Newtonian fluids kinematic viscosity

Define rheology, shear force, shear stress, shear rate, Newtonian fluid, dynamic viscosity, centi-poise, kinematic viscosity, centistokes, viscometry, and viscometer. 

The emphasis of this section is on Newtonian fluids whose viscosity is independent of shear rate. Most methods are discussed in an lUPAC volume [69]. Because most of these methods actually measure the kinematic viscosity (ratio of viscosity to density), knowledge of the density of the fluid is required to obtain the viscosity itself. 

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... 

Gla.ss Ca.pilla.ry Viscometers. The glass capillary viscometer is widely used to measure the viscosity of Newtonian fluids. The driving force is usually the hydrostatic head of the test Hquid. Kinematic viscosity is measured directly, and most of the viscometers are limited to low viscosity fluids, ca 0.4—16,000 mm /s. However, external pressure can be appHed to many glass viscometers to increase the range of measurement and enable the study of non-Newtonian behavior. Glass capillary viscometers are low shear stress instmments 1—15 Pa or 10—150 dyn/cm if operated by gravity only. The rate of shear can be as high as 20,000 based on a 200—800 s efflux time. 

Because the quantitative analysis of transport processes in terms of the microscopic description of turbulence is difficult, Kdrmdn suggested (K2) the use of a macroscopic quantity called eddy viscosity to describe the momentum transport in turbulent flow. This quantity, which is dimensionally and physically analogous to kinematic viscosity in the laminar motion of a Newtonian fluid, is defined by... 

Non-Newtonian fluids are generally those for which the viscosity is not constant even at constant temperature and pressure. The viscosity depends on the shear rate or, more accurately, on the previous kinematic history of the fluid. The linear relationship between the shear stress and the shear rate, noted in Equation (1), is no longer sufficient. Strictly speaking, the coefficient of viscosity is meaningful only for Newtonian fluids, in which case it is the slope of a plot of stress versus rate of shear, as shown in Figure 4.2. For non-Newtonian fluids, such a plot is generally nonlinear, so the slope varies from point to point. In actual practice, the data... 

Many modifications of the basic Ostwald geometry are employed in different situations. One example is the Cannon-Fenske routine viscometer (Fig. 6.37b) which is used in the oil industry for measuring kinematic viscosities of 0.02 m2/s and less(4<). As viscosity is sensitive to variations in temperature, these types of viscometer are always immersed in a constant temperature bath. They are not normally suitable for non-Newtonian fluids although FAROOQI and Richardson(47) have employed a capillary viscometer to characterise a power-law fluid. 

Attempts to use the analytical result of Equation 3 to correlate experimental data have consistently failed (17). Consequently, empirical and semi-empirical models which include various factors to account for evaporation and non-Newtonian behavior have been proposed (17) but these too have not been able to satisfactorily fit the available data. We have considered the coating flow problem with simultaneous solvent evaporation (11). In the regime of interface mass transfer controlled evaporation, i.e. at high solvent concentration, the fluid mechanics problem can be decoupled from the mass transfer problem via an experimental parameter a which measures the changing time-dependent kinematic viscosity due to solvent evaporation. An analytical expression for the film thickness has been obtained (11) ... 

A solution or melt composed of such stretchable molecules can be highly springy, especially in extensional flows (Tirtaatmadja and Sridhar 1993). The kinematics of an extensional flow are described in Section 1.4.1.2. From Eqs. (1-6) and (1-9), one can show that for a Newtonian fluid (for which a = 2rjD) the Trouton ratio Tr = f)u/hQ the uniaxial extensional viscosity to the zero-shear viscosity /jo is numerically equal to 3. For polymers, Tr can be much higher than this. Figure 3-2, for example, shows Tr for a... 

Capillary viscometers have been widely used in determining the viscosity of Newtonian fluids. In these viscometers, the driving force is usually the hydrostatic head of the test liquid itself, although, application of external pressure is also used in order to increase the range of measurement and allow non-Newtonian behavior to be studied. In operation, the efflux time of a fixed volume of test liquid is measured, from which the kinematic viscosity is calculated. 

Nusselt provided a simple model for laminar liquid flow down an inclined plane. This assumed that the liquid had reached fully developed conditions in which drag due to viscous shear exactly balanced the weight of the film. Under these conditions, Nusselt showed that for a Newtonian fluid of kinematic viscosity, v, film thickness, /, could be written in terms of the liquid flow rate, Q, moving over a vertically inclined surface of width, w, under a gravitational acceleration, g, using the following relationship ... 

A simple closure for Uf <8 Uf]f in Eq. (4.92) that includes the effects of the microscale fluid-velocity fluctuations is to replace it with Uf 8 Uf, and then to model Sf as a Newtonian fluid for the fluid velocity Uf with an effective viscosity equal to the sum of the molecular kinematic viscosity of the fluid (vf) and a microscale effective kinematic viscosity (Veff). This leads to Sf = -pf + Tf, where pi is the pressure in the fluid phase (e.g. that found from an equation of state) and Tf = 2gi(V( + Vefr)[Df - trace(Df) ]... 

This is the Navier-Stokes equation of motion for an incompressible, isothermal Newtonian fluid. Two comments are in order with regard to this equation. First, we shall always assume that p and // are known-presumably by independent means - and attempt to solve (2-89) and the continuity equation, (2 20) for u andp. Second, the ratio pjp, which is called the kinematic viscosity and denoted as v, plays a fundamental role in determining the fluid s motion. In particular, it can be seen from (2 89) that the contribution to acceleration of a fluid element (Du/Di) that is due to viscous stresses is determined by v rather than by ti. 

Problem 10-8. Boundary Layer on a Moving Web. A flat plate is pulled through a wall with a constant velocity Uq into a Newtonian fluid of kinematic viscosity v. Assume that l/o/v 1. 

Given the sample density, Eq. [49] produces a good estimation trf vi.sco.sity for Newtonian fluids, provided Did < 10 for the falling-bail conflgurotton. and for Did 10 for the rolling-ball. However, the results are not accurate Uterefore should only be used for comparison purposes. Note that the sample density, p. is necessary for the viscosity calculation. Otherwise, it is the kinematic viscosity. > - p/p, which is directly measured. 

A non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is non-linear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate, is not constant at a given temperature and pressure but is dependent on flow conditions such as flow geometry, shear rate, etc. and sometimes even on the kinematic history of the fluid element under eonsideration. Such materials may be conveniently grouped into three general elasses ... 

A brief derivation of the turbulent velocity profile for Newtonian fluids in smooth pipes will first be presented and then extended to power-law fluids. The shear stress at any point in the fluid, at a distance y Irom the wall, is made up of viscous and turbulent contributions, the magnitudes of which vary with distance irom the wall. Expressing shear stress in terms of a dynamic viscosity and an eddy momentum diflnsivity (or eddy kinematic viscosity), E,... 

With an increase in the number of methyldichlorosiloxane units the kinematic viscosity rises and low-temperature parameters deteriorate for oligomers with similar chain lengths. A rise in the viscosity dependence on temperature and density is also observed. All the oligomers analyzed demonstrate Newtonian fluid properties in the shear rate range from 30 to 2.2 x 10 s. ... 

Figure 3.17 Explanation of the viscosity of a Newtonian fluid. Sometimes also, the kinematic viscosity...

Intrinsic viscosity Kinematic viscosity Laminar flow Melt-flow index Newtonian flow Pseudoplastic fluid... 

When a Newtonian liquid, such as a hydrocarbon mixture, is subjected to a shearing stress, a velocity gradient develops within the fluid. Viscosity (or dynamic viscosity) is defined as the shear stress per unit area at any point within the fluid divided by the velocity gradient at that point. Consequently, the viscosity is a dynamic property nevertheless, for Newtonian liquids it is a state property, that is, it depends only on state properties such as temperature and pressure or density. The dimensions of viscosity are force x time/length or equivalently mass/length x time. Occasionally kinematic viscosity, which is the ratio of dynamic viscosity to fluid density, is used instead of dynamic viscosity. The dimensions of kinematic viscosity are length /time. 

Most of the recently published kinematic viscosity correlations appear to be accurate enough for design calculations. Therefore, point i) through iii) should have the same level of importance as accuracy. In other words, a specific correlation for kinematic viscosity may be very accurate +(0.2 — 0.3)% for Newtonian fluids, within the limits of experimental accuracy of conunercially available measurement equipment. 

When the viscosity is a function of shear rate, then the relationship between shear stress and shear rate is given by equation (2.9). Since its form is similar to equation (2.36) except for Ae shear rate dependent viscosity, the equation is said to represent a Generalized Newtonian fluid. In such a fluid, the presence of normal stresses defined by equations (2.10) and (2.11) is considered to be negligible for a specific flow situation. In effect, equation (2.5b) represents the constitutive equation for a Generalized Newtonian fluid. The hypothesis of a Generalized Newtonian fluid differs from the simple Newtonian case by the assumption that the functional relationship between the stress tensor and the kinematic variable need not be only linear. It holds, however, the suggestion that only the kinematic variable of the first order can influence the state of stress in the fluid and no attempt is to be made to describe the normal stresses in it. 

Consider a fluid boimded by a flat plate at its bottom. The plate oscillates at a vibration frequency in a horizontal plane (as indicated in Figure 2.11.1 by the double arrow). The magnitude of the plate s vibrational motion is 2a. The fluid is a Newtonian fluid having a kinematic viscosity v and a density p. Due to the effect of viscosity, the vibrational motion induces movements in the fluid, which are restricted to a boundary layer having a thickness 5. 

There is some equipment to be used for viscosity measurement which broadly classified into two categories dynamic and kinematic viscometer. A dynamic viscometer is one of the shear rate can be controlled and measured (rotational viscometer). It is the only typ>e of viscosity measurement that is relevant to fluids where the viscosity is related to the shear rate (non-Newtonian fluids). A kinematic viscometer is where the shear rate can neither be controlled nor measured, for example capillary viscometer. 

When we consider non-Newtonian liquids, the viscosity is not constant, because of the influence of shear rate and time. So for non-Newtonian fluids we refer to their apparent viscosity (p ), or effective viscosity, and we have to specify the conditions of shear rate to which this applies. When we speak of time-dependent fluids, we must also specify the shear history or kinematic history, at the point that their apparent viscosity is quoted. As long as we keep these restrictions in mind for a non-Newtonian fluid, we can still think of the apparent viscosity as ... 

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