Parameters of the liquid phase

Sintering with liquid phase vitrifieation 3.6.1. Parameters of the liquid phase 

In general, the presence of a hquid phase facilitates sintering. Vitrification is the rale for silicate ceramics where the reactions between the starting components form compounds melting at a rather low temperature, with the development of an abundant quantity of viscous liquid. Various technical ceramics, most metals and cermets are all sintered in the presence of a liquid phase. It is rate that sintering with liquid phase does not imply any chemical reactions, but in the simple case where these reactions do not have a marked influence, surface effects ate predominant. The main parameters are therefore i) quantity of liquid phase, ii) its viscosity, iii) its 

When YsL is high, the drop minimizes its interface with the solid, hence a high value of 0 0 90° corresponds to non-wetting (depression of the hquid in a capihaiy). On the contrary, when Ysl YsV the liquid spreads on the surface of the solid 0 90° corresponds to wetting (rise of the hquid in a capillary) and for 0 = 0, the wetting is perfect. 

In a granttlar sohd that contains a liqiud, the respechve values of Ysl and Ygb (grain botmdary energy) determine the value of the dihedral angle  

Low solubility of the liquid in the solid Low assistance to densification High assistance to densification 

---

Since the hydrogenation of MAA with unmodified RNi did not proceed as mentioned in the previous section, the kinetic parameters of the liquid-phase reaction with MRNi under atmospheric pressure could not be compared with those of RNi. However, it can be expected that the modification does not change the nature of hydrogenation with RNi since the activation energies of MRNis were exactly the same as each other and independent of the sort of modifying reagent. This expectation was confirmed by the results... 

With the help of the calculated molar volume and the various pure component and mixture parameters of the liquid phase both fugacity coefficients for the liquid phase (fl can be calculated using Eq. (4.101). For nitrogen (1) the following value is obtained ... 

Bubble columns. Tracers are used in bubble columns and gas-sparged slurry reactors mainly to determine the backmixing parameters of the liquid phase and/or gas-liquid or liquid-solid mass transfer parameters. They can be used for evaluation of holdup along the lines reviewed in the previous Section 6.2.1. However, there are simpler means of evaluating holdup in bubble columns, e.g. monitoring the difference in liquid level with gas and without gas flow. Numerous liquid phase tracer studies of backmixing have been conducted (132-149). Steady-state or continuous tracer inputs (132,134,140,142) as well as transient studies with pulse inputs (136,141,142,146) were used. Salts such as KC Jl or NaCil, sulfuric acid and dyes were employed as tracers. Electroconductivity detectors and spectrophotometers were used for tracer detection. The interpretation of results relied on the axial dispersion model. Various correlations for the dispersion... 

The liquid phase cage model accounts for appearance in the spectrum of resolved rotational components by effective isotropization of the rapidly fluctuating interaction. This interpretation of the gas-like spectral manifestations seems to be more adequate to the nature of the liquid phase, than the impact description or the hypothesis of over-barrier rotation. Whether it is possible to obtain in the liquid cage model triplet IR spectra of linear rotators with sufficiently intense Q-branch and gas-like smoothed P-R structure has not yet been investigated. This investigation requires numerical calculations for spectra at an arbitrary value of parameter Vtv. 

The central difficulty in applying Equations (11.42) and (11.43) is the usual one of estimating parameters. Order-of-magnitude values for the liquid holdup and kiA are given for packed beds in Table 11.3. Empirical correlations are unusually difficult for trickle beds. Vaporization of the liquid phase is common. From a formal viewpoint, this effect can be accounted for through the mass transfer term in Equation (11.42) and (11.43). In practice, results are specific to a particular chemical system and operating mode. Most models are proprietary. 

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

Table V. Variation of different parameters as a function of the nature of the liquid phase of the B -type synthesis.

Ammonia - Water System. Interaction parameter for the ammonia - water system was obtained using the data of Clifford and Hunter (1 4) and of Macriss et al. (15). A single - valued parameter was capable of representing the composition of the liquid phase reasonably well at all temperatures, however, the calculated amount of water in the vapor phase in the very high ammonia concentration region was somewhat lower than the data of Clifford and Hunter and Macriss et al. Edwards et al. (16) have applied a new thermodynamic consistency test to the data of Macriss et al and have concluded that the data appear to be inconsistent and that the reported water content of the vapor phase is too high. 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

Die next parameter we need is the diffusion coefficient Df of hydrogen peroxide in water. Here, we can assume the approximate value of 10 9 m2/s. However, this coefficient will be needed further in this example for the determination of the effective solid-phase diffusion coefficient, in a calculation that is extremely sensitive to the value of the liquid-phase diffusion coefficient. For this reason, coefficient should be evaluated with as much accuracy as possible. The diffusion coefficient of solutes in dilute aqueous solutions can be evaluated using the Hayduk and Laudie equation (see eq. (1.26) in Appendix I) ... 

First, all of what we believe to be the reliable phase diagram and thermodynamic data are considered simultaneously. If a particular set of data is not considered in fixing the values of the adjustable parameters of the liquid model, it is still required that the final values for these adjustable parameters lead to a good fit to this data as well as all the rest. 

Various high temperature thermochemical properties of the liquid phase were then calculated for comparison with experiment using the parameter set... 

Note that both a small disc in the large volume of a liquid and a large disc in the small volume of a liquid will hardly produce reliable data on the dissolution kinetics of the solid in the liquid. In the former case, the small disc will not ensure suffucient convective agitation of the liquid phase. In the latter, the treshould of turbulency may happen to be exceeded. Turbulence is known to occur at Reynolds numbers in excess of 105. The Reynolds number, Re = wr2/v, r being the disc radius, is a dimensionless parameter characterising the hydrodynamic regime of flow of liquids.299 300 Reproducible results are readily obtained if the flow is laminar. 

The calculation of viscosities of electrolyte mixtures can be accomplished with the method of Andrade (see Ref. [40]) extended with the electrolyte correction by Jones-Dole [44]. First, the pure component viscosities of molecular species are determined by the three-parametric Andrade equation, which allows a mixing rule to be applied and the mixture viscosity of an electrolyte-free liquid phase to be obtained. The latter is transformed into the viscosity of the liquid phase using the electrolyte correction term of Jones and Dole [44], whereas the ionic mobility and conductivity are used as model parameters. 

According to these premises, the relevance list must be formed with the following parameters Target quantity. kLa physical properties density p, viscosity i, diffusivity D and the coalescence parameters S of the liquid phase. Despite extensive research, coalescence phenomena have still not been clarified to such an extent as to permit explicit formulation of the coalescence parameters (see [22], section 4.10). Process parameters volume-related mixing power P/V, superficial velocity v of the gas and gravitational acceleration g. (The decision in favour of P/V and v instead of P/q and q/V was based on extensive research results obtained in the last three decades, see Section 10.4.1)... 

The structure electrical double layer at the silica-aqueous electrolyte interface was one of the earlier examined of the oxide systems. At the beginning the investigations were performed with application of electrokinetic methods next, with potentiometric titrations. The properties of this system were very important for flotation in mineral processing. Measurements proved that pHpZC and pHiep are equal to 3, but presence of some alkaline or acidic contaminants may change the position of these points on pH scale. Few examples, concerning edl parameters are shown in Table 3. Presented data concern a group of systems of different composition of the liquid phase and solid of a different origin. The latest measurements of this system takes into account the kinetics of the silica dissolution [152], and at zeta measurements, also the porosity of dispersed solid [155]. 

Table 12.2 shows the results of a P, T-flash calculation for the system n-hexane( 1)/ethanol(2)/methylcyclopentane(3)/benzene(4). This is the same system for which the results of a BUBL T calculation were presented in Table 12.1, and the same correlations and parameter values have been used here. The given P and T are l(atm) and 334.15 K. The given overall mole fractions for the system Zi are listed in the table along with the calculated values of the liquid-phase and vapor-phase mole fractions and the K-values. The molar fraction of the system that is vapor is here found to be V = 0.8166. 

The parameters in the correlations were obtained using nonlinear parameter estimation software and by minimizing the sum of the relative errors between experimental and predicted conversions for the 2.5% Pd catalyst. A comparison between predicted and experimental values of conversion for both solvents is given in Figure 2. The agreement between the two is seen to be satisfactory except for hexane at the highest conversion where deviations of the liquid-phase from plug flow may influence the result. 

The initial expansion ratio and dispersity of polyhedral foams are related through the quantitative dependence, given by Eq. (4.9). There at Ap > 103 Pa the content of the liquid phase in the films can be neglected. Thus, the connection of the structure parameters n, a and r can be expressed by the simple relation in Eq. (4.10). It follows from it that under given foaming conditions a definite expansion ratio can be reached by changing the border pressure, foam dispersity and surface tension of the foaming solution. 

The studies discussed expand the use of the method for assessment of foetal lung maturity with the aid of microscopic foam bilayers [20]. It is important to make a clear distinction between this method [20] and the foam test [5]. The disperse system foam is not a mere sum of single foam films. Up to this point in the book, it has been repeatedly shown that the different types of foam films (common thin, common black and bilayer films) play a role in the formation and stability of foams (see Chapter 7). The difference between thin and bilayer foam films [19,48] results from the transition from long- to short-range molecular interactions. The type of the foam film depends considerably also on the capillary pressure of the liquid phase of the foam. That is why the stability of a foam consisting of thin films, and a foam consisting of foam bilayers (NBF) is different and the physical parameters related to this stability are also different. Furthermore, if the structural properties (e.g. drainage, polydispersity) of the disperse system foam are accounted for it becomes clear that the foam and foam film are different physical objects and their stability is described by different physical parameters. 

This expression describes the analyte retention in binary system using only the total volume of the liquid phase in the column, Vq, and total adsorbent surface area S as parameters and the derivative of the excess adsorption by the analyte equihbrium concentration. It is important to note that the position of Gibbs dividing plane in the system has not been defined yet. 

Adsorption model of HPLC retention mechanism allows clear definition of the column void volume as the total volume of the liquid phase in the column, but this model requires the use of the surface-specific retention and the correlation of the HPLC retention with the thermodynamic (and thus energetic) parameters, which is not well-developed. This model requires the selection of the standard state of given chromatographic system and relation of all parameters to that state. 

So far the solution of the mass-balance equation for models with a single dominating process (partitioning or adsorption) was discussed in Sections 2.8 and 2.9. In both cases the solutions have similar form, with the difference in the definition of the parameters (volumes of the mobile and stationary phases in the case of partitioning total volume of the liquid phase and adsorbent surface area in the case of adsorption model). 

The void volume is the volume of the liquid phase inside the column. The importance of this parameter has been discussed in Chapter 2. Despite the very long debates, this is still a subject of significant controversy. Essentially, anyone who intends to measure the column void volume has to answer the question if he/she wants correct or estimated (convenient) measurements. 

The dispersion coefficients of the liquid phase are dependent on the gas velocity and on the column diameter. The liquid flow, the type of gas sparger and physico-chemical properties like viscosity do not influence the dispersion coefficient, El/ or,at best, these parameters are of very minor importnace. For instance, Hikita and Kikukawa (46) found only a slight viscosity influence, i.e. El0Ci ... 

---