Taylor equation

ET40)/PET blends, and in the 100/0 wt% P(HB80-ET20)/PET blend. This is because of either (a) a high content of rigid rod-like liquid crystalline component, or (b) an enthalpy which was too small to detect. The dependence of Tg on the blend composition can be evaluated by using the Gordon-Taylor Equation [37],... 

For values of the Eotvos number higher than 40 (for the air-water system, this corresponds to dbub > 17 mm), the above equation simplifies to the well-known Davies-Taylor equation ... 

The rise velocity of a single spherical cap bubble in an infinite liquid medium can be described by the Davies and Taylor equation [Davies and Taylor, 1950] (Problem 9.6). Experimental results indicate that the Davies and Taylor equation is valid for large bubbles (4oo > 0.02 m, in general) with bubble Reynolds numbers greater than 40, while for bubbles in fluidized beds, the bubble Reynolds numbers are typically on the order of 10 or less [Clift, 1986]. By analogy, the rise velocity of an isolated single spherical cap bubble in an infinite gas-solid medium can be expressed in terms of the volume bubble diameter by [Davidson and Harrison, 1963]... 

It is possible to take these effects into account, but the actually found scale of dispersion in practical blending operations is never properly matched by these calculations the observed particles are much bigger (up to ten times) than according to the Taylor equation. The explanation of this discrepancy is coalescence small droplets join together when they collide. 

The Taylor equation can then be applied to obtain the dispersion arising from this effect ... 

Glass-transition temperatures of the three diblocks and the two homopolymers are plotted against isoprene content in Figure 3. The values plotted in Figure 3 were determined by TMA at a heating rate of 5°C/min. The points fall near a straight line which can be described by a simplified version of the Gordon-Taylor equation (20) ... 

Figure 3. Tg data for PVC/PCL and NC/PCL blends plotted according to the Gordon-Taylor equation. The lines are fit to the quenched data (1).

Figure 3 shows that the Gordon-Taylor equation fits the quenched data for the PVC/PCL blends quite well. The thermograms for the blends of 25, 35, and 50% PVC display PCL heats of fusion, and conse-... 

A logarithmic form of this equation is given by Pochan et al. Other expressions include the Wood equation the Kelley-Bueche expression the Gordon-Taylor equation and the DiMarzio-Gibbs equation None of these Equations directly take into account the specific interactions within a blend. 

The marked differences in flow profiles have a significant effect on the efficiency of separation in open tubes. This is discussed in many publications including Knox and Grant (41. In the case of an open tube, the flow variation across the tube in pressure drive means that as the solute moves along it is dispersed. This is counteracted by transverse molecular diffusion to give a resulting net dispersion that is described by the Taylor equation 16. The additional effects of axial dispersion leads to the HETP equation... 

Figure 33 The temperature response function r of the first-order decomposition rate constants ki and ky.. The r-function is a scalar that relates k at any given temperature to its maximal rate at a reference temperature (Tref = 30 °C, see text for details). Also shown is the modeled fit of the Lloyd and Taylor equation (Equation (12),...

Fig. 7 Glass transition vs. water content relationship for amorphous indomethacin. Lines show fit to the Gordon-Taylor equation with K values of 0.33 (predicted) and 0.11...

The glass transition temperature of amorphous multicomponent mixtures can be used to determine the miscibility of the components. If the mixture is miscible, then a single glass transition temperature is usually obtained. Various equations can be used to predict the glass transition temperature of miscible mixtures. Examples include the Gordon-Taylor equation [Eq. (11)] or the Fox-Flory equation [Eq. (12)]. 

Calculated using Gordon-Taylor equation with an intrinsic glass transition, 7 of 74°C (347 K) and - 139°C (135 K) for sucrose and water, respectively, and a Gordon-Taylor constant value of 0.13675. 

The glass-transition temperature curve of the maltodextrin RD-111, MOR-REx 1910, and MOR-REX 1914 were obtained using the Gordon-Taylor equations for binary systems, according to the procedure described by Collares et al. (2004). 

Firstly the effect of on Tg of a food polymer is considered. To establish moisture content and relationship, the sorption isotherm for water/soy flour system is developed. Information of this kind is readily available in the literature for various systems (Labuza and Hyman, 1998). The Gordon-Taylor equation (Gordon and Taylor, 1952) is used to predict the effect of (using moisture content vs. relationship obtained from MSI) on Tg. The Gordon-Taylor equation has been used to predict the Tg of several binary mixtures (Roos, 1995 Morales-Diaz and Kokini, 1998). In general for most food polymers with a distribution of hydrophilic groups an increase in a results in a decrease in Tg (Slade and Levine, 1995). The Tg predicted with the Gordon-Taylor equation is used as a first part of our modification. 

Experimental Tg values as a function of moisture content predicted well with the Gordon-Taylor equation. 

Differential scarming calorimetry (DSC) was used to measure the glass transition (Tg) of samples humidified over saturated solutions of LiCl, CH3COOK, MgCl2, and K2CO3. The Gordon-Taylor equation was fitted to the glass-transition data. 

Water plasticized the food models and caused a substantial decrease of the glass-transition temperature. The Gordon-Taylor equation was successfully fitted to experimental glass transition temperatures of the three model systems, as shown in Figure 53.2b. The constant, k, for the Gordon-Taylor equation was found to be 7.6 0.8 for lactose/reactant systems, 7.2 0.7 for lactose/trehalose/reactant systems, and 7.9 0.9 for trehalose/reactant systems. The three model systems had corresponding glass-transition behaviors, which were typical of lactose-based dairy products. The critical water contents at 23°C obtained from Tg data for lactose/reactant, lactose/trehalose/reactant, and trehalose/reactant systems were 7.0, 7.4, and 7.1 g/100 g of dry solids, respectively. 

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