Relation of viscosity

No comprehensive review of the literature dealing with the relations of viscosity and shape has been attempted here. Very useful reviews in this field have been given by Burgers (id) and Lauffer 65). 

In many engineering problems, viscosity appears only in the relation of viscosity divided by density. Therefore, to save writing, we define... 

Of the two temperature scales, T relates actual temperature to changes in curve direction, T shows relation of viscosity to second power of temperature. Figures on T should be multiplied by 1000. 

Figure 6. Relation of Viscosity to Concentration of Solutions of Carrageenin in Water...

THE RELATION OF VISCOSITY AND MOLECULAR WEIGHT FOR ISOTOPIC SPECIES OF HYDROCARBON GASES. M.S. THESIS. 

Relation of Viscosity to Molecular Weight and Shape of the Particles in Sols... 

The traverse speed can characterize coefficient of resistance to corpuscle motion in a liquid, so, and a d5mamic coefficient of viscosity of a liquid. Possibility of effect of viscosity of a liquid on efficiency of capture of corpuscles of a dust a drop by simultaneous Act of three mechanisms the inertia, capture the semiempirical equation Slinna(1981) considering the relation of viscosity of a liquid to viscosity of gas also presents. 

Ghatee et al.[131] described a correlation study with two linear relations of viscosities of ILs. The first one presents the temperature dependence of imidazolium, pyridinium. 

When the viscosities are not known, they can be estimated by the relations of Abbott et al. (1971) ... 

Rather than discuss the penetration of the flow streamlines into the molecular domain of a polymer in terms of viscosity, we shall do this for the overall friction factor of the molecule instead. The latter is a similar but somewhat simpler situation to examine. For a free-draining polymer molecule, the net friction factor f is related to the segmental friction factor by... 

For some materials the linear constitutive relation of Newtonian fluids is not accurate. Either stress depends on strain in a more complex way, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known collectively as non-Newtonian. Many different types of behavior have been observed, ranging from fluids for which the viscosity in the Navier-Stokes equation is a simple function of the shear rate to the so-called viscoelastic fluids, for which the constitutive equation is so different that the normal stresses can cause the fluid to flow in a manner opposite to that predicted for a Newtonian fluid. 

Viscosity—Temperature. Oil viscosity decreases with increa sing temperature in the general pattern shown in Eigure 8, an example of ASTM charts which are available in pad form (ASTM D341). A straight line drawn through viscosities of an oil at any two temperatures permits estimation of viscosity at any other temperature, down to just above the cloud point. Such a straight line relates kinematic viscosity V in mm /s(= cSt) to absolute temperature T (K) by the Walther equation. 

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

Linear equations of the type u = ct — C, where c and C are constants, relate kinematic viscosity to efflux time over limited time ranges. This is based on the fact that, for many viscometers, portions of the viscosity—time curves can be taken as straight lines over moderate time ranges. Linear equations, which are simpler to use in determining and applying correction factors after caUbration, must be appHed carefully as they do not represent the tme viscosity—time relation. Linear equation constants have been given (158) and are used in ASTM D4212. 

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. 

Curves for the viscosity data, when displayed as a function of shear rate with temperature, show the same general shape with limiting viscosities at low shear rates and limiting slopes at high shear rates. These curves can be combined in a single master curve (for each asphalt) employing vertical and horizontal shift factors (77—79). Such data relate reduced viscosity (from the vertical shift) and reduced shear rate (from the horizontal shift). 

This equation is based on the approximation that the penetration is 800 at the softening point, but the approximation fails appreciably when a complex flow is present (80,81). However, the penetration index has been, and continues to be, used for the general characteristics of asphalt for example asphalts with a P/less than —2 are considered to be the pitch type, from —2 to +2, the sol type, and above +2, the gel or blown type (2). Other empirical relations that have been used to express the rheological-temperature relation are fluidity factor a Furol viscosity P, at 135°C and penetration P, at 25°C, relation of (H—P)P/100 and penetration viscosity number PVN again relating the penetration at 25°C and kinematic viscosity at 135 °C (82,83). 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

The term aK2v", derived from reptation theory, describes the velocity-dependent energy necessary to fracture the bulk adhesive. K2 is the consistency which relates the viscosity to the shear rate for a non-newtonian fluid. a = TtraL fh", with r being the chain radius, L the chain length, a the density of chains crossing over the fracture plane, and h is the distance between the chain and reptation tube. 

When log (viscosity) is plotted against log (shear rate) or log (shear stress) for the range of shear rates encounterd in many polymer processing operations, the result is a straight line. This suggests a simple power law relation of the type... 

There are several similar relationships for centrifugal pumps that can be used if the effects of viscosity of the pumped fluid can be neglected. These relate the operating performance of any centrifugal pump for one set of operating conditions to those of another set of operating conditions, say conditions, and conditions 2. 

Indeed, one often observes a more or less direct relationship between the rheological properties of melts and the mechanical strength of the condensed material. This is a commonplace statement in regard of, say, stiffness, since the equations relating the viscosity of heterogeneous materials with their composition... 

The problem of the influence of molecular parameters of a polymer (i.e. of an average molecular weight and molecular-weight distribution) on yield stress is related with the problem of the role of viscosity of a dispersion medium. 

Interpretation of data obtained under the conditions of uniaxial extension of filled polymers presents a severe methodical problem. Calculation of viscosity of viscoelastic media during extension in general is related to certain problems caused by the necessity to separate the total deformation into elastic and plastic components [1]. The difficulties increase upon a transition to filled polymers which have a yield stress. The problem on the role and value of a yield stress, measured at uniaxial extension, was discussed above. Here we briefly regard the data concerning longitudinal viscosity. 

Ya.B. ZeFdovich, FizGoreniyaVzryva 7 (4), 463-76 (1971) CA 77, 64194 (1972) The influence of turbulence and nonturbulence is examined relative to a proplnt burning in a gas flow. Equations indicate exptl methods for determining the magnitudes of the thermal conductivity and viscosity under turbulent flow, and permit a study of thermal flow distribution and temps in a gas wherein an exothermic chem reaction occurs. Equations for non turbulent conditions can be used to calculate the distance from the surface of the proplnt to the zone of intense chem reaction and establish the relation of bulk burning rate to the vol reaction rate. 

The heat of dissociation in hexane solution of lithium polyisoprene, erroneously assumed to be dimeric, was reported in a 1984 review 71) to be 154.7 KJ/mole. This value, taken from the paperl05> published in 1964 by one of its authors, was based on a viscometric study. The reported viscometric data were shown i06) to yield greatly divergent AH values, depending on what value of a, the exponent relating the viscosity p of a concentrated polymer solution to DPW of the polymer (q DP ), is used in calculation. As shown by a recent compilation 1071 the experimental a values vary from 3.3 to 3.5, and another recent paper 108) reports its variation from 3.14 to 4. Even a minute variation of oe results in an enormous change of the computed AH, namely from 104.5 KJ/mole for oe = 3.38 to 209 KJ/mole for oe = 3.42. Hence, the AH = 154.7 KJ/mole, computed for a = 3.40, is meaningless. For the same reasons the value of 99.5 KJ/mole for the dissociation of the dimeric lithium polystyrene reported in the same review and obtained by the viscometric procedure is without foundation. 

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