Viscoelastic fluid behavior

Eig. 7. Viscoelastic behavior of encapsulant materials (a) Newtonian fluid (b) non-Newtonian fluid. 

The Maxwell model is also called Maxwell fluid model. Briefly it is a mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus (E) in series with a dashpot of coefficient of viscosity (ji). It is an isostress model (with stress 5), the strain (f) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as d /dt = (l/E)d5/dt + (5/Jl)-This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis. 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Elastic behavior of liquids is characterized mainly by the ratio of first differences in normal stress, Ni, to the shear stress, t. This ratio, the Weissenberg number Wi = Nih, is usually represented as a function of the rate of shear y. Figure 7 depicts flow curves of some viscoelastic fluids, and Figure 8 presents a dimensionless standardized material function of these fluids. It again verifies that they behave similarly with respect to viscoelastic behavior under shear stress. 

Figure 8 Dimensionless standardized material function of the fluids in Figure 7, verifying the similar viscoelastic behavior under shear stress. (From Ref. 12.)...

The response of simple fluids to certain classes of deformation history can be analyzed. That is, a limited number of material functions can be identified which contain all the information necessary to describe the behavior of a substance in any member of that class of deformations. Examples are the viscometric or steady shear flows which require, at most, three independent functions of the shear rate (79), and linear viscoelastic behavior (80,81) which requires only a single function, in this case a relaxation function. The functions themselves must be determined experimentally for each substance. 

Viscoelastic behavior is classified as linear or non-linear according to the manner by which the stress depends upon the imposed deformation history (SO). Insteady shear flows, for example, the shear rate dependence of viscosity and the normal stress functions are non-linear properties. Linear viscoelastic behavior is obtained for simple fluids if the deformation is sufficiently small for all past times (infinitesimal deformations) or if it is imposed sufficiently slowly (infinitesimal rate of deformation) (80,83). In shear flow under these circumstances, the normal stress differences are small compared to the shear stress, and the expression for the shear stress reduces to a statement of the Boltzmann superposition principle (15,81) ... 

Real world materials are not simple liquids or solids but are complex systems that can exhibit both liquid-like and solid-like behavior. This mixed response is known as viscoelasticity. Often the apparent dominance of elasticity or viscosity in a sample will be affected by the temperature or the time period of testing. Flow tests can derive viscosity values for complex fluids, but they shed light upon an elastic response only if a measure is made of normal stresses generated during shear. Creep tests can derive the contribution of elasticity in a sample response, and such tests are used in conjunction with dynamic testing to quantity viscoelastic behavior. 

To fully understand the behavior of biological materials we need to address the issue of viscoelasticity. When a weight is placed on viscoelastic material, there is an instantaneous elastic response and a time-dependent viscous response (see Figure 7.1). For polymers the elastic response reflects the change in macromoleular conformation, which is usually time independent if no bonds are broken. The viscous response is the flow of macromolecules by each other similar to what happens during the flow of fluids in a tube. Fluid flow is a time-dependent process. Polymers exhibit viscoelastic behavior because they have both a time-independent response and a time-dependent response. 

N2 values are always lower than Nj values, see e.g. [40]. Therefore for many processes taking into consideration only Nj will suffice. The normal stress differences are independent of the direction of flow and, in laminar flow (low y), are proportional to y2. In following p = x/y for a Newtonian fluid, normal stress coefficients ipi = Nj/y2 and ip2 = N2/y2 are occasionally used. Their dependence on the shear rate i j(y) describes the non-linear viscoelastic behavior of the fluid. 

For a correct dimensional-analytical representation of the viscoelastic behavior of a fluid, the ratio of normal stress to shear stress is used. The so-called Weissenberg number is defined as... 

Polymeric (and other) solids and liquids are intermediate in behavior between Hookean, elastic solids, and Newtonian, purely viscous fluids. They often exhibit elements of both types of response, depending on the time scale of the experiment. Application of stresses for relatively long times may cause some flow and permanent deformation in solid polymers while rapid shearing will induce elastic behavior in some macromolecular liquids. It is also frequently observed that the value of a measured modulus or viscosity is time dependent and reflects the manner in which the measuring experiment was performed. Tliese phenomena are examples of viscoelastic behavior. 

Foods can be classified in different manners, including as solids, gels, homogeneous liquids, suspensions of solids in liquids, and emulsions. Fluid foods are those that do not retain their shape but take the shape of their container. Fluid foods that contain significant amounts of dissolved high molecular weight compounds (polymers) and/or suspended solids exhibit non-Newtonian behavior. Many non-Newtonian foods also exhibit both viscous and elastic properties, that is, they exhibit viscoelastic behavior. 

In this book, we review the most basic distinctions and similarities among the rheological (or flow) properties of various complex fluids. We focus especially on their linear viscoelastic behavior, as measured by the frequency-dependent storage and loss moduli G and G" (see Section 1.3.1.4), and on the flow curve— that is, the relationship between the "shear viscosity q and the shear rate y. The storage and loss moduli reveal the mechanical properties of the material at rest, while the flow curve shows how the material changes in response to continuous deformation. A measurement of G and G" is often the most useful way of mechanically characterizing a complex material, while the flow curve q(y ) shows how readily the material can be processed, or shaped into a useful product. The... 

The shearing characteristics of non-Newtonian fluids are illustrated in Fig. 7. Curves A and B represent viscoelastic behavior. Curve C illustrates the behavior if the fluid thins with increasing shear, generally referred to as shear thinning or pseudoplasticity. The opposite effect of shear thickening or dilatancy is shown as curve D. 

This section discusses viscoelastic fluid viscosity, pressure drop during viscoelastic flow, and factors affecting viscoelastic behavior. 

Basically, Eq. 6.17 results from combining Eqs. 6.12, 6.13, and 6.15 with Cei = 1. According to Marshall and Mentzner (1964), the onset of viscoelastic behavior occurs at a Deborah number around 0.1. From the work of Durst et al. (1982), the Deborah number is 0.5. The smaller the Deborah number, the more the material appears like a fluid. 

Up to this point, the information about the monolayers has looked at the structural properties as if the lipopolymer monolayers were static and fixed above a body of water. However, a truly remarkable aspect of these monolayers is their fascinating fluidity and visoelastic properties, and the range of distinct fluid and viscoelastic behavior they exhibit under different conditions and with different lipopolymers. These properties can be studied by analyzing the viscosity and elasticity of the monolayer, as discussed in Sect. 2.2, as well as by investigating the lateral diffusion of individual lipopolymers within the monolayer, as discussed in Sect. 2.3. 

The relaxation spectrum may include a term corresponding to x = 0. This may be expressed as t) on the first line of Eq. (1.10) and gives rise to an additional term icot] x in Eq. (1.11). Ordinary solvents, usually of low molecular weights, are Newtonian fluids which have only one mechanism corresponding to t = 0 with rj m = t]s, where % is the viscosity. It is customary to describe the viscoelastic behavior of dilute polymer solutions with G ((o) — icoris instead of G (w) This corresponds to the exclusion of a term tjs d (t) from the definition of H (t) which is assumed to be the contribution of the solvent with viscosity ris. 

Very low density PE (VLDPE), 52 Vinizene BP 5-5, 449 Vinyl alkoxysilanes, 172 Vinyl silanes, 172 Vinyl trimethoxysilane grafted polyethylene, 172 Vinyltriethoxy-silane, 194 Virgin plastics, 51 Viscoelastic behavior, 225 Viscoelastic fluid, 622 Viscoelastic materials, 631 Viscosity of polyethylene hot melts, 633 Viscosity of polymers, 620 Viscosity of water, 620 Viscosity, 622... 

Figure 15.5 shows a plot of the friction factor versus the Reynolds number as defined in Eq. 15.10. Because the Reynolds number has been defined by Eq. 15.10, the laminar-flow data must fall on the line shown. For flow at Reynolds numbers greater than 2000, two possible kinds of behavior are known. All slurries and many polymer solutions are represented by the solid curve in Fig 15.5. These do not seem to significantly suppress the turbulent behavior of the fluid. However, some polymer solutions and polymer melts, particularly those which show distinct viscoelastic behavior (such as rubber cement) obey the curves shown dotted at the right in Fig. 15.5. Visual observation [7] indicates that for these fluids the turbulence in the fluid is much less than it would be for a newtonian fluid at the same Reynolds number.

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