Viscosity models model

Eddy Viscosity Models. A large number of closure models are based on the Boussinesq concept of eddy viscosity ... 

Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

In ventilation problems, it is often sufficient to use simpler turbulence models, such as eddy-viscosity models. and Ujt are then re... 

Commonly used eddy-viscosity turbulence models are the k-e model and the k-(ji) model. The eddy viscosities for these models have the form... 

Menter, F. R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA ., vol. 32, pp. 1598-1605, 1994. 

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

One of the possible ways to account for the effect of roughness on the pressure drop in a micro-tube is to apply a modified-viscosity model to calculate the velocity distribution. Qu et al. (2000) performed an experimental study of the pressure drop in trapezoidal silicon micro-channels with the relative roughness and hydraulic diameter ranging from 3.5 to 5.7% and 51 to 169 pm, respectively. These experiments showed significant difference between experimental and theoretical pressure gradient. 

A roughness-viscosity model was proposed to interpret the experimental data. An effective viscosity /tef was introduced for this purpose as the sum of physical and imaginary = Mm(f) viscosities. The momentum equation is... 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

The two-phase pressure drop was measured by Kawahara et al. (2002) in a circular tube of d = too pm. In Fig. 5.30, the data are compared with the homogeneous flow model predictions using the different viscosity models. It is clear that the agreement between the experimental data and homogeneous flow model is generally poor, with reasonably good predictions (within 20%) obtained only with the model from Dukler et al. (1964) for the mixture viscosity. 

The Martinelli correlations for void fraction and pressure drop are used because of their simplicity and wide range of applicability. France and Stein (6 ) discuss the method by which the Martinelli gradient for two-phase flow can be incorporated into a choked flow model. Because the Martinelli equation balances frictional shear stresses cuid pressure drop, it is important to provide a good viscosity model, especially for high viscosity and non-Newtonian fluids. 

Dynamic simulations for an isothermal, continuous, well-mixed tank reactor start-up were compared to experimental moments of the polymer distribution, reactant concentrations, population density distributions and media viscosity. The model devloped from steady-state data correlates with experimental, transient observations. Initially the reactor was void of initiator and polymer. 

TFL is essentially a transition lubrication regime between EHL and boundary lubrication. A new postulation based on the ordered model and ensemble average (rather than bulk average) was put forward to describe viscosity in the nanoscale gap. In TFL, EHL theories cannot be applied because of the large discrepancies between theoretical outcomes and experimental data. The effective viscosity model can be applied efficiently to such a condition. In thin him lubrication, the relation between Him thickness and velocity or viscosity accords no longer with an exponential one. The studies presented in this chapter show that it is feasible to use a modi-Hed continuous scheme for describing lubrication characteristics in TFL. 

With further understanding how molecular rotors interact with their environment and with application-specific chemical modifications, a more widespread use of molecular rotors in biological and chemical studies can be expected. Ratiometric dyes and lifetime imaging will enable accurate viscosity measurements in cells where concentration gradients exist. The examination of polymerization dynamics benefits from the use of molecular rotors because of their real-time response rates. Presently, the reaction may force the reporters into specific areas of the polymer matrix, for example, into water pockets, but targeted molecular rotors that integrate with the matrix could prevent this behavior. With their relationship to free volume, the field of fluid dynamics can benefit from molecular rotors, because the applicability of viscosity models (DSE, Gierer-Wirtz, free volume, and WLF models) can be elucidated. Lastly, an important field of development is the surface-immobilization of molecular rotors, which promises new solid-state sensors for microviscosity [145]. 

A stress-dependent viscosity model, which has the same general characteristics as the Carreau model, is the Meter model (Meter, 1964) ... 

What viscosity model best represents the following data Determine the values of the parameters in the model. Show a plot of the data together with the line that represents the model, to show how well the model works. Hint The easiest way to do this is by trial and error, fitting the model equation to the data using a spreadsheet.)... 

As discussed in Chapter 3, the Carreau viscosity model is one of the most general and useful and reduces to many of the common two-parameter models (power law, Ellis, Sisko, Bingham, etc.) as special cases. This model can be written as... 

Eddy-current separation, 75 435 of nonferrous metallics, 75 455-457 Eddy-current separator, 27 447-448 Eddy-current technique, in nondestructive evaluation, 77 420 Eddy diffusion, 9 658 Eddy viscosity, 77 779 Eddy-viscosity-based models, 77 780 Edecrin, 5 169... 

In order to use this equation for CFD simulations, the unclosed term involving the Reynolds stresses ((u, u j)) must be modeled. Turbulent-viscosity-based models rely on the following... 

The next level of turbulence models introduces a transport equation to describe the variation of the turbulent viscosity throughout the flow domain. The simplest models in this category are the so-called one-equation models wherein the turbulent viscosity is modeled by... 

The last term on the right-hand side is unclosed and represents scalar transport due to velocity fluctuations. The turbulent scalar flux ( , varies on length scales on the order of the turbulence integral scales Lu, and hence is independent of molecular properties (i.e., v and T).17 In a CFD calculation, this implies that the grid size needed to resolve (4.70) must be proportional to the integral scale, and not the Batchelor scale as required in DNS. In this section, we look at two types of models for the scalar flux. The first is an extension of turbulent-viscosity-based models to describe the scalar field, while the second is a second-order model that is used in conjunction with Reynolds-stress models. 

Durbin, P. A., N. N. Mansour, and Z. Yang (1994). Eddy viscosity transport model for turbulent flow. Physics of Fluids 6, 1007-1015. 

Germano, M., U. Piomelli, P. Moin, and W. H. Cabot (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids 7, 1760-1765. 

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