Viscosity calculation methods

When viscous liquids are handled in centrifugal pumps, the brake horsepower is increased, the head is reduced, and the capacity is reduced as compared to the performance with water. The corrections may be negligible for viscosities in the same order of magnitude as water, but become significant above 10 centistokes (10 centipoise for SpGr = 1.0) for heavy materials. While the calculation methods are acceptably good, for exact performance charts test must be run using the pump in the service. 

The validity of a practical method of direct viscosity calculation from size exclusion chromatographic analysis is demonstrated. The method is convenient to use and is not limited by the availability of narrow MWD standards. It is possible to accurately measure polymer Mark-Houwink constants using the suggested broad standard SEC-[n] and SEC-MW calibration procedure. 

The numerical efficiency of the viscosity lower bound method has allowed calculations on considerably longer chains. The long chain Hmit results for 12-arm stars without intramolecular interactions and with EV (up to 325 beads) and in the theta region (up to 145 beads) [164] are close to the previous estimates with shorter chains (the extrapolated ratio g obtained in this study is also included in Table 4). The lower bound method has also served to characterize globule-coil transitions of 12-arm star chains from intrinsic viscosity calculations [143], though finite size effects are considerably more important than in the characterization of this transition from the radius of gyration data (see Fig. 17). This is due to the noticeable increase in the solvent permeabiHty associated with the chain expansion in better solvent conditions. However, the permeability effects are smaller in the more compact star chains than in their linear counterparts. 

The calculation method and equations presented in the previous sections are for Newtonian fluids such that the flow due to screw rotation and the downstream pressure gradient can be solved independently, that is, via the principle of superposition. Since most resins are highly non-Newtonian, the rotational flow and pressure-driven flow in principle cannot be separated using superposition. That is, the shear dependency of the viscosity couples the equations such that they cannot be solved independently. Potente [50] states that the flows and pressure gradients should only be calculated using three-dimensional (3-D) numerical methods because of the limitations of the Newtonian model. 

Two different calculation methods were used for the simulations (1) the generalized Newtonian method as developed above, and (2) the three-dimensional numerical method presented in Section 7.5.1. The generalized Newtonian method used a shear viscosity value that was based on the average barrel rotation shear rate and temperature in the channel. The average shear rate based on barrel rotation (7ft) is provided by Eq. 7.52. Barrel rotation shear rate and the generalized Newtonian method are used by many commercial codes, and that is why it was used for this study. 

The reader is cautioned that there is often a considerable divergence in the literature for values of rate constants [Buback et al., 1988, 2002], One needs to examine the experimental details of literature reports to choose appropriately the values to be used for any needed calculations. Apparently different values of a rate constant may be a consequence of experimental error, experimental conditions (e.g., differences in conversion, solvent viscosity), or method of calculation (e.g., different workers using different literature values of kd for calculating Rt, which is subsequently used to calculate kp/kXJ2 from an experimental determination of Rp). 

The calculational methods for the friction and the viscosity have been presented in Sections IX and X, respectively. Here we will not describe them but just state the results. 

In addition to the API Technical Data Book and Gas Processors Suppliers Association (GPSA) methods [8], a new gas viscosity method is presented herein that may be used for a computer program application or a hand-calculation method ... 

However, predictions from simple flows, such as those described in Example 7.3 above, cannot be generalized to more realistic systems. Bigg and Middleman (23) analyzed a somewhat more realistic system of flow in a rectangular channel, shown in Fig. 7.15. The motion of the upper surface induces partial mixing of the fluids, and the interfacial area, which was calculated as a function of time, is used as a quantitative measure of the laminar mixing. The marker and cell calculation method, developed by Harlow and Welch (24), was used to solve the flow field and calculate the position of the interface. The evolution of the interface of two fluids of equal viscosities and densities in a channel with an aspect ratio of 0.52, and a... 

A comprehensive discussion of the most important model parameters covers phase equilibrium, chemical equilibrium, physical properties (e.g., diffusion coefficients and viscosities), hydrodynamic and mass transport properties, and reaction kinetics. The relevant calculation methods for these parameters are explained, and a determination technique for the reaction kinetics parameters is represented. The reaction kinetics of the monoethanolamine carbamate synthesis is obtained via measurements in a stirred-cell reactor. Furthermore, the importance of the reaction kinetics with regard to axial column profiles is demonstrated using a blend of aqueous MEA and MDEA as absorbent. 

Another method to determine viscosity uses the falling-ball viscometer. Determine viscosity by noting the time it takes for a ball to fall through the distance between two marks on a tube filled with the unknown liquid (the tube is generally in a constant-temperature bath). Use balls of different weights to measure a wide range of viscosities. Calculate the viscosity by using manufacturer-supplied constants for the ball used. These instruments can be quite precise for Newtonian liquids, that is, liquids that do not have viscosities that vary with flow (more correctly, shear) rate. 

From the Eq. (4) it follows, that the e q)onent aq, earlier assumed purely empirical characteristic, has a clear structural interpretation. One from the calculated methods of Df determination uses the known Huggins equation, which gives the dependence of reduced viscosity qred on concentration c for diluted polymer solutions [8] ... 

The theoretical principles will not be discussed here because of lack of space, but the calculation method will be described. To calculate the pressure drop, the flow rate in the channel, the shear rate for a channel, the melt viscosity and the shear stress must be calculated, in turn ... 

It is additionally noted that the polymers need a minimum chain length for significant entanglement, which is on the order of 10,000 kDa. For a detailed calculation method of the entanglement chain length, see Ref. [93]. The viscosity at the entanglement concentration is according to Ref. [24]. tj n f/j 50f/j, which is comparable to the equivalent one for neutral polymers. 

Ramesh, N.S., Lee, S.T. Blowing agent effect on extensional viscosity calculated from fiber spinning method for foam processing , SPE Foams 99 (1999), 85-96 Werner, R, Verdejo, R., Wdllecke, F., Altstadt, V., Sandler, J.K.W., Shaffer, M.S.P. Carbon nanofibres allow foaming of semicrystalline poly(ether ether ketone) , Adv. Mater. 17(23) (2005), 2864-2869... 

The correction for the pressure dependence of transport properties of gases can be piade by use of various correlations. These include the gas density which in turn is calculated from the compressibility factor. For viscosity the method proposed by Dean, Stiel [9] can be used, and for the thermal conductivity the method proposed by Stiel, Thodos [54] can be used. For the bulk diffusion coefficient it is normally assumed that it is inversely proportional to the density. 

The viscosity calculated by the confined shear simulation is 1.11 Pa s at lOSO C. This agrees very well with the value measured previously for this composition within the (NNL). It also seems to have accounted for the mixed alkali effect, which could not be modeled using the simpler analytical methods. Comparisons at other temperatures and with other silicate, borosilicate, and aluminosilicate melts showed similar agreement. 

Liquid viscosity is one of the most difficult properties to calculate with accuracy, yet it has an important role in the calculation of heat transfer coefficients and pressure drop. No single method is satisfactory for all temperature and viscosity ranges. We will distinguish three cases for pure hydrocarbons and petroleum fractions ... 

Mole fraction of hexane Experimental viscosity mPa-s Calculated viscosity method 1 mPa-s Calculated viscosity method 2 mPa-s Calculated viscosity method 3 mPa-s Molecular weight kg/kmol Density kg/m ... 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

The surface viscosity can be measured in a manner entirely analogous to the Poiseuille method for liquids, by determining the rate of flow of a film through a narrow canal under a two-dimensional pressure difference Ay. The apparatus is illustrated schematically in Fig. IV-7, and the corresponding equation for calculating rj is analogous to the Poiseuille equation [99,100]... 

The equations and methods for determining viscosity vary greatly with the type of instmment, but in many cases calculations may be greatly simplified by calibration of the viscometer with a standard fluid, the viscosity of which is known for the conditions involved. General procedures for calibration measurement are given in ASTM D2196. The constant thus obtained is used with stress and shear rate terms to determine viscosity by equation 25, where the stress term may be torque, load, or deflection, and the shear rate may be in rpm, revolutions per second (rps), or s F... 

Viscosity can also be determined from the rising rate of an air bubble through a Hquid. This simple technique is widely used for routine viscosity measurements of Newtonian fluids. A bubble tube viscometer consists of a glass tube of a certain size to which Hquid is added until a small air space remains at the top. The tube is then capped. When it is inverted, the air bubble rises through the Hquid. The rise time in seconds may be taken as a measure of viscosity, or an approximate viscosity in mm /s may be calculated from it. In an older method that is commonly used, the rate of rise is matched to that of a member of a series of standards, eg, with that of the Gardner-Holdt bubble tubes. Unfortunately, this technique employs a nonlinear scale of letter designations and may be difficult to interpret. 

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