Density of ternary mixtures

The aim of this chapter is to demonstrate the good predictive power of ANNs for determination of the density of ternary mixtures of ethanol + water + ionic liquid. 

An example of ANN is the following ANN that corresponds with a network with five neurons in the input layer corresponds with the input variables (x, x, x M, and / (,), nine neurons in the intermediate layers, and finally one neuron in the output layer and corresponds with the density of ternary mixtures (Pp, [Pg.450]

The first step to develop an MLR in order to predict the density of ternary mixtures of ionic liquid consists on performing a Pearson correlation analysis to determine which variables can be better fitted to the linear model (Table 21.1). 

Figure 2L2 Artifidal neural network with an input layer with five neurons, one hidden layer with nine neurons and one input layer with one neuron to determinate the density of ternary mixtures.

We have implemented several ANNs with different architectures to predict the density of ternary mixtures of ionic liquid and to overcome the MLR model fits. The tests consisted of carrying out different ANNs with different number of training cycles, modifying the level of error and also modifying the number of layers and the neurons used in each one [27]. 

ANNs were developed with different neurons in the intermediate layer. As the number of neurons is more difficult to determinate, we have used the following expression (Eq. 21.7) to determinate by trial and error, which is the best topology to predict the density of ternary mixtures of ionic liquids ... 

The sum of the absolute value of all weights for each input neuron gives us an idea of the importance of input neuron in the neural system. Taking into account the weight matrix (Table 21.6), we found that the most important variables to predict the density of ternary mixtures of ionic liquid were the mole fraction of ionic liquid (38.35), density of pure ionic liquid (23.83), and molar fraction of ethanol (23.70) (Table 21.7). Molar fraction of water and molecular weight of ionic liquid present an importance of 784 and 6.28, respectively, and they had not shown significant to determine the density of ternary mixtures of ionic liquid (Table 21.7). 

As quoted previously, densities of ternary mixtures of ethanol + water + ionic liquid were obtained using ANNs. The model that achieves better predictions consists in five input neurons, one middle layer with four neurons and one output neuron. This model presents RMSEs of 0.024g cm" (R =0.982) for the training set and 0.008g-cm (R = 0.977) for the vahdation set. The average percentage deviation for training and validation phase is 1.96%. 

Visak, Z.P., Ferreira, A.G.M. and Fonseca, I.M.A. Densities and viscosities of ternary mixtures water + butyl acetate + methanol and water + ethyl propionate + methanol at 303.15 K, J. Chem. Eng. Data, 45(5) 926-931, 2000. 

In the studies described here, we examine in more detail the properties of these surfactant aggregates solubilized in supercritical ethane and propane. We present the results of solubility measurements of AOT in pure ethane and propane and of conductance and density measurements of supercritical fluid reverse micelle solutions. The effect of temperature and pressure on phase behavior of ternary mixtures consisting of AOT/water/supercritical ethane or propane are also examined. We report that the phase behavior of these systems is dependent on fluid pressure in contrast to liquid systems where similar changes in pressure have little or no effect. We have focused our attention on the reverse micelle region where mixtures containing 80 to 100% by weight alkane were examined. The new evidence supports and extends our initial findings related to reverse micelle structures in supercritical fluids. We report properties of these systems which may be important in the field of enhanced oil recovery. 

Solutropes are not uncommon they may occur in any of the classes of ternary mixtures shown in Figure 9.25. Their practical significance arises from their ability to inhibit separations by liquid extraction, because transfers of components between phases are often hindered when a mole fraction becomes the same in both phases. Such inhibitions may be compounded if the densities of the phases also become equal, as they may near solutropes. Since liquid extractions exploit density differences, no separation occurs in an extraction process when the densities of the two phases become equal, even if their compositions differ. 

The packing density of binary mixtures of spheres can be increased further by going to ternary mixtures, quaternary mixtures, and so on. For example if each... 

In practice, little is gained beyond the use of ternary mixtures because the finer particles do not locate into their ideal positions to maximize the packing density. Additional practical problems may arise as the number of size classes in the mixture increases. As described earlier, a particle size ratio of at least 7 is required for optimum packing. For a ternary mixture of fine, medium and large particles, assuming that the fine particles are 1 xm in size, then the medium, and large particles will be 7 p,m and 49 xm, respectively. The ability to produce some advanced ceramic powders with such widely different sizes is limited. 

Density Prediction of Ternary Mixtures of Ethanol + Water + Ionic Liquid Using Backpropagation Artificial Neural Networks... 

DENSITY PREDICTION OF TERNARY MIXTURES OF ETHANOL + WATER + IONIC LIQUID... 

Rilo, E. Ferreira, A.G.M. Fonseca, I.M.A. Cabeza, O. (2010c). Densities and derived thermodynamic properties of ternary mixtures l-butyl-3-methyl-imidazolium... 

An important example is the one-order-parameter model invented by Gompper and Schick [77], which describes a ternary mixture in temis of the density difference between water and oil ... 

Solvents used here for a general liquid-liquid extraction method were selected from Snyders solvent selectivity triangle. As extraction liquids have to be composed of mixtures of three solvents which may enter into maximum interaction with the analyte, three solvents had to be selected that represent a wide variety of selective interactions. In addition, the solvents should be sufficiently polar to ensure quantitative extraction. Besides selectivity and polarity requirements, the solvents should also meet a few other criteria, mainly for practical reasons they should not be miscible with water, have low boiling points (for relatively fast evaporation procedures) and have densities sufficiently different from the density of water, for pure solvents as well as for selected binary or ternary mixtures of solvents. 

Upon hydrogenation the hydrogen atoms will bond with an A atom but they will also be in contact with B atoms. The atomic contact between A and B that was responsible for the heat of formation of the binary compound is lost. The contact surface is approximately the same for A-H and B -H thus implying that the ternary hydride AB H2m is energetically equivalent to a mechanical mixture of AH, and Bniim [37]. More specifically, this could be explained by two terms one is due to the mismatch of the electronic density of metals A and B at the boundary of their respective Wigner-Seitz cells, the other term is associated with the difference in chemical potential of the electrons in metals A and B. From these considerations, a semi-empirical relation for the heat of formation of a ternary hydride can be written as [70] ... 

The first chiral separation using pSFC was published by Caude and co-workers in 1985 [3]. pSFC resembles HPLC. Selectivity in a chromatographic system stems from different interactions of the components of a mixture with the mobile phase and the stationary phase. Characteristics and choice of the stationary phase are described in the method development section. In pSFC, the composition of the mobile phase, especially for chiral separations, is almost always more important than its density for controlling retention and selectivity. Chiral separations are often carried out at T < T-using liquid-modified carbon dioxide. However, a high linear velocity and a low pressure drop typically associated with supercritical fluids are retained with near-critical liquids. Adjusting pressure and temperature can control the density of the subcritical/supercritical mobile phase. Binary or ternary mobile phases are commonly used. Modifiers, such as alcohols, and additives, such as adds and bases, extend the polarity range available to the practitioner. 

Table II and Fig. 1 give density (p) values as a function of temperature for various binary or ternary mixtures. It can be seen from Fig. 1 that the variations of p are linear as a function of temperature, so that corrections are easy to make on spectroscopic recordings.

Figure 5 Diffusion of charged spherical macroion of radius 10 A and a uniform surface charge density of le per 93 A2 on mixed membranes. The panels show the local surface charge densities after 0.6 ps of simulations (shades) and the entire macroion trajectories in that time (connected lines) for binary (71 29 PC/PS) mixture, D =10 (a), for ternary (74 25 1 PC/PS/PIP2) mixture, D =10 (c), for binary (PC/PS) mixture, D =2 (b), and for ternary (PC/PS/PIPJ mixture, D = 2 (d). The dashed circles on each panel represent the projected size of the macroion with arrows indicating the starting position for the macroion center of mass. For clarity, the figures zoom on the relevant membrane surface region explored by the macroion, and a scale bar of 20 A is shown for reference.

Example 2. The second example presents the analysis of the volume properties of a ternary system, which is experimentally accessible only in part of the concentration triangle. In order to perform the analysis, the density of one component must be approximated. In addition, the ternary eutectic mixture was chosen for a following component. 

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