Effective viscosity definition

Here, the internal viscosity is defined as the contribution of the glassy-relaxation process to the zero-shear viscosity. This definition is different from the common understanding of the term used in literature/ although both have similar notions as to the existence of an effect of fast sub-Rouse-segmental motions on polymer viscoelasticity. In the literature the term internal viscosity generally refers to the effect that would lead to a plateau value of the intrinsic viscosity at high frequencies. 

A number of workers have reported evidence that electron transfer rate constants involving species in solution are a function of the viscosity of the medium [32,54,103,104]. However, Smalley and Creager [105] and Creager and Weber [106] saw no definitive viscosity effect on the electron transfer rate constant for ferrocene attached to a gold electrode. Even if there were a small effect, neither the temperature dependence nor the pressure depen-... 

Other SFA studies complicate the picture. Chan and Horn [107] and Horn and Israelachvili [108] could explain anomalous viscosities in thin layers if the first layer or two of molecules were immobile and the remaining intervening liquid were of normal viscosity. Other inteipretations are possible and the hydrodynamics not clear, since as Granick points out [109] the measurements average over a wide range of surface separations, thus confusing the definition of a layer thickness. McKenna and co-workers [110] point out that compliance effects can introduce serious corrections in constrained geometry systems. 

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

Same definitions as 5-26-M. ILff = effective viscosity from power law model, Pa-s. <3 = surface tension liquid, N/m. 

The correction of mean free path, hi by the nanoscale effect function results in a smaller mean free path, or a smaller Knudsen number in other word. As a matter of fact, a similar effect is able to be achieved even if we use the conventional definition of mean free path, / = irSn, and the Chapmann-Enskog viscosity equation, /r = (5/16)... 

A final comment has to do with the concept of effective viscosity In strongly Inhomogeneous fluids. For these systems the definition of the effective viscosity depends on the type flow, hence different effective viscosities will be measured for different flow situations In the same system with the same density profile. Therefore, the effective viscosity Is a concept of limited value and measurements of this quantity do not provide much information about the effects of density structure on the flow behavior. 

At pH 3.0, all enzymatic activities are lower than the ones at pH 6.0. This effect is especially marked for the PL because its optimum pH value is definitely higher than those of PG and PE (Table 1). PG is very efficient in depolymerising the polygalacturonic acid. The solution viscosity reaches its minimum value, which corresponds to a rather low molar mass, after 40 min at both pH 4.1 and 6.0. 

In a practical sense, stability of a dispersion ofttimes is accompanied by a retarded separation of the phases. Unfortunately, a quantitative definition cannot be based on this rate of separation because of the overwhelming influence of density, viscosity, and thermal effects. In short, a kinetic criterion, such as sedimentation rate, is not as likely to portray stability as one based on thermodynamic considerations. In this latter category are sediment volumes, turbidity, consistency, and electrical behavior. 

These two examples show that regular patterns can evolve but, by definition, dissipative structures disappear once the thermodynamic equilibrium has been reached. When one wants to use dissipative structures for patterning of materials, the dissipative structure has to be fixed. Then, even though the thermodynamic instability that led to and supported the pattern has ceased, the structure would remain. Here, polymers play an important role. Since many polymers are amorphous, there is the possibility to freeze temporal patterns. Furthermore, polymer solutions are nonlinear with respect to viscosity and thus strong effects are expected to be seen in evaporating polymer solutions. Since a macromolecule is a nanoscale object, conformational entropy will also play a role in nanoscale ordered structures of polymers. 

Using the definition for the turbulent viscosity (jit — /An /xmoi), which gives a result similar to the standard k-s model with only a small difference in the modeling constant, the effective viscosity is now defined as a function of k and s in Eq. (16) in algebraic form. 

It was also noted by Farrington and co-workers that the chemical nature of the end-groups may have a substantial effect on the viscosity of bulk dendrimers, even under iso-free volume conditions [49]. This seems consistent with the establishment of interdendrimer interactions and supramolecular organization at rest in the bulk state. However, as in most other areas of dendrimer rheology, more data are desirable before definite conclusions can be drawn. 

The current is zero at equilibrium. Indeed, = 0 is one definition of equilibrium (see Chapter 2). As the potential is shifted away from V equilibrium so the electrode is polarized (cf Section 6.1). We recall that the deviation of the potential from its equilibrium value is termed the overpotential q (as defined by equation (6.1)). The portion of the Tafel graph at extreme overpotentials represents insufficient flux at the electrode in effect, the potential is so extreme that extra charge could flow if sufficient flux were available but, because of solvent viscosity, rate of solution stirring, etc., the flux is simply not large enough for the behaviour to follow the Tafel equation. 

The question of the cause of the sharp change in effectiveness over a very small range in viscosity or molecular size is still not precisely known. However, it is believed from some limited data available that volatility is definitely involved. Certainly volatility accounts for the almost complete ineffectiveness of the lightest compositions as well as fractions of petroleum within the kerosene range. The studies of Smith and Pearce (I )... 

A good example of the effect of transformations on the variation of data around some given true value is found in viscosity measurements Here the variability is definitely related to the level of viscosity However, the logarithm of the viscosity is homoscedastic, as can be seen below. 

The remarkable variations in the viscosity of molten sulphur have already been mentioned. Definite measurements have been made at a series of temperatures by the method of rotating cylinders,5 and it, has been found that exposure of the liquid to air, especially below 160° C., has a marked effect on the viscosity from 160° C. onwards. The viscosity of purified (twice distilled but not gas-free) sulphur lias a value at 123° C. of 0 1094 C.G.S. units this falls to a minimum of 0 0709 at 150° C., rises gradually up to about 159° then rapidly increases above this temperature an exact transition point is not observed, however. The maximum for purified unexposed (gas-frcc) sulphur occurs at about 200° C. and has a value of 215 C.G.S. units. For purified (not gas-free) sulphur after prolonged exposure to the air, the maximum occurs at about 190° C, and may have a value as high as 800 C.G.S. units. Such high viscosity appears to be due to impurities, the chief being sulphuric acid, resulting from exposure to the air sulphur dioxide and ammonia in solution also have an appreciable effect. 

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