Newtonian fluids, characterization

The most common non-Newtonian fluid characterization in polymeric and biological applications is the power-law model... 

In modeling the interaction of a liquid with plate modes, the high frequency of operation necessitates the consideration of viscoelastic response by the liquid. For the simple liquids examined, good agreement was obtained by modeling the liquid as a Maxwellian fluid with a single relaxation time r. When the Maxwellian fluid is driven in oscillatory flow with cot < 1, it responds as a Newtonian fluid characterized by the shear viscosity, rj. For wt > 1, the oscillation rate approaches the rate of molecular motion in the liquid and energy ceases to be dissipated in... 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Orifice viscometers should not be used for setting product specifications, for which better precision is required. Because they are designed for Newtonian and near-Newtonian fluids, they should not be used with thixotropic or highly shear-thinning materials such fluids should be characterized by using multispeed rotational viscometers. 

Many materials are conveyed within a process facility by means of pumping and flow in a circular pipe. From a conceptual standpoint, such a flow offers an excellent opportunity for rheological measurement. In pipe flow, the velocity profile for a fluid that shows shear thinning behavior deviates dramatically from that found for a Newtonian fluid, which is characterized by a single shear viscosity. This is easily illustrated for a power-law fluid, which is a simple model for shear thinning [1]. The relationship between the shear stress, a, and the shear rate, y, of such a fluid is characterized by two parameters, a power-law exponent, n, and a constant, m, through... 

Fig. 4.3.2 (a) The relationships of shear stress and shear rate for several types of common materials, where the slope is the viscosity T). A non-Newtonian fluid is characterized by its... 

The ratio of extensional viscosity r e to shear viscosity r s is known as the Trouton ratio, which is three for Newtonian fluids in uniaxial extension and larger than three for non-Newtonian fluids. For a viscoelastic fluid such as a polymer in solution, the uniaxial extensional viscosity characterizes the resistance of the fluid... 

The consistency index K (or K ), which characterizes the consistency or thickness of a fluid. It is analogous to the viscosity of a Newtonian fluid and similarly enables quantitative comparison of the consistency of fluids having identical flow-behavior indexes. 

It should be noted that two constants are the minimum number which can be used to characterize any non-Newtonian fluid completely. Therefore, the form of the generalized Reynolds number is as simple as it can be made if it is to characterize all types of fluid behavior (Mil). 

Equation (46) may lead to predictions of zero or even negative heat transfer coefficients for the authors fluids within the range of Reynolds numbers for which the equation is claimed to be applicable. The parameter y, which is included to account for the deviation from non-Newtonian behavior, has a value of zero for Newtonian fluids and increases gradually toward infinity as the non-Newtonian character increases in the direction of pseudoplasticity. However, the peculiar form of the chosen function of this parameter does not uniquely characterize non-Newtonian behavior it has been shown by Branch (B7) that the term 1 — yv first increases as po/pa increases, then goes through a maximum, and finally decreases, reaching negative values for po/pa > 2.0. 

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

This last value compares very well to that given by Blauch and Anson [12]. An extension of this application was proposed by Deslouis and Tribollet to the diffusivity measurement in non-Newtonian fluids [63, 64]. They considered a power-law fluid characterized by a rheological law ... 

Abdel-Goad M, Potschke P (2005) Rheological characterization of melt processed polycarbonate-multiwalled carbon nanotube composites. J Non-Newtonian Fluid Mech 128 2-6... 

The dynamic response of a particle in gas-solid flows may be characterized by the settling or terminal velocity at which the drag force balances the gravitational force. The dynamic diameter is thus defined as the diameter of a sphere having the same density and the same terminal velocity as the particle in a fluid of the same density and viscosity. This definition leads to a mathematical expression of the dynamic diameter of a particle in a Newtonian fluid as... 

A full analytical solution of the cross channel flow vx(x,y) and vy x, y), for an incompressible, isothermal Newtonian fluid, was presented recently by Kaufman (18), in his study of Renyi entropies (Section 7.4) for characterizing advection and mixing in screw channels. The velocity profiles are expressed in terms of infinite series similar in form to Eq. 6.3-17 below. The resulting vector field for a channel with an aspect ratio of 5 is shown... 

The thermal stress is characterized by the distribution of the dissipation in the polymer melt. For a Newtonian fluid, dissipation is calculated as follows... 

Consider an unbounded, incompressible, Newtonian fluid undergoing a homogeneous shear flow characterized by the position-independent velocity gradient dyadic G, which can be decomposed into symmetric and antisymmetric contributions S and A, respectively, as... 

The Reynolds number is useful for characterizing flow of a Newtonian fluid through a tube. The variables in dimensional analysis can be arranged to suggest a valid ratio when none exists. Therefore, established dimensionless variables should be used where applicable. A number of these dimensionless variables have been proven to work in scaleup applications. Examples include the Reynolds, Nusselt, Grashof, and Sherwood numbers, all of which are completely described in Perry s Chemical Engineers Handbook. 

Other types of viscometers, sueh as an oseillation viscometer, that are useful for eharaeterizing Newtonian foods are also available. However, their use for characterizing non-Newtonian fluid foods can be justified only if the complex flow fields can be analyzed and expressions are derived for the shear rate and shear stress. 

To further illustrate the differences in the swallowing processes of Newtonian and non-Newtonian fluids, tcv was coined to represent the time to swallow a critical volume and was defined as the number of seconds needed to transport the first 1.0 mL of fluid into the esophagus. The greater the fcv value, the safer is the swallow, as the muscles in the pharynx have more time to close off entryway to the air passages before food arrives. The parameter tcv may be useful for characterizing the severity of deglutition in a particular patient. It may also be used as a benchmark for any improvement or deterioration in the patient. Because it would be difficult to obtain... 

Hard sphere systems are characterized by viscous flow and for low solids loading (less than 5%) they can be described as Newtonian fluid. At higher loadings, cluster formation takes place and the fluid cau acquire shear thinning or thickening behavior. The viscosity and solids loading are correlated with the... 

To be more precise, the general tensor equation of Newton s law of viscosity should be obeyed by a Newtonian fluid (2) however, for onedimensional flow, the applicability of eq 1 is sufficient. For a Newtonian fluid, a linear plot of t versus 7 gives a straight line whose slope gives the fluid viscosity. Also, a log-log plot of t versus 7 is linear with a slope of unity. Both types of plots are useful in characterizing a Newtonian fluid. For a Newtonian fluid, the viscosity is independent of both t and 7, and it may be a function of temperature, pressure, and composition. Moreover, the viscosity of a Newtonian fluid is not a function of the duration of shear nor of the time lapse between consecutive applications of shear stress (3). 

Time-Independent Non-Newtonian Fluids. Time-independent non-Newtonian fluids are characterized by having the fluid viscosity as a function of the shear rate (or shear stress). However, the fluid viscosity is independent of the shear history of the fluid. Such fluids are also referred to as non-Newtonian viscous fluids". Figure 1 shows a typical shear diagram for the various time-independent non-Newtonian fluids. 

Pseudoplastic Fluids, A pseudoplastic or a shear-thinning fluid is one of the most commonly encountered non-Newtonian fluids. The variation of the shear stress, t, versus the shear rate, 7, for a pseudoplastic fluid is shown in Figure 2. A plot of t versus 7 is characterized by linearity at very low and very high shear rates. The slope at very low shear rate gives the... 

Time-Dependent Non-Newtonian Fluids. Time-dependent non-Newtonian fluids are characterized by the property that their viscosities are a function of both shear rate and shear history. 

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