Equation for liquids

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Equations for Liquid-Phase Nonidealities A. Modified UNIQUAC Equation... 

Leslie F M 1968 Some constitutive equations for liquid crystals Arch. Ration. Mech. Analysis 28 265-83... 

Table 1. Equations for Liquid-Liquid Mass Transfer in Single Drops ...

These equations when combined with Eq. (13-5) lead to the following equations for liquid-phase activity coefficients in terms of measurable quantities ... 

The heat input from fire is discussed in API RP 520 (Reference 4). One form of their equation for liquid containing vessels is... 

As indicated in the previous section, infonnation on liquid emissions for a variety of conditions is available in the literature, including equations for two phase flow "°. Key equations for liquid and two-phase discliarges liave been adopted from CCPS and provided below ,... 

Solution of the design equations for liquid-phase piston flow reactors is usually easier than for gas-phase reactors because pressure t5q)icaUy has no effect on the fluid density or the reaction kinetics. Extreme pressures are an exception that theoretically can be handled by the same methods used for gas-phase systems. The difficulty will be finding an equation of state. For ordinary pressures, the... 

Nolte (1978) gives detailed methods for the selection of economic pipe diameters, taking into account all the factors involved. He gives equations for liquids, gases, steam and two-phase systems. He includes in his method an allowance for the pressure drop due to fittings and valves, which was neglected in the development of equation 5.12, and by most other authors. 

The AIChE design manual recommends the Wilke and Chang (1955) equation for liquid diffusivities and the Wilke and Lee (1955) modification to the Hirschfelder, Bird and Spotz equation for gas diffusivities. 

Scale-up equations for liquid, gas-liquid, and solid-liquid systems are detailed in [167,199,201,206]. 

Linear stability theories have also been applied to analyses of liquid sheet breakup processes. The capillary instability of thin liquid sheets was first studied by Squire[258] who showed that instability and breakup of a liquid sheet are caused by the growth of sinuous waves, i.e., sideways deflections of the sheet centerline. For a low viscosity liquid sheet, Fraser et al.[73] derived an expression for the wavelength of the dominant unstable wave. A similar formulation was derived by Li[539] who considered both sinuous and varicose instabilities. Clark and DombrowskF540 and Reitz and Diwakar13161 formulated equations for liquid sheet breakup length. 

B. SIZE. Sizing of control valves is one of the more controversial subjects in process control. The flow rate through a control valve depends on the size of the valve, the pressure drop over the valve, the stem position, and the fluid properties. The design equation for liquids (nonflashing) is... 

The geometrical force balance is considered only in the X-Y plane. This assumes that the liquid does not affect the solid surface (in any physical sense). This assumption is safe in most cases. However, only in very special cases, if the solid surface is soft (such as with contact lens), then tangential forces will also need to be included in this equation (as extensively described in the literature). There exists extensive data that convincingly support the equation for liquids and solids. 

The Volmer (VI) equation for liquids in tension has been modified by Remath (B4). The principal alteration was the designation of the molecular heat of vaporization X as being equivalent to AF. ... 

Solubility-Partition Coefficient Relationships A critical review on the applicability of empirically derived solubility -Kow models has been given by Yalkowsky et al. [24], Isnard and Lambert [26], Lyman [1], and Muller and Klein [27]. Equations 10.4.3 to 10.4.5 are examples of solubility-Kow models. Isnard and Lambert developed a model based on 300 structurally diverse compounds. The model equation for liquids (Tm < 25°C) is... 

Quantitative relationships between Kow and Csw have been reviewed by Isnard and Lambert [11]. These authors developed a model based on 300 structurally diverse compounds. The model equation for liquids (Tm < 25°C) is... 

There are many simple two-parameter equations for liquid mixture constituents, including the Wilson (25), Margules (2,3,18), van Laar (3,26), nonrandom two-liquid (NRTL) (27), and universal quasichemical (UNIQUAC) (28) equations. In the case of the NRTL model, one of the three adjustable parameters has been found to be relatively constant within some homologous series, so NRTL is essentially a two-parameter equation. The third parameter is usually treated as a constant which is set according to the type of chemical system (27). A third parameter for Wilson s equation has also been suggested for use with partially miscible systems (29,30,31). These equations all require experimental data to fit the adjustable constants. Simple equations of this type have the additional attraction of being useful for hand calculations. 

This is a simple problem since Ca and /i occur in the same equation. For liquid-phase systems when there is no change in volume, this problem is trivial. For gas-phase systems with a change in the number of moles accompanying the reaction, it is simple enough, but not as trivial as will be shown later. 

To maintain the condition Eref+Ed = const, numerical corrections are possible, e.g., using the Henderson equation for liquid-junction potential. 

Schut, J. H. Novel Low-VOC Paint Technology. Plast. Technol. 1991, 37, 29-37. Scriven, L. E. Higgins, B. G. Interfacial Shape and Evolution Equations for Liquid Films and Other Viscocapillary Flows. Ind. Eng. Chem. Fundam. 1979, 18, 208-215. 

Grain (1982) presented several methods for estimating the vapor pressure of a wide variety of organic chemicals in an earlier handbook. He recommended the Antoine equation for liquids with vapor pressures above 1(H kPa and the modified Watson method for solids and liquids with vapor pressures above 10 7 kPa. Section 3.2 discusses both methods in detail. Lyman (1984) recommended the Grain-Watson method and a method that Mackay and coworkers (1982) developed. Myrdal and Yalkowsky (1997) used a method similar to... 

General case. In practice many flow problems approach either the isothermal or the adiabatic process, but in the event that neither applies it is possible to use Eq. (10.5) or Eq. (10.10). The same procedure may be used for vapors when they depart too widely from the perfect gas laws. If the pressure ratio p2/pi is of the order of 0.95 or more, the error will be negligible if the fluid is treated as incompressible and the equations for liquids are used. 

A standard regression analysis can be performed on each set of data by applying a commercial regression software [95,96], The calculation can be also carried out by nonlinearly regressing each set of experimental data using directly the Langmuir equation for liquid-phase adsorption. 

Enthalpies Ideal gas for vapour, Watson equation for liquid. Densities Rackett equation. ... 

Applications of Clapeyron-Clauslus Equation for Liquid = Vapour Equilibria... 

A generalization of the Boltzmann equation for liquids and dense gases is... 

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