Newtonian fluids flow regimes

Using the described algorithm the flow domain inside the cone-and-plate viscometer is simulated. Tn Figure 5.17 the predicted velocity field in the (r, z) plane (secondary flow regime) established inside a bi-conical rheometer for a non-Newtonian fluid is shown. 

Li et al. [36] performed an extensive study on AP in a Sulzer SMX statie mixer with both Newtonian and non-Newtonian fluids. They showed that AP inereased by a faetor of 23 in a SMX statie mixer in the laminar flow regime. Figure 7-24 shows their eorrelation between the Fanning frietion faetor and the Reynolds number for experimental points under various operating eonditions. 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

Metzner, A.B. and Reed, J.C., Flow of non-Newtonian fluids - correlation of the laminar, transition, and turbulent-flow regimes, AIChE Journal, 1, pp. 434-40 (1955). 

The complex flow field created by the impeller does not allow the direct calculation of shear rate (6,8). It is assumed that the dimensionless power number (pNo) is inversely proportional to the impeller Reynolds number (Re,) for Newtonian fluids in a laminar flow regime in which the RE, is <10 ... 

Of interest is a recent theoretical relation for eg in gas-liquid bubble columns based on liquid circulation and claimed to be valid both in the homogeneous bubble flow regime and in the chum-turbulent regime, also for non-Newtonian fluids. For power law fluids with... 

Taguchi and Miyamoto (1966) showed that for non-Newtonian fermentation broth, the power requirement in the turbulent flow regime was well correlated by the above correlation of Michel and Miller (1962). Broth from the production of gluco-amylase by Endomyces species and carboxymethyl-cellulose solutions were used as non-Newtonian fluids. For non-Newtonian fluids in laminar and transition regions, particularly for fluids with apparent viscosities greater than 300 cP, the impeller diameter and impeller blade width had considerable effects on power consumption in a non-gassed system. They proposed... 

For the mass balance, the following assumptions and operating conditions are considered (i) steady state, (ii) unidirectional, incompressible, continuous flow of a Newtonian fluid under laminar flow regime, (iii) only ordinary diffusion is significant for a mixture where the main component is water, (iv) azimuthal symmetry, (v) axial diffusion neglected as... 

N. El Kissi and J.-M. Piau, The diiferent capillary flow regimes of entangled poly-dimethylsiloxane polymers macroscopic slip at the wall, hysteresis and cork flow, J. Non-Newtonian Fluid Mech., 37 (1990) 55-94. 

Problem 8-5. The annular region between two concentric rigid spheres of radii a and A.a (with k > 1) is filled with Newtonian fluid of viscosity /i and density p. The outer sphere is held stationary whereas the inner sphere is made to rotate with angular velocity fl. Assume that inertia is negligible so that the fluid is in the Stokes flow regime. 

The flow regime in a pipe is determined by the Reynolds number. For a Newtonian fluid ... 

Newtonian Flow Fluid flow that obeys Newton s law of viscosity. Non-Newtonian fluids may exhibit Newtonian flow in certain shear rate or shear stress regimes. See also Newtonian Fluid. 

In practical applications, flow of the material through an orifice is perhaps the most frequently encountered rheological phenomenon. It is then natural to be used for the viscosity measurement of suspensions (53-55). However, the flow through an orifice is not precise in terms of shear measurement because the shear rate is not well defined under such circumstances. To meet this objection, the orifice is in most cases extended to a tube. This leads to the capillary flow type of viscometers, the simplest, and for Newtonian fluids, the most accurate type, comprising the familiar Ostwald und Ubbelohde viscometers. The fully developed axial velocity in the laminar regime is given by... 

The Oroskar-Turian s correlation and previous ones were developed to determine the critical deposit velocity of Newtonian carrier fluids with various particle sizes and concentrations. Shah and Lord (7) generalized equation 2 to extend its capability to correlate the critical deposit velocity for non-Newtonian carrier fluids (power law). The parameter X was eliminated from equation 2 because of its insignificant contribution to the correlation results and because it would be undefined for the laminar flow regime of non-Newtonian fluids. The generalized form of equation 2, which can be applied to either critical deposit (VD) or resuspension velocity (Vs), is as follows ... 

---