Viscous fluids mechanical behavior

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

From a technical standpoint, it is also important to note that colloids display a wide range of rheological behavior. Charged dispersions (even at very low volume fractions) and sterically stabilized colloids show elastic behavior like solids. When the interparticle interactions are not important, they behave like ordinary liquids (i.e., they flow easily when subjected to even small shear forces) this is known as viscous behavior. Very often, the behavior falls somewhere between these two extremes the dispersion is then said to be viscoelastic. Therefore, it becomes important to understand how the interaction forces and fluid mechanics of the dispersions affect the flow behavior of dispersions. 

From a fluid mechanical point of view, we concentrate on viscous behavior in boundary layers. It is often the boundary-layer behavior near a surface that is responsible for important outcomes, like uniform thin-film growth. Quite often the analysis of boundary-layer flows can take advantage of some major mathematical simplifications of the general flow equations. Moreover, and perhaps more important, it is the characteristics of certain boundary layers that are responsible for desirable properties of the process. Unlike much fluid-mechanical literature, which con-... 

S. Bhattacharji and P. Savic, Real and Apparent Non Newtonian Behavior in Viscous Pipe flow of Suspensions Driven by a Fluid Piston, Proc. Heat and Mass Transfer Fluid Mechanics Institute, 15, 248 (1965). 

TABLE 12.4 Mechanical Behavior of Viscous Fluid, Elastic Solid, Visco-elastic Fluid, and Visco-elastic Solid... 

The nature of the dependence of the shear stress (or viscosity) upon shear rate determines the class of viscous fluid behavior (Figures 5.2 and 5.3). The shear stress and shear rate may both be either positive or negative, although (by the usual mechanics convention) they always have the same sign. A Newtonian fluid obeys the equation... 

At present, there exist several dozens of rheological (mostly empirical) models of nonlinear viscous fluids. This is due to the fact that for the vast variety of fluid media of different physical nature, there is no rigorous general theory, similar to the molecular kinetic theory of gases, which would enable one to calculate the characteristics of molecular transport and the mechanical behavior of a medium on the basis of its interior microscopic structure. 

Constitutive equations that capture the essential features of the responses of red blood cells and passive leukocytes have been formulated, and material parameters characterizing the ceUular behavior have been measured. The red ceU response is dominated by the ceU membrane which can be described as a hyper-viscoelastic, two-dimensional continuum. The passive white ceU behaves like a highly viscous fluid drop, and its response to external forces is dominated by the large viscosity of the cytosol. Refinements of these constitutive models and extension of mechanical analysis to activated white ceUs is anticipated as the ultrastmctural events that occur during ceUular deformation are delineated in increasing detail. 

Bhattacharji, S. and Savic, R, Real and apparent non-Newtonian behavior in viscous pipe flow of suspension driven by a fluid pressure, in Heat Transfer and Fluid Mechanics Institute Proceedings, Charwat, A.F, et al. (eds.), Stanford University Press, Stanford, Calif., 1965, p. 248. 

At pH values ranging from 6 to 9, the electrode departs from ideal behavior and measurement errors occur. Quinhydrone electrodes tend not to be so long-lived as other electrodes. They are, however, mechanically rugged and can be used in extremely viscous fluids where glass electrodes (next section) would break. Electrical impedance is low. 

The viscoelastic nature of polymers (filled or unfilled) and their peculiarities in the viscous as well as elastic response to deformation under applied stresses bring them under the category of non-Newtonian fluids. There is distinctive difference in flow behavior between Newtonian and non-Newtonian fluids to an extent that, at times, certain aspects of non-Newtonian flow behavior may seem abnormal or even paradoxical [12-16]. An interesting movie about polymer fluid mechanics has been prepared [17] which clearly depicts certain peculiarities of such fluids. The dramatic differences between the qualitative responses of Newtonian and non-Newtonian fluids grossly affect their industrial and practical applications. 

Polymeric materials, such as rubber, exhibit a mechanical response which cannot be properly described neither by means of elastic nor viscous effects only. In particular, elastic effects account for materials which are able to store mechanical energy with no dissipation. On the other hand, a viscous fluid in a hydrostatic stress state dissipates energy, but is unable to store it. As the experimental results reported in Part 1 have shown, filled rubber present both the characteristics of a viscous fluid and of an elastic solid. Viscoelastic constitutive relations have been introduced with the intent of describing the behavior of such materials able to both store and dissipate mechanical energy. 

As discussed briefly in the next section, polymers have a unique response to mechanical loads and are properly treated as materials which in some instances behave as elastic solids and in some instances as viscous fluids. As such their properties (mechanical, electrical, optical, etc.) are time dependent and cannot be treated mathematically by the laws of either solids or fluids. The study of such materials began long before the macromolecu-lar nature of polymers was understood. Indeed, as will be evident in later chapters on viscoelasticity, James Clerk Maxwell (1831-79), a Scottish physicist and the first professor of experimental physics at Cambridge, developed one of the very first mathematical models to explain such peculiar behavior. Lord Kelvin (Sir William Thomson, (1824-1907)), another Scottish physicist, also developed a similar mathematical model. Undoubtedly, each had observed the creep and/or relaxation behavior of natural materials such as pitch, tar, bread dough, etc. and was intrigued to explain such behavior. Of course, these observations were only a minor portion of their overall contributions to the physics of matter. 

---