Coefficient interaction

a remaining problem is how to determine the value of the interaction coefficient. An approach was presented by Bay (1991) based on experimental values of an in steady simple shear flows for different concentrations. These experimental results were fitted to the numerically calculated an and the value of Ci that best fits the experimental results was obtained. The polymer matrices used in the experiments were nylon, polycarbonate and polybutylene terephthalate. The data of Cl were then plotted against a cp to give an empirical relationship 

It also needs to be mentioned that, in Bay s work, the hybrid closure was used to model the data. With this closure, the values of C/ were found around 0.01 to match the experimental an values. However, if one uses the orthotropic closure, the data are matched with C/ = 0(0.001). Therefore, it is important to notice that, although the measured values of an are irrelevant to any closure schemes, the data of Cl, and hence the coefficients of the empirical equation (5.25), depend on the closure-scheme chosen. 

Ranganathan and Advani (1991) assumed a relationship between C/ and the average inter-fiber spacing a for semi-dilute suspensions  

Phan-Thien et al. (2002) proposed the following empirical expression based on calculations of the diffusion coefficient using a direct simulation of fiber suspension dynamics  

The results of the direct simulation and the empirical equation 5.26 are comparable with the data of Folgar and Tucker (1984), as shown in Fig. 5.3. 

---

TAUS CALCULATES TEMPERATURE DEPENDENT INTERACTION COEFFICIENTS TAU FOf 4 USE IN SUBROUTINE GAMMA. IF SYSTEM DATA ARE MISSING (SOME REQUIRED 4 ENTRY IN MATRIX U IN COMMON/BINARY IS ZERO) CORRESPONDING TAU IS 4 SET TO 1 AND lER IS RETURNEO AS +/- 1. FOR NONCONDENSABLES PRESENT 4 IER IS -2 OR -I (OTHERWISE 0). 

Fugacity is expressed as a function of the molar volume, the temperature, the parameters for pure substances Oj and h, and the binary interaction coefficients )... 

The constants k- enable the improved representation of binary equilibria and should be carefully determined starting from experimental results. The API Technical Data Book has published the values of constants k j for a number of binary systems. The use of these binary interaction coefficients is necessary for obtaining accurate calculation results for mixtures containing light components such as ... 

Graham-Uranoff They studied multicomponent diffusion of electrolytes in ion exchangers. They found that the Stefan-Maxwell interaction coefficients reduce to limiting ion tracer diffusivities of each ion. 

Table 14.1 shows some experimental data for the interaction coefficients in iron as solvent. 

Table 14.1 Interaction coefficients of solutes (xlO ) in liquid iron at 1850 K...

The above relations can also be used as a first approximation to find the temperature drop in interacting jets by substituting A0y, A6o and AA2 for V , i/y, and K2, respectively. The values of interaction coefficient for even and odd numbers of outlets are given in Fig. 7.51, reproduced from Grimitlyn. ... 

Figure32.34 Interaction coefficient combination bends (after Miller )...

Burnham, Hower, and Jones18 have used an IBM Card Programmed Calculator for the calculation of the interaction coefficients needed in setting up the analysis of multicomponent systems by x-ray emission spectrography according to an earlier treatment of Sherman.19... 

Punched cards, used to calculate interaction coefficients, 171... 

From the changes in the obtained potential profiles, we evaluated the interaction coefficient P and, compared it with the theoretical calculation of p, we also confirmed that the proposed method could evaluate the interaction force without any fitting parameters, which have usually been required in the typical correlation method. 

Eor example, let consider the case in the direction between the central axes of the two trapped particles, which is indexed as V x and V2x- The correlation of the kinetic potential in the v -directions changes depending on the coefficients of y — P in the (v x + 2x) direction and y + p in (v x — direction. Thus, as the interaction coefficient P changes vhth the distance between the two particles, the shape of the kinetic potential plotted against v x and v x should change in the (Vi + V2x) and (vix — t>2x) directions. 

From the theoretical calculations of the hydrodynamic force, we can estimate the distance dependences of the interaction coefficients in the x- and y-directions. According to ref [29], the interaction coefficients P /y and Py/y are calculated from the following approximated equations, assuming that the two particles are spherical in shape with the same diameter. 

In the same way it was found through analysis incorporating second-order interaction coefficients that the aldehyde AfT is not conditioned by the CHO effect on the close hydrocarbon groups as was the case with ketonic carbonyl, but by the effect of close groups on aldehydic C-H. 

Fig. 4.8 The Frumkin adsorption isotherm. The value of the interaction coefficient a is indicated at each curve. The transition in the metastable region is indicated by a dashed...

Alguacil, F. J. Cobo, A. Coedo, A. G. Dorado, M. T. Sastre, A. Extraction of platinum(TV) from hydrochloric acid solutions by amine alamine 304 in xylene. Estimation of the interaction coefficient between PtCl62- and H+. Hydrometallurgy 1997, 44, 203-212. 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

The coefficients J B are called interaction coefficients of order i. The coefficient of... 

The orders of magnitude of the coefficients depend very much on the system studied. Generally stronger atomic interactions give larger interaction coefficients. An illustration of low order terms in the Taylor series expansion of In y-n in the binary system Tl-Hg is given in Figure 3.9 [8]. 

A graphical integration of the Gibbs-Duhem equation is not necessary if an analytical expression for the partial properties of mixing is known. Let us assume that we have a dilute solution that can be described using the activity coefficient at infinite dilution and the self-interaction coefficients introduced in eq. (3.64). 

The relationship between the different self-interaction coefficients of component A and B, 7A and 7 , may in general be obtained in a similar way. 

Thompson [8]). Pure A and B are assumed to melt at 800 and 1000 K with the entropy of fusion of both compounds set to 10 J K-1 mol-1 (this is the typical entropy of fusion for metals, while semi-metals like Ga, In and Sb may take quite different values - in these three specific cases 18.4, 7.6 and 21.9 J K-1 mol-1, respectively). The interaction coefficients of the two solutions have been varied systematically in order to generate the nine different phase diagrams given in Figure 4.10. 

At the critical point xA = xB = 0.5 and the critical temperature and the interaction coefficient are related through... 

---