Viscosity Arrhenius model

Table 2.6 presents constants for Carreau-WLF (amorphous) and Carreau-Arrhenius models (semi-crystalline) for various common thermoplastics. In addition to the temperature shift, Menges, Wortberg and Michaeli [50] measured a pressure dependence of the viscosity and proposed the following model, which includes both temperature and pressure viscosity shifts ... 

The viscosity was modeled using a Carreau model with an Arrhenius temperature... 

Carreau model parameter Carreau model parameter Zero shear rate viscosity Arrhenius law parameter Reference temperature Density Specific heat Thermal conductivity... 

Figure 2-14 Applicability of the Arrhenius Model to the Apparent Viscosity versus Temperature Data on a Concentrated Orange Juice Serum Sample (Vitali and Rao, 1984b) is Shown.

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986) ... 

Because many liquid foods are subjected to a wide range of temperatures during processing, storage,and transportation the effect of temperature on the viscosity function is of interest. The Arrhenius model (Equation 7)... 

SOI. Tomato concentrates are very shear-thinning fluids with reported magnitudes of the flow behavior index being in the range of 0.22 to 0.26. The effect of temperature on the apparent viscosity can be described by the Arrhenius model. The magnitude of Eaof twelve out of sixteen concentrates was about 9.63 kJ/mol (AS) ... 

Normally, the viscosity of a liquid decreases with increasing temperature, as seen in Table 1.6 for pure liquid water. For quantitative expression of the temperature effect on the viscosity, several models, such as the Eyring model, the exponential model,Arrhenius model, and Williams—Landel—Ferry model,have been proposed and validated using experimental data. The typical equation relating kinematic viscosity (i/) of the solution to temperature may be expressed as an Arrhenius form ... 

Hrma P. Arrhenius model for high-temperature glass-viscosity with a constant pre-exponential factor. J Non-Ciyst Solids 2008 354(18) 1962—8. 

In all these cases of simulation inside extruders, the major focus has been the development of efficient geometry modules to describe in a quick and user-friendly way the complicated geometrical characteristics of screws and extruder charmels. The question of adequately describing the rheology of the polymer melt is usually resolved with good viscosity data as a function of shear rate and temperature (Eq. (4.19)). The Carreau model (Eq. (4.6)) for the former and the exponential model (Eq. (4.9)) or Arrhenius model (Eq. (4.10)) for thelatter are sufficientin these computations, where viscoelasticity does not seem to be of importance or has not been attempted in any meaningful way. The predominance of shear flow inside the extruder seems to be the justification for that. 

The DPD viscosity was initially converted to an Arrhenius form, ln(fj )/hi(fj) against TJT, where represents the experimental value of the glass transition tanperature of 1500 K. A Min-Max normalization was then applied to the viscosity data. A numerical error in the viscosities computed by DPD of 4% was estimated from the magnitude of the deviation in the mean velocity as a function of simulation time step. A first-order Arrhenius fit was then calculated to the trend. A similar normalization and Arrhenius fit was then applied to Si02 viscosity data obtained from published sources [58,59]. The resulting data can be compared with the DPD model calculations, as shown in Figure 21.10. The DPD model and the experimental data both show excellent agreement with a first-order Arrhenius model. The difference in the slopes and intercepts of the two trends was found to be less than 3% in both cases. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

Polymer viscosity is often classically modeled as an Arrhenius exponential function of temperature as follows ... 

Temperature Dependence of Pure Metal Viscosity. Practically speaking, empirical and semiempirical relationships do a much better job of correlating viscosity with nsefnl parameters such as temperature than do equations like (4.7). There are nnmerons models and their resnlting equations that can be used for this purpose, and the interested student is referred to the many excellent references listed at the end of this chapter. A useful empirical relationship that we have already studied, and that is applicable to viscosity, is an Arrhenius-type relationship. For viscosity, this is... 

To use the Roller model requires the measurement of cure curves at several different temperatures so that Arrhenius plots may be made for the rate constant, k, and the Isothermal melt viscosity, n. The four model constants are then obtained from the Arrhenius plots. This entails considerable experimental work, especially for a method one would like to use in a more or less routine fashion. In addition, it is invalid in principle to... 

Estimation of Parameters. The resin viscosity, tj, as a function of time and/or temperature can be obtained using either a generalized dual-Arrhenius rheology model (Equation 5) or the thickness - time relationship for the neat resin from a separate squeeze-flow experiment (7). 

To examine the adequacy of the proposed diffusion model. Dp and Dr are measured at various temperatures. The temperature dependence of both D can be well expressed by the Arrhenius relation with activation energies close to that of the viscosity of the solution. 

A wide range of temperatures are encountered during processing and storage of fluid foods, so that the effect of temperature on rheological properties needs to be documented. The effect of temperature on either apparent viscosity at a specified shear rate (Equation 2.42) or the consistency index, K, of the power law model (Equation 2.43) of a fluid can be described often by the Arrhenius relationship. The effect of temperature on apparent viscosity can be described by the Arrhenius relationship ... 

Dolan et al. (1989) developed a model (Equations 4.34 and 4.35) to describe apparent viscosity as a function of time during starch gelatinization under non-isothermal conditions and additional discussion on its application to starch dispersions can be found in Dolan and Steffe (1990). The model contains an exponential function of the temperature-time history and the Arrhenius equation to describe the gelatinization reaction. The special form of the model for constant shear rate and starch concentration is ... 

In order to understand or study heat transfer phenomenon, the rheological behavior of a fluid food must be known as a function of both temperature and shear rate. For convenience in computations, the effect of shear and temperature may be combined in to a single thermorheological (TR) model. A TR model may be defined as one that has been derived from rheological data obtained as a function of both shear rate and temperature. Such models can be used to calculate the apparent viscosity at different shear rates and temperatures in computer simulation and food engineering applications. For a simple Newtonian fluid, because the viscosity, r), is independent of shear rate, one may consider only the influence of temperature on the viscosity. For many foods, the Arrhenius equation (Equation 2.42) is suitable for describing the effect of temperature on t] ... 

The simplest model for the temperature dependence of the viscosity is that proposed by Arrhenius for a reaction rate constant which leads to the equation... 

Martin et al. (1989b) focus on cure of epoxies and cyanate ester resins for lamination of prepregs into multilayered circuit boards. The following dual Arrhenius engineering model was fitted to viscosity profiles ... 

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