Shear viscosities defined

The shear viscosity is an important property of a Newtonian fluid, defined in terms of the force required to shear or produce relative motion between parallel planes [97]. An analogous two-dimensional surface shear viscosity ij is defined as follows. If two line elements in a surface (corresponding to two area elements in three dimensions) are to be moved relative to each other with a velocity gradient dvfdx, the required force is... 

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

For practical purposes, it is convenient to define the relaxation time in terms of macroscopic quantities which can be readily determined. Within the validity limit of Hookean connectors (Eq. 13), the low-shear viscosity of a polymer solution is given by the relation ... 

Fig. 4.3.3 (a) Shear flow of a Newtonian fluid defined as the ratio of the shear stress and trapped between the two plates (each with a shear rate, (b) A polymeric material is being large area of A). The shear stress (a) is defined stretched at both ends at a speed of v. The as F/A, while the shear rate (y) is the velocity material has an initial length of L0 and an gradient, dvx/dy. The shear viscosity (r s) is (instantaneous) cross-sectional area of A. 

Viscosity, defined as the resistance of a liquid to flow under an applied stress, is not only a property of bulk liquids but of interfacial systems as well. The viscosity of an insoluble monolayer in a fluid-like state may be measured quantitatively by the viscous traction method (Manheimer and Schechter, 1970), wave-damping (Langmuir and Schaefer, 1937), dynamic light scattering (Sauer et al, 1988) or surface canal viscometry (Harkins and Kirkwood, 1938 Washburn and Wakeham, 1938). Of these, the last is the most sensitive and experimentally feasible, and allows for the determination of Newtonian versus non-Newtonian shear flow. 

The surface shear viscosity of a monolayer is a valuable tool in that it reflects the intermolecular associations within the film at a given thermodynamic state as defined by the surface pressure and average molecular area. These data may be Used in conjunction with II/A isotherms and thermodynamic analyses of equilibrium spreading to determine the phase of a monolayer at a given surface pressure. This has been demonstrated in the shear viscosities of long-chain fatty acids, esters, amides, and amines (Jarvis, 1965). In addition,... 

If we extrapolate this slope toward low rates, where the tangent equates with the low shear viscosity and assume the Peclet number here is unity we eventually obtain a value of b = 2.55. This defines the Peclet number as unity, at a stress somewhere just after the curvature of the viscosity curve deviates from the low shear limit. This seems quite an appropriate reference system. By setting the Peclet number to the appropriate value of b we can determine the variation in packing fraction with stress between the high and low shear limits to the viscosity ... 

At this point it is appropriate to define viscosity and how it is measured. In the text that follows, the shear viscosity is referred to as viscosity. It is important to realize that fluids also have an extensional or elongational viscosity when stretched however, this property is not dealt with here. The shear mode of deformation is assumed henceforth, such that the motion in the fluid is similar to the action of the blades of a pair of shears. 

In principle, slip can only be confirmed by comparing measurements of the velocity profile with the predicated velocity profile calculated from shear viscosity measurements of the fluid in a slip-free viscometer. This explains, in part, why attempts to define slip have followed three main approaches ... 

Since the flow is axially symmetric, the stress is also symmetric and analogous to shear viscosity, the extensional viscosity can be defined as... 

Non-Newtonian Viscosity In the cone-and-plate and parallel-disk torsional flow rheometer shown in Fig. 3.1, parts la and 2a, the experimentally obtained torque, and thus the % 2 component of the shear stress, are related to the shear rate y = y12 as follows for Newtonian fluids T12 oc y, implying a constant viscosity, and in fact we know from Newton s law that T12 = —/ . For polymer melts, however, T12 oc yn, where n < 1, which implies a decreasing shear viscosity with increasing shear rate. Such materials are called pseudoplastic, or more descriptively, shear thinning Defining a non-Newtonian viscosity,2 t],... 

The ordering parameter Fx/2 is defined as Fx/2 = 2 Tg/Tx/2 — 1, where Ti/2 is such that the relaxation time x(7)/2) = 10 6s. In deriving Eq. (2.49), VTF temperature dependence for relaxation time x(T) or shear viscosity r (7 ) was assumed, and it was further assumed that between lower and upper ends of the glass transition region, the relaxation time and shear viscosity changed by 2.3 orders of magnitude [37],... 

In the case of the oscillatory motion, equation (6.19) defines, in accordance with equation (6.8), the complex shear viscosity r](co) = rf I iif with components... 

Then, equation (9.5) defines the non-zero components of the stress tensor, which makes it possible to formulate expressions for the shear viscosity and the differences between the normal stresses ... 

An elongational or extensional viscosity (%) develops as a result of a conformational transition when disperse systems are forced through constrictions, or compressed or stretched (Kulicke and Haas, 1984 Rinaudo, 1988 Barnes et al., 1989 Odell et al., 1989 Clark, 1992). The intuitive logic is that the random coils resist the initial distortion. % is believed to elicit the human sensation of stringiness (Clark, 1995). If shear viscosity is denoted iq, rheologists define a Trouton ratio as %/ti, wherein % > T) by a factor approximating 3 for uniaxial extension and 6 for biaxial extension. Alternatively stated, the Newtonian ly calculates to one-third to one-sixth % (Steffe, 1992). 

A fundamental rheological value is the viscosity function, i.e., the shear viscosity as a function of the shear rate r] = f(y). The relationship between rj and y is determined by experiments and is described by means of heuristic functions. The viscosity measurement of fluids is shown here by shearing a fluid between two parallel plates (Fig. 3.1). The lower plate is fixed [u(x2 = 0)=0] and the upper plate is drawn across it at a speed of uo [u(x2 = H) = Uo], for which a force F is required. The shear rate is defined as a time derivation of the deformation 6L relative to the height H in a time period dt, or as a quotient ... 

In the case of fluids without yield stress, viscous and viscoelastic fluids can be distinguished. The properties of viscoelastic fluids lie between those of elastic solids and those of Newtonian fluids. There are some viscous fluids whose viscosity does not change in relation to the stress (Newtonian fluids) and some whose shear viscosity T] depends on the shear rate y (non-Newtonian fluids). If the viscosity increases when a deformation is imposed, we define the material as a shear-thickening (dilatant) fluid. If viscosity decreases, we define it as a shear-thinning fluid. 

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