Viscosity of non-Newtonian fluids

Although most physical properties (e.g., viscosity, density, heat conductivity and capacity, and surface tension) must be regarded as variable, it is of particular value that viscosity can be varied by many orders of magnitude under certain process conditions (5,11). In the following, dimensional analysis will be applied exemplarily to describe the temperature dependency of the viscosity and the viscosity of non-Newtonian fluids (pseudoplastic and viscoelastic, respectively) as influenced by the shear stress. 

Apparent viscosity of a non-Newtonian fluid at some specified shear rate, lb.M/(sec.)(ft.) or lb.ii/(hr.)(ft.). mo and m refer to the apparent viscosities of non-Newtonian fluids at zero and infinite shear rates, respectively... 

Measuring the Viscosity of Non-Newtonian Fluids The exact start and end poin ts of the ramp can be decided from the ramp performed in Basic Protocol 1. A stress of 1/lOth to l/100th of the apparent yield stress to the nearest order of magnitude should be set. 

The apparent viscosity shows some dependence on shear rate the magnitude of which is a function of pH as shown in Figures 8 and 9 for batch and semicontinuous carboxylated latexes respectively. It is difficult to compare the viscosities of non-Newtonian fluids. One possible method for comparison is to take the apparent viscosity value at a certain shear rate for all samples In this work, the viscosity values at a shear rate of 215 (sec ) were taken to compare the behavior of the samples. The results of viscosity as a function of pH obtained in this manner are shown in Figure 10 for batch latexes, and in Figure 11 for semi-continuous latexes. 

The shear rate in this geometry depends on the radius, and since the viscosity of non-Newtonian fluids depends on the shear rate and thus changes with the radius, integration of Eq. (13.79) gives... 

This equation suggests that the determination of the viscosity of non-Newtonian fluids with plate-plate geometry requires that InM first be plotted against InKj . Consequently, the determination of the shear-dependent viscosity requires that the torque be measured at different shear rates. The value of the viscosity is then determined with the value of the local slope in conjunction with Eq. (13.84). If the fluid obeys a power law, then... 

Chevalier J.L., Effective Viscosity of non-Newtonian fluids in a mechanically stirred tank, Chem. Eng. Commun. 21 (1983), p. 29-36... 

Absolute viscosity, P or Ib/ft-s p , apparent viscosity of non-newtonian fluid p viscosity of continuous phase in liquid-liquid dispersion /ij, of dispersed phase Kinematic viscosity, mVs or ft s... 

Keck et al. (19) studied the effect of proppant on the effective viscosity of non-Newtonian fluids and presented the following modified Eiler s (20) expression that includes the effect of shear rate, temperature, gel concentration, and proppant concentration. 

Conversely, the viscosity of non-Newtonian fluids is dependent on the applied shear stress and is referred to as apparent viscosity. When a fluid exhibits plastic flow, a certain minimum shear stress must be applied, called yield stress, before the fluid starts to flow (Fig. 18.6b). At a shear stress of less than the yield stress, the viscosity is thus infinitely large and the liquid behaves like a solid. Above the yield stress, the viscosity decreases with increasing shear stress. Also in the straight part of the curve in Fig. 18.6c, the viscosity decreases with increasing shear stress. This is... 

An alternative procedure, to ensure no external force is applied to the powder bed by the vaned paddle, is to place the compacted sample on a balance and when the paddle is immersed in the powder to raise the vaned head slowly until the balance reading is zero. This dynamic method of bulk powder characterisation is allied to the rheological method for measurement of the viscosity of non-Newtonian fluids and suspensions. Commercial instruments based on the WSL cohesion tester are now available in the form of the FT4 Powder Rheometer (Freeman Technology) and the Stable Micro Systems Powder Flow Analyser (Stable Micro Systems). 

The method of ultrasound Doppler velocimetry (UDV) [9] was proposed to measure the viscosity of non-Newtonian fluids over a wide range of shear rates and in a short period of time. This is a noninvasive, nondisturbing, quick, and accurate procedure. The distribution of shear-stress can be found by pressure drop. At a radial position, the ratio of shear-stress to shear rate, by definition, yields the viscosity at that point. Thus, for the shear rate range in the flow, viscosity values can be obtained by means of only one online experiment. This is a method known in the literature as pointwise rheological measurement [10,11]. 

Heat Exchangers Using Non-Newtonian Fluids. Most fluids used in the chemical, pharmaceutical, food, and biomedical industries can be classified as non-Newtonian, ie, the viscosity varies with shear rate at a given temperature. In contrast, Newtonian fluids such as water, air, and glycerin have constant viscosities at a given temperature. Examples of non-Newtonian fluids include molten polymer, aqueous polymer solutions, slurries, coal—water mixture, tomato ketchup, soup, mayonnaise, purees, suspension of small particles, blood, etc. Because non-Newtonian fluids ate nonlinear in nature, these ate seldom amenable to analysis by classical mathematical techniques. 

Some concerns directly related to a tomizer operation include inadequate mixing of Hquid and gas, incomplete droplet evaporation, hydrodynamic instabiHty, formation of nonuniform sprays, uneven deposition of Hquid particles on soHd surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

The Martinelli correlations for void fraction and pressure drop are used because of their simplicity and wide range of applicability. France and Stein (6 ) discuss the method by which the Martinelli gradient for two-phase flow can be incorporated into a choked flow model. Because the Martinelli equation balances frictional shear stresses cuid pressure drop, it is important to provide a good viscosity model, especially for high viscosity and non-Newtonian fluids. 

A. G., Goloshevsky, J. H. Walton, M. V. Shutov, J. S. de Ropp, S. D. Collins, M. J. McCarthy 2005, (Nuclear magnetic resonance imaging for viscosity measurements of non-Newtonian fluids using a miniaturized rf coil), Meas. Sci. Technol. 16, 513-518. 

For non-Newtonian fluids, any model parameter with the dimensions or physical significance of viscosity (e.g., the power law consistency, m, or the Carreau parameters r,]co and j/0) will depend on temperature in a manner similar to the viscosity of a Newtonian fluid [e.g., Eq. (3-34)]. 

Corresponding expressions for the friction loss in laminar and turbulent flow for non-Newtonian fluids in pipes, for the two simplest (two-parameter) models—the power law and Bingham plastic—can be evaluated in a similar manner. The power law model is very popular for representing the viscosity of a wide variety of non-Newtonian fluids because of its simplicity and versatility. However, extreme care should be exercised in its application, because any application involving extrapolation beyond the range of shear stress (or shear rate) represented by the data used to determine the model parameters can lead to misleading or erroneous results. 

Background on Spin Casting. As early as 1958, Emslie, et al. (A) proposed a theoretical treatment of spin casting for nonvolatile Newtonian fluids. This theory predicted that films formed on a flat rotating disc would have radial thickness uniformity. They predicted that the final film thickness would depend on spin speed (w) and viscosity (ij) as well as other variables such as liquid density and initial film thickness. The dependence of thickness on u> and ij was also recognized by many of the other authors reviewed in this paper, and their proposed relationships are compared in Table I. Acrivos, et al. (5) extended the Emslie treatment to the general case of non-Newtonian fluids, a category into which most polymers fall. Acrivos predicted that non-Newtonian fluids would yield films with non-uniform radial thickness. 

Chapter HI relates to measurement of flow properties of foods that are primarily fluid in nature, unithi.i surveys the nature of viscosity and its relationship to foods. An overview of the various flow behaviors found in different fluid foods is presented. The concept of non-Newtonian foods is developed, along with methods for measurement of the complete flow curve. The quantitative or fundamental measurement of apparent shear viscosity of fluid foods with rotational viscometers or rheometers is described, unithi.2 describes two protocols for the measurement of non-Newtonian fluids. The first is for time-independent fluids, and the second is for time-dependent fluids. Both protocols use rotational rheometers, unit hi.3 describes a protocol for simple Newtonian fluids, which include aqueous solutions or oils. As rotational rheometers are new and expensive, many evaluations of fluid foods have been made with empirical methods. Such methods yield data that are not fundamental but are useful in comparing variations in consistency or texture of a food product, unit hi.4 describes a popular empirical method, the Bostwick Consistometer, which has been used to measure the consistency of tomato paste. It is a well-known method in the food industry and has also been used to evaluate other fruit pastes and juices as well. 

The above equations can be used to simulate the flow of non-Newtonian fluids with a shear thinning viscosity. This requires an iterative under-relexation scheme where a Newtonian solution is found first. The initial velocity field is used to compute rates of deformation and viscosity. Next, a corrected velocity field is computed with the updated velocities, at which point an under-relaxation is performed using... 

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