Non-Newtonian suspensions

In the food industry it has often been difficult to obtain true viscosity measurements (unithj.j) of complex fluid foods such as coarse fruit suspensions. These are usually non-Newtonian suspensions. Fruit concentrates are dispersions of solid particles (pulp) in aqueous media (serum). Their rheological properties are of interest in practical applications related to processing, storage stability, and sensory properties. Expensive rheometers are often not available in quality control and product development laboratories. However, viscosity is nonetheless an important quality factor of these products. 

Newtonian and non-Newtonian calibration fluids were used to determine the necessary calibration constants for the impeller method. It has been previously determined that the impeller method is only valid for a Reynolds number (Re) <10. Impeller rotational speed and torque data from Newtonian calibration fluids of known viscosity were employed to determine the Newtonian calibration constant, c. Cone-and plate-viscometer data from non-Newtonian calibration fluids were used to determine a viscosity vs shear rate relationship. Impeller rotational speed and torque data of the non-Newtonian calibration fluids combined with a determined viscosity vs shear rate correlation were utilized to calculate the shear rate constant, k. The impeller method calibration constants allow the calculation of viscosity, shear rate, and shear stress data of non-Newtonian suspensions. Metz et al. (2) have thoroughly discussed the equations utilized in the impeller method. 

Viscosity, shear stress, and shear rate can be calculated for any non-Newtonian suspension using the impeller method calibration constants. Viscosity is determined using Eq. 4. The shear stress can be calculated for any impeller speed and measured torque ... 

For non-Newtonian suspensions, pcfr is obtained from the Ostwald-de Waelc equation... 

Blood is a non-Newtonian suspension showing a shear-dependent viscosity. At low rates of shear, erythrocytes form cylindrical aggregates (rouleaux), which break up when the rate of shear is increased. Calculations show that the shear rate (D) associated with blood flow in large vessels such as the aorta is about 100 s b but for flow in capillaries it rises to about 1000 s b The flow characteristics of blood are similar to those of emulsions except that, while shear deformation of oil globules can occur with a consequent change in surface tension, no change in membrane tension... 

Many (semi-)empirical relationships have been proposed to describe non-Newtonian suspension behaviour. For more information the reader is referred to Ref. [15] or other textbooks on suspension rheology. 

Moshev, V. V. and Ivanov, V. A., Rheological Behavior of Concentrated Non-Newtonian Suspensions, Nauka, Moscow, 1990 [in Russian]. 

Calculate the thermal conductivity of 35% (by volume) non-Newtonian suspensions of alumina (thermal conductivity = 30 W/mK) and thorium oxide (thermal conductivity = 14.2 W/mK) in water and in carbon tetra chloride at 293 K. 

COMPARISON OF NUMERICAL AND EXPERIMENTAL RHEOLOGICAL DATA OF HOMOGENEOUS NON-NEWTONIAN SUSPENSIONS... 

The rheological behavior of non-Newtonian suspensions is often characterized by a power law model ... 

It is noticeable that at low flow rates the agreement between all the calculated and measured data is excellent, but the simplified analytical solution deviates from the other results at Reynolds numbers of between 300 and 1,000. Above these values a comparison of the analytical and modified analytical data clearly demonstrates the increasing importance of even relatively minor changes of pipe geometry in affecting the overall pressure drop when pumping non-Newtonian suspensions. 

By far, the most imderstood behaviors are those of Newtonian fluids and time-independent non-Newtonian suspensions. A series of flow equations and charts have been developed in order to predict their flow characteristics. For other types of non-Newtonians the flow equations, if they can be developed at all, are much more complicated. However, under certain assumptions, for example, steady-state flow without acceleration (flow in straight pipes without nozzles, bends, orifices, etc.), these fluids can often be treated as time independent too. 

By far, most of the study of the flow behavior of non-Newtonian suspensions has been devoted to monosized and monoshaped systems, mainly of spherical particle geometry. In reality, however, solid-liquid mixtures usually consist of dissolved solids with a variety of particle sizes, shapes, and concentrations. The available theory for the behavior of non-Newtonian... 

For the case of settling of non-Newtonian suspensions, it has been reported (Ortega-Rivas and Svarovsky, 1993) that the Stokes number Stkjo can also be expressed in terms of the parameters of characterization of non-Newtonian suspensions, using a procedure similar to that described above for the Reynolds number. A generalized Stokes number (Stk )5o for settling of power-law suspensions can be expressed as follows ... 

Thomas, D. G. 1963. Non-Newtonian suspensions. Part I Physical properties and laminar transport characteristics. Industrial and Engineering Chemistry 55 18-29. 

Dedegil, M. Y. 1987. Drag coefficient and settling velocity of particles in non-Newtonian suspensions. Journal of Fluids Engineering, 71 (September), 319-323. 

Several theoretical and empirical relationships have been proposed to describe the viscosity of suspensions in Newtonian or non-Newtonian viscous liquids. These relationships have also been used, with ranging degrees of success, to correlate viscosity data when the suspending medium is viscoelastic [62]. In the following various relationships are reviewed. The viscosity of Newtonian as well as non-Newtonian suspensions is affected by the characteristics of the solid phase such as shape, concentration and dimensions of the particles, its size distribution, flie nature of the surface, etc. The influence of each of these factors is examined below. 

Lakshmana Rao, N.S. Shridharan, K. 1972. Orifice losses for laminar approach flow. ASCE Journal of Hydraulics Division, Vol.98, No.ll, (November), pp. 2015-2034 Lakshmana Rao, N.S., Srhidharan, K. Alvi, S.H. (1977). Critical Reynolds Number for orifice and nozzle flows in pipes. Journal of Hydraulic Research, International Association for Hydraulic Research, Vol. 15, No. 2, pp. 167-178 Ma, T. W. (1987). Stability, rheology and flaw in pipes, fittings and venturi meters of concentrated non-Newtonian suspensions. Unpublished PhD thesis. University of Illinois, Chicago... 

Chen, B, Tatsumi, D., Matsumoto, T. 2002. Floe Structure and Flow Properties of Pulp Fiber Suspensions. /, Soc. Rheol, fpn. 30 (1) 19-25 Dedegil, M.Y. 1987. Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions. Journal of Fluids Engineering 109 (3) 319-323. 

The same equation may be used for non-Newtonian suspensions, provided that the "apparent viscosity, Ha, is substituted for the viscosity. 

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