Viscosity-constitutional constant

For alkanes, the logarithm of viscosity has been correlated with atomic and with bond contributions to estimate tj at 0 and 20°C [13]. Considering a broader range of structural variety, neither the viscosity nor its logarithm is a constitutionally additive property. Application of the group contribution approach is based on additive parameters that allow viscosity estimations in combination with other experimental data such as density or vapor pressure. The viscosity-constitutional constant, /vc, is such an additive parameter ... 

Revised material for Section 5 includes the material on surface tension, viscosity, dielectric constant, and dipole moment for organic compounds. In order to include more data at several temperatures, the material has been divided into two separate tables. Material on surface tension and viscosity constitute the first table with 715 entries included is the temperature range of the liquid phase. Material on dielectric constant and dipole... 

For almost steady flows one can expand yl1 or y about t t and obtain second-order fluid constitution equations in the co-deforming frame. When steady shear flows are considered, the CEF equation is obtained, which, in turn, reduces to the GNF equation for T i = 2 = 0 and to a Newtonian equation if, additionally, the viscosity is constant. 

Non-Newtonian behavior of complex fluids is usually governed by various constitutive laws which relate the viscosity of liquids to the rate of shear. The power-law constitutive model is used in most instances due to its ability to predict rheological behaviors of a wide range of non-Newtonian liquids. The power-law model is characterized with a flow behavior index, n, and a flow consistency index, m. Specifically, n=l corresponds to Newtonian fluids whose viscosity is constant, n< corresponds to shear-thinning fluids whose viscosity decreases with increasing the rate of shear, and n>l... 

Consider an A -component Newtonian electrolyte of density Pf, dynamic viscosity p = constant, and dielectric constant e, flowing with velocity u(R, t) in interstices of a porous material. Let 4 (R, t) be the electric potential prevailing within the solute. The flux j of each ith ion species composing the solute is given by the constitutive equation [1]... 

Additionally, ionic liquids are generally described in the literature as Newtonian fluids, in other words, their viscosities remain constant with increasing shear rates. For example, Newtonian behaviors for alkylimidazolium (wifli die alkyl chain length between 1 and 8 carbon atoms) based ionic liquids with tetrafluoroborate, hexafluorophosphate, and bis(trifluoromethylsulfonyl)imide anions are reported in the literature. Nevertheless, this rheological behavior is strongly affected by the choice of ions constituting the ionie liquid. In fact, non-Newtonian behavior has been described for several ionic liquids. 

Once the value of the constant and the a value in Eq. (2.36) have been evaluated for a particular system, viscosity measurements constitute a relatively easy method for determining the molecular weight of a polymer. Criticize or defend the following proposition Since viscosity is so highly dependent on molecular weight for M > M, a 10% error in 17 will result in a 34% error in M above M, but only a 10% error in M below M, . 

Non-Newtonian Fluids Die Swell and Melt Fracture. Eor many fluids the Newtonian constitutive relation involving only a single, constant viscosity is inappHcable. Either stress depends in a more complex way on strain, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known coUectively as non-Newtonian and are usually subdivided further on the basis of behavior in simple shear flow. 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

The initiation step could also be positively affected by the above-mentioned transport properties, as the efficiency factor f assumes higher values with respect to conventional liquid solvents due to the diminished solvent cage effect One further advantage is constituted by the tunability of the compressibility-dependent properties such as density, dielectric constant, heat capacity, and viscosity, all of which offer additional possibilities to modify the performances of the polymerization process. This aspect could be particularly relevant in the case of copolymerization reactions, where the reactivity ratios of the two monomers, and ultimately the final composition of the copolymer, could be controlled by modifying the pressure of the reaction system. 

In this case, p is an arbitrary constant, chosen as the zero shear rate viscosity. The expression for the non-Newtonian viscosity is a constitutive equation for a generalized Newtonian fluid, like the power law or Ostwald-de-Waele model [6]... 

Despite the apparent deficiency of description (9.58) when applied to a real system, we may note that the set of constitutive equations (9.58)-(9.60) represent qualitatively the behaviour of concentrated polymer solutions and melts under shear. The set of equations include two material constants which are the individual characteristics of the system, namely, the initial shear viscosity and... 

It has already been pointed out that in model experiments the pi-number and not the x-quantity should be varied. This results in various advantages. On the one hand, the pi-number is varied by changing the most available, the most manageable or the cheapest x-quantity constituting it (example changing the Reynolds number by varying the kinematic viscosity of the fluid). In addition, the evaluation of the test results is made easier, because in varying a certain pair of pi-numbers, the numerical values of all the other pi-numbers remain constant (11 = idem). 

In Fig. 15.27, the transient extensional viscosity of a low-density polyethylene, measured at 150 °C for various extensional rates of strain, is plotted against time (Munstedt and Laun, 1979). Qualitatively this figure resembles the results of the Lodge model for a Maxwell model in Fig. 15.26. For small extensional rates of strain (qe < 0.001 s ) 77+(f) is almost three times rj+ t). For qe > 0. 01 s 1 r/+ (f) increases fast, but not to infinite values, as is the case in the Lodge model. The drawn line was estimated by substitution of a spectrum of relaxation times of the polymer (calculated from the dynamic shear moduli, G and G") in Lodge s constitutive equation. The resulting viscosities are shown in Fig. 15.28 after a constant value at small extensional rates of strain the viscosity increases to a maximum value, followed by a decrease to values below the zero extension viscosity. 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

The filler network break-down with increasing deformation amplitude and the decrease of moduli level with increasing temperature at constant deformation amplitude are sometimes referred to as a thixotropic change of the material. In order to represent the thixotropic effects in a continuum mechanical formulation of the material behavior the viscosities are assumed to depend on temperature and the deformation history [31]. The history-dependence is implied by an internal variable which is a measure for the deformation amplitude and has a relaxation property as realized in the constitutive theory of Lion [31]. More qualitatively, this relaxation property is sometimes termed viscous coupling1 [26] which means that the filler structure is viscously coupled to the elastomeric matrix, instead of being elastically coupled. This phenomenological picture has... 

Being a disperse system, the foam exhibits a more complex behaviour when subjected to mechanical loading, compared to that of its constituting phases liquid and gas. Of all rheological parameters the latter are characterised by the viscosity alone. The complete description of the foam system requires knowledge of the constants of elasticity (modulus of... 

In the story of numerical flow simulation, the ability to predict observed and significant viscoelastic flow phenomena of polymer melts and solutions in an abrupt contraction has been unsuccessful for many years, in relation to the incomplete rheological characterization of materials, especially in elongation. The numerical treatments have often been confined to flow of elastic fluids with constant viscosity, described by differential constitutive equations as the Upper Convected Maxwell and Oldroyd-B models. Fortunately, the recent possibility to use real elastic fluids with constant viscosity, the so-called Boger fluids [10], has narrowed the gap between experimental observation and numerical prediction [11]. 

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