Newtonian body viscosity

The value of Pi is equal to the viscosity rj, and Eq. (15) thus describes the Newtonian body. The mechanical model of a Newtonian body is the dashpot, which is illustrated in Fig. 10. The rate of extension of the dashpot depends on the stress exerted, and if the dashpot becomes stress free at any time, it will remain in its current state of extension. 

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

Falling ball viscometers are based on Stokes law, which relates the viscosity of a Newtonian fluid to the velocity of the falling sphere. If a sphere is allowed to fall freely through a fluid, it accelerates until the viscous force is exactly the same as the gravitational force. The Stokes equation relating viscosity to the fall of a soHd body through a Hquid may be written as equation 34, where ris the radius of the sphere and d are the density of the sphere and the hquid, respectively g is the gravitational force and p is the velocity of the sphere. 

In the Irvine-Park falling needle viscometer (FNV) (194), the moving body is a needle. A small-diameter glass or stainless steel needle falls vertically in a fluid. The viscous properties and density of the fluid are derived from the velocity of the needle. The technique is simple and useflil for measuring low (down to lO " ) shear viscosities. The FNV-100 is a manual instmment designed for the measurement of transparent Newtonian and non-Newtonian... 

Gum arable comes from various species of Acacia. The gum exudes through cracks, injuries, and incisions in the bark and is collected by hand as dried tears. Gum arable is unique among gums because of its high solubiUty and the low viscosity and Newtonian flow of its solutions. While other gums form highly viscous solutions at 1—2% concentration, 20% solutions of gum arable resemble a thin sugar symp in body and flow properties. 

The rheological characteristics of AB cements are complex. Mostly, the unset cement paste behaves as a plastic or plastoelastic body, rather than as a Newtonian or viscoelastic substance. In other words, it does not flow unless the applied stress exceeds a certain value known as the yield point. Below the yield point a plastoelastic body behaves as an elastic solid and above the yield point it behaves as a viscoelastic one (Andrade, 1947). This makes a mathematical treatment complicated, and although the theories of viscoelasticity are well developed, as are those of an ideal plastic (Bingham body), plastoelasticity has received much less attention. In many AB cements, yield stress appears to be more important than viscosity in determining the stiffness of a paste. 

Consistency, working time, setting time and hardening of an AB cement can be assessed only imperfectly in the laboratory. These properties are important to the clinician but are very difficult to define in terms of laboratory tests. The consistency or workability of a cement paste relates to internal forces of cohesion, represented by the yield stress, rather than to viscosity, since cements behave as plastic bodies and not as Newtonian liquids. The optimum stiffness or consistency required of a cement paste depends upon its application. 

For a concentrated system this represents the ratio of the diffusive timescale of the quiescent microstructure to the convection under an applied deforming field. Note again that we are defining this in terms of the stress which is, of course, the product of the shear rate and the apparent viscosity (i.e. this includes the multibody interactions in the concentrated system). As the Peclet number exceeds unity the convection is dominating. This is achieved by increasing our stress or strain. This is the region in which our systems behave as non-linear materials, where simple combinations of Newtonian or Hookean models will never satisfactorily describe the behaviour. Part of the reason for this is that the flow field appreciably alters the microstructure and results in many-body interactions. The coupling between all these interactions becomes both philosophically and computationally very difficult. 

Application of Newton s second law of motion to an infinitesimal element of an incompressible Newtonian fluid of density p and constant viscosity p, acted upon by gravity as the only body force, leads to the Navier-Stokes equation of motion ... 

In equations 5-8, the variables and symbols are defined as follows p0 is reference mass density, v is dimensional velocity field vector, p is dimensional pressure field vector, x is Newtonian viscosity of the melt, g is acceleration due to gravity, T is dimensional temperature, tT is the reference temperature, c is dimensional concentration, c0 is far-field level of concentration, e, is a unit vector in the direction of the z axis, Fb is a dimensional applied body force field, V is the gradient operator, v(x, t) is the velocity vector field, p(x, t) is the pressure field, jl is the fluid viscosity, am is the thermal diffiisivity of the melt, and D is the solute diffiisivity in the melt. The vector Fb is a body force imposed on the melt in addition to gravity. The body force caused by an imposed magnetic field B(x, t) is the Lorentz force, Fb = ac(v X v X B). The effect of this field on convection and segregation is discussed in a later section. 

The ratio of shearing stress and rate of shear in such materials is not a constant value, so the value is designated apparent viscosity. To be useful, a reported value for apparent viscosity of a non-Newtonian material should be given together with the value of rate of shear or shearing stress used in the determination. The relationship of shearing stress and rate of shear of non-Newtonian materials such as the dilatant and pseudoplastic bodies of Figure 8-5 can be represented by a power law as follows ... 

Newtonian behavior can be observed only for ideally viscous bodies. The flow curve shows a direct proportionality between shear stress and shear strain rate (Fig. 4) with the straight line going through zero. The viscosity remains constant over the complete range of shear stresses applied and is independent of the shear strain rate (Fig. 5). The stress in the material goes back... 

Fig. 5 Viscosity as a function of shear strain rate for a Newtonian (a) and a Bingham body (b).

The Bingham body model describes materials with an apparent yield strength above which Newtonian flow is observed. This is illustrated in Figs. 4 and 5, which show a typical flow curve and viscosity as a function of shear strain rate, respectively. 

FIG. 155. Types of rheological behaviour (a) Newtonian liquid (b) anomalous (pseudoplastic) liquid (c) Bingham body (d) real plastic body (e) thixotropic body (f) dilatant body. The viscosity is given by the tangent of the indicated angle. 

Newtonian viscosity leads to an interesting aspect for materials undergoing a drawing process. The normalized rate of change of the cross-sectional area for a linear viscous material is given by (dA/dt)IA = (deldt)=—a-/q or dAldt) = —Flq, where Fis the applied uniaxial force. This derivation shows that, for a constant F, dAldt) must be constant, i.e., the body can be reduced in cross-section at a constant rate. Thus, a section with an initially narrow section will not neck down faster than elsewhere. 

When the shear stress changes in Newtonian, dilatant, or pseudoplastic liquids, as well as in Bingham bodies or fluids above the flow limit, the corresponding shear gradient or the corresponding viscosity is reached almost instantaneously. In some liquids, however, a noticeable induction time is necessary, i.e., the viscosity also depends on time. If, at a constant shear stress or constant shear gradient, the viscosity falls as the time increases, then the liquid is termed thixotropic. Liquids are termed rheopectic or antithixotropic, on the other hand, when the apparent viscosity increases with time. Thixotropy is interpreted as a time-dependent collapse of ordered structures. A clear molecular picture for rheopexy is not available. 

Body n. (1) A term used loosely in the paint and adhesives industries to denote overall consistency, i.e., a combination of viscosity, density, pastiness, tackiness, etc. (2) An aspect of fabric quality, akin to drape and hand. (3) A general term referring to viscosity, consistency, and flow of a vehicle or ink. (4) Used also to describe the increase in viscosity by polymerization of drying oils at high temperatures. (5) A practical term widely used to give a qualitative picture of consistency. For Newtonian liquids, both is the same as viscosity. 

See dilatancy, Newtonian, non-Newtonian, thixotropy, rheopectic, viscoelasticity, viscosity and Bingham body, and yield value. 

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