Flow properties 166 viscosity coefficients

Flow properties (viscosity, thixotropy) Bond line thickness Coefficient of thermal expansion Shrinkage... 

Simha and Zakin (126), Onogi et al (127), and Comet (128) develop overlap criteria of the same form but with different numerical coefficients. Accordingly, flow properties which depend on concentration and molecular weight principally through their effects on coil overlap should correlate through the Simha parameter c[ /], or cM , in which a is the Mark-Houwink viscosity exponent (0.5 < a < 0.8). If coil shrinkage, caused by the loss of excluded volume in good... 

The relationship between shearing stress and rate of shear can be used to define the flow properties of materials. In the simplest case, the shearing stress is directly proportional to the mean rate of shear x = fly (Figure 8-5). The proportionality constant T is called the viscosity coefficient, or dynamic viscosity, or simply the viscosity of the liquid. The metric unit of viscosity is the dyne.s cm-2, or Poise (P). The commonly used unit is 100 times smaller and called centiPoise (cP). In the SI system, t is expressed in N.s/m2. or... 

Sarman and Evans [24, 32] performed a comprehensive study of the flow properties of a variant of the Gay-Beme fluid. In order to make the calculations faster the Lennard-Jones core of the Gay-Beme potential was replaced by a 1/r core. This makes the potential more short ranged thereby decreasing the number of interactions and making the simulation faster. The viscosity coefficients were evaluated by EMD Green-Kubo methods both in the conventional canonical ensemble and in the fixed director ensemble. The results were cross checked by shear flow simulations. The studies covered nematic phases of both prolate ellipsoids with a length to width ratio of 3 1 and oblate ellipsoids with a length to width ratio of 1 3. The complete set of potential parameters for these model systems are given in Appendix II. 

The rate of interphase mass transfer is affected by the physical and chemical characteristics of the system and the mechanical features of the equipment. The former include viscosities and densities of the phases, interfacial surface properties, diffusion coefficients, and chemical reaction coefficients. The latter include, for example, the type and diameter of the impeller, vessel geometry, the flow rate of each phase, and the rotational speed of the impeller. 

Note that the turbulent viscosity parameter has an empirical origin. In connection with a qualitative analysis of pressure drop measurements Boussinesq [19] introduced some apparent internal friction forces, which were assumed to be proportional to the strain rate ([20], p 8), to fit the data. To explain these observations Boussinesq proceeded to derive the same basic equations of motion as had others before him, but he specifically considered the molecular viscosity coefficient to be a function of the state of flow and not only on the system properties [135]. It follows that the turbulent viscosity concept (frequently referred to as the Boussinesq hypothesis in the CFD literature) represents an empirical first attempt to account for turbulence effects by increasing the viscosity coefficient in an empirical manner fitting experimental data. Moreover, at the time Boussinesq [19] [20] was apparently not aware of the Reynolds averaging procedure that was published 18 years after the first report by Boussinesq [19] on the apparent viscosity parameter. 

Viscosity is a property of liquids which describes their resistance to flow. Glycerol is a more viscous fluid than water, which is more viscous than acetone (nail polish remover). Viscosity is quantified by a viscosity coefficient, rj. Table 5-3 lists some representative values measured at 20 °C. Glycerol, whose viscosity is about the same as maple syrup, is over 1000 times more viscous than... 

As mentioned earlier, for non-Newtonian fluids, the coefficient of viscosity is not a constant, but is itself a function of the shear rate. This leads to some very interesting flow properties. Some convenient ways to summarize the flow properties of... 

If the average life time of the junction points is small, this quantity will play a part in the flow properties of the system and enters into the mathematical expressions. We have already earlier discussed that the shearing of a continuous structure with junction points having a limited life time, is the base of the usual form of anomalous viscosity in concentrated macromolecular solutions (decrease of viscosity coefficient with increasing shear). 

Mobility n. The property of a material which allows it to flow when a shearing force larger than the yield value has been applied. The coefficient of mobility is the rate of shear induced by a shearing force per square cm of 1 dyne in excess of the yield value. Mobility pertains to plastic materials and is the analogue of fluidity. It is calculated firom the slope of the straight-line portion of the flow curve. The coefficient of mobility is the reciprocal of the coefficient of plastic viscosity. 

Viscosity coefficient, i/ n. Resistance to flow, a fundamental property of fluids, first quantitatively defined by Issac Newton in his Principia. A modern version of his equation of viscosity is ... 

The performance of an extruder is determined as much by the characteristics of the feedstock as it is by the machine. Feedstock properties that affect the extrusion process inciude buik properties, meit flow properties, and thermal properties. Important buik flow properties are the buik density, compressibility, particle size, particle shape, external and internal coefficient of friction, and agglomeration tendency. Important melt flow properties are the shear and eiongational viscosity as a function of strain rate and temperature. The commonly used melt indexer provides only limited information on the meit viscosity. Important thermal properties include the specific heat, the glass transition temperature, the crystalline melting point, the latent heat of fusion, the thermal conductivity, the density, the degradation temperature, and the induction time as a function of temperature. 

During processing of polymer melts, strain rates are usually so high that a characterization of the flow properties by a constant viscosity coefficient, as for a low molar mass Newtonian liquid, is no longer adequate. 

The other two examples deal with the flow properties of polymer melts as they are encountered under ordinary processing conditions. Figure 7.2 presents results of measurements of the viscosity of a melt of polyethylene, obtained at steady state for simple shear flows under variation of the shear rate. Data were collected for a series of different temperatures. At low strain rates one finds a constant value for the viscosity coefficient, i.e. a strict proportionality between shear stress and shear rate, but then a decrease sets in. This deviation from linearity is commonly found in polymers and begins even at moderate strain rates. As one observes a decrease in the viscosity, i.e. the ratio between shear stress and shear rate, the effect is usually called shear thinning . 

The flow properties of a SmC phase with fixed director orientation and a flow parallel to the layers can, therefore, be described by seven independent viscosity coefficients. The experimental determination of these coefficients should be connected with a series of problems. If the coefficients 774 or 775 are determined in a capillary with a rectangular cross section with T< W and the layer parallel to one of the plates as in Fig. 20 I. The thickness has to be constant over the whole sample with an accuracy that is not easy achieved [63,64]. There are similar problems in the measurement of the other coefficients. Minor difficulties should occur in a shear experiment with a small lateral movement of one of the plates. 

Contemporary applications of liquid crystals [1,2] exploit the unique properties of these materials arising from their anisotropic response to external fields and forces. For example, the anisotropy in the dielectric properties makes it possible to construct electro-optical displays, and the characteristic response time of such devices is determined by the anisotropic viscoelastic properties of the liquid crystal [3]. In turn, these viscoelastic properties are related to various kinds of flows and deformations of the material in question. The exact number and nature of viscoelastic constants required to characterise fully the properties of the phase are determined by careful consideration of both static and dynamic behaviour [4]. The specific focus of this Datareview is the description of experimental techniques for measuring the various types of viscosity coefficients allowed in nmiatic phases. 

The nematic liquid crystal is orientationally soft, since restoring forces associated with deformation in the director field are very weak. This softness makes alignment of n in bulk samples occur even in very weak external magnetic or electric fields, F s H or E, or by interaction with boundary surfaces and flows in the liquid. This softness also allows for long wavelength thermal fluctuations in the director field. The Leslie viscosity parameters rather than the viscosity coefficients are the more natural quantities of interest for those methods that monitor the viscoelastic response of the nematic to director field modulations. Modulation of n in space and time manifests itself in variations of many bulk properties, e.g. the refractive index [27-37,41-44,48,51,94-106], electric susceptibility [38,39,107-110], or magnetic resonance spectra [40,45-47,111-113]. However, only a limited number of the viscosity parameters/coefficients can be precisely determined by these methods. 

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

The identity tensor by is zero for i J and unity for i =J. The coefficient X is a material property related to the bulk viscosity, K = X + 2 l/3. There is considerable uncertainty about the value of K. Traditionally, Stokes hypothesis, K = 0, has been invoked, but the vahdity of this hypothesis is doubtful (Slattery, ibid.). For incompressible flow, the value of bulk viscosity is immaterial as Eq. (6-23) reduces to... 

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