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** Chain Model and Naive Two Parameter Theory **

** The Two-Parameter UNIQUAC Model **

** The Two-Parameter Wilson Model **

** Two- and Three-parameter Model **

A useful two-parameter model is the power-law model, or Ostwald-de Waele law to identify its first proponents. The relation between shear stress and shear rare is given by [Pg.108]

Although two-parameter models are rather restrictive, three-parameter models of the intermolecular potential have been developed which provide reasonable descriptions of the thermodynamic behavior of solids. Examples include the Morse potential, the exponential-six potential, and, more recently, a form proposed by Rose et al. (1984) for metals. [Pg.268]

These results are familiar from the trivial invariance of the two-parameter model (cf. Eq. (8.4)). As a consequence, the terms ne 2 taken along in the two-parameter model drop out from Eqs. (8.27), (8.28), leaving the n-independent sublcadmg terms to determine A (A) and Bi(A). A little calculation yields [Pg.134]

Fig. 10. Effect of bed height on fluoride removal from water. Two-parameter model simulation is represented by continuous line. |

Temperature (K) Experimental Pressure (MPa) Calculated Pressure with three-parameter model (MPa) Calculated Pressure with two-parameter model (MPa) [Pg.39]

A proportionality between the theoretical spall strength and the bulk modulus is obtained when a two-parameter model is chosen to represent the intermolecular potential. Other two-parameter representations of the intermolecular potential, such as the Lennard-Jones 6-12 potential, will yield a similar proportionality although the numerical coefficients will differ slightly. [Pg.268]

Luedeking and Piret<56) proposed that the formation of microbial products could be described by a two parameter model. This was based on their studies of lactic acid fermentation using Lactobacillus delbruekii in which the accumulation of the acid is not directly linked to the growth rate. The function used was [Pg.352]

However, there is no reason to use more complicated isotherm models if two-parameter models, such as Langmuir and Freundlich, can fit the data well. It should be clarified that these models are only mathematical functions and that they hardly represent the adsorption mechanisms. [Pg.270]

Historical data were obtained on U.S. refinery operations and the production of sulfur from U.S. refineries from 1971-1977. A two-parameter model was developed correlating past levels of sulfur recovery with the quality and rate of crude processed and the qualities and amounts of end products. An overall correlation coefficient of 0.91 was obtained. [Pg.114]

Figure4.9 shows the best Freundlich quenching model plots. While more complex models could fit the data, this simple two-parameter model fits all the data within experimental error. Since the decays are highly nonexponential, the parameters represent lumped parameters that are some average over the available sites, lifetimes, and A sv s. A detailed discussion of the different models tried is given elsewhere. |

A more convenient extrapolation technique is to approximate the experimental data with a viscosity model. The Power Law, shown in Eq. 6, is the most commonly used two-parameter model. The Bingham model, shown in Eq. 7, postulates a linear relationship between x and y but can lead to overprediction of the yield stress. Extrapolation of the nonlinear Casson model (1954), shown in Eq. 8, is straightforward from a linear plot of x°5 vs y05. Application of the Herschel-Bulkley model (1926), shown in Eq. 9, is more tedious and less certain although systematic procedures for determining the yield value and the other model parameters are available (11) [Pg.350]

Three empirical models were utilized to fit the rheologic characteristics of the wet grain slurries power law, Herschel-Bulkley, and Casson. The power law and Casson models are two-parameter models and are ideal for [Pg.726]

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 [Pg.358]

To summarise, the fracture data and type of crack growth over a wide range of rates and temperatures may all be rationalised by the concept of a critical stress acting over a critical distance and this two-parameter model provides a unique failure criterion for thermosetting polymers. [Pg.66]

Let us carry out a so-called screening experiment in which we attempt to discover if the fermentation temperature (factor x ) has a significant effect on the response (% alcohol content). We will choose two levels of temperature, 23°C and 27°C. This is the minimal number of factor levels required to fit the two-parameter model [Pg.230]

** Chain Model and Naive Two Parameter Theory **

** The Two-Parameter UNIQUAC Model **

** The Two-Parameter Wilson Model **

** Two- and Three-parameter Model **

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