with the static limit, corresponds to the experimental data shown in Fig. 2.33. 

Inherent Errors in Using the Power Law Model in Pressure Flows The shear rate during pressure flow between parallel plates varies from zero at the center to maximum shear rate at the wall, yw. Most polymer melts show Newtonian behavior at low shear rates, hence using the Power Law model for calculating flow rate introduces a certain error. How would you estimate the error introduced as a function of C, where C is the position below which the fluid is Newtonian [See Z. Tadmor, Polym. Eng. Sci., 6, 202 (1966).]... 

When the impeller tip speed is held constant, the same maximum shear rate is maintained. However, the average impeller shear rate related to impeller speed drops dramatically, and the power per unit volume drops inversely to the tank size ratio. In general, this is a very unconservative scaleup technique and can lead to insufficient process results on full scale. 

Looking at the average velocity at a point. Fig. 4 gives the result that the maximum shear rate around an impeller increases with impeller diameter at a given RPM, while the average shear rate around the impeller remains essentially a constant with impeller diameter. 

This yields a further relationship, as shown in Fig. 5, which shows that typically on scaleup, maximum shear rates increase, while average shear rates decrease. These now are shear rates that affect large scale particle, variously estimated at 100 to 200 microns and larger. 

Figure 4, Data showing that maximum shear rate around an impeller increases, while average shear rate remains constant with different diameters having the same RFM...

Substitution of equation 22 in equation 19 shows that the maximum shear rate of 6 s l will result in values of (S av range... 

Figure 6.39 Hysteresis loops of viscosity versus shear rate of a 3% by weight suspension of fumed silica (surface area = 325 m /g) in poly(dimethyl-siloxane), (PDMS molecular weight = 67,000, ris 125 P) at 30°C. In each run, the shear rate was first increased up to a maximum shear rate /max located at the arrow, and then decreased. After a rest of 23 hours, another run was made, with a different /max, thus producing the series of curves shown. (Reprinted from J Non-Newt Fluid Mech 17 45, Ziegelbaur and Caruthers (1985), with kind permission from Elsevier Science NL, Sara Burgerhartstraat 25,1055 KV Amsterdam, The Netherlands.)...

The shear rate at the VSEP membrane is created by the inertial-induced relative motion of the fluid, and can be of the order 10 s The shear rate varies sinusoidally and increases proportionally with local membrane azimuthal displacement to radius. The maximum shear rate at the periphery can be related to the vibrating frequency (F) and the membrane displacement at the periphery (d) by the following equation [66] ... 

Jaffrin et al. [57] have made a hydrodynamic comparison between the rotating disk and the VSEP system based on the flux achieved under similar maximum shear rates for baker s yeast microfiltration with an 0.2 p,m ME and skim mUk UF at 50 kDa. They found that the flux variation with time in these two modules was nearly identical when they were operated at the same maximum shear rate, suggesting the dominant effect of shear rate on the filtration performance. 

MAXIMUM SHEAR RATE (l/ SEC) RATE DERIVATIVE (RPM/SEC) DATA INTERVAL (MILLISEC)... 

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