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Solutal model

It has been pointed out [138] that algebraically equivalent expressions can be derived without invoking a surface solution model. Instead, surface excess as defined by the procedure of Gibbs is used, the dividing surface always being located so that the sum of the surface excess quantities equals a given constant value. This last is conveniently taken to be the maximum value of F. A somewhat related treatment was made by Handa and Mukeijee for the surface tension of mixtures of fluorocarbons and hydrocarbons [139]. [Pg.89]

The potential model has been applied to the adsorption of mixtures of gases. In the ideal adsorbed solution model, the adsorbed layer is treated as a simple solution, but with potential parameters assigned to each component (see Refs. 76-79). [Pg.629]

Not all of the isotherm models discussed in the following are rigorous in the sense of being thermodynamically consistent. For example, specific deficiencies in the Freundhch, Sips, Dubinin-Radushkevich, Toth, and vacancy solution models have been identified (14). [Pg.273]

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). [Pg.274]

Mixtures. A number of mixtures of the hehum-group elements have been studied and their physical properties are found to show Httle deviation from ideal solution models. Data for mixtures of the hehum-group elements with each other and with other low molecular weight materials are available (68). A similar collection of gas—soHd data is also available (69). [Pg.9]

Thus, usiag these techniques and a nonideal solution model that is capable of predictiag multiple Hquid phases, it is possible to produce phase diagrams comparable to those of Eigure 15. These predictions are not, however, always quantitatively accurate (2,6,8,91,100). [Pg.192]

Equation 22 is a special appHcation of the general Lewis-RandaH ideal solution model (3,10) that is typically used for near-ambient pressures and concentrated nonpolar solutes. [Pg.235]

Thermodynamics gives limited information on each of the three coefficients which appear on the right-hand side of Eq. (1). The first term can be related to the partial molar enthalpy and the second to the partial molar volume the third term cannot be expressed in terms of any fundamental thermodynamic property, but it can be conveniently related to the excess Gibbs energy which, in turn, can be described by a solution model. For a complete description of phase behavior we must say something about each of these three coefficients for each component, in every phase. In high-pressure work, it is important to give particular attention to the second coefficient, which tells us how phase behavior is affected by pressure. [Pg.141]

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. [Pg.333]

From these results it is possible to make another estimate of a property of the solution system. It is known that the freezing point of a solvent is lowered by approximately 1.86°C for every mole of the solute present. From the estimates of the temperature of the solvent and the solution modeled above, the decrease in the temperature can be estimated. From this value, the number of cells comprising a mole of solute may be reckoned. Thus, a value may be stated for an imaginary molecular weight of the cells used in the study. [Pg.70]

Figure 3. Mathematical statement of Solutal Model (SM) for microscopic solidification. Figure 3. Mathematical statement of Solutal Model (SM) for microscopic solidification.
Mullins and Sekerka (17) were the first to construct continuum descriptions like the Solutal Model introduced above and to analyze the stability of a planar interface to small amplitude perturbations of the form... [Pg.303]

Table 1. Dimensionless values of parameters in the Solutal Model for two cases studied here. The systems I and II are representative of the thermophysical properties of the succinonitrile-acetone systems with differing values of the dif-fusivity ratio Rm, temperature gradient G and capillary parameter F. System III corresponds to parameters for a Pb-Sb alloy with equal diffusivities in melt and crystal... Table 1. Dimensionless values of parameters in the Solutal Model for two cases studied here. The systems I and II are representative of the thermophysical properties of the succinonitrile-acetone systems with differing values of the dif-fusivity ratio Rm, temperature gradient G and capillary parameter F. System III corresponds to parameters for a Pb-Sb alloy with equal diffusivities in melt and crystal...
Walshe, J.L. (1986) A six-component chlorite solid solution model and the conditions of chlorite formation in hydrothermal and geothermal systems. Econ. Geol, 81, 681-703. [Pg.291]

One can further elaborate a model to have a concrete form of /(ft), depending on which aspect of the adsorption one wants to describe more precisely, e.g., a more rigorous treatment of intermolecular interactions between adsorbed species, the activity instead of the concentration of adsorbates, the competitive adsorption of multiple species, or the difference in the size of the molecule between the solvent and the adsorbate. An extension that may be particularly pertinent to liquid interfaces has been made by Markin and Volkov, who allowed for the replacement of solvent molecules and adsorbate molecules based on the surface solution model [33,34]. Their isotherm, the amphiphilic isotherm takes the form... [Pg.123]

Many minerals are solid solutions (e.g., clays, amphiboles, and plagioclase feldspars). Solid-solution models are either not available or appropriate algorithms have not been incorporated into computer codes. [Pg.826]

R.F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te... [Pg.650]

Bourcier, W. L., 1985, Improvements to the solid solution modeling capabilities of the EQ3/6 geochemical code. Lawrence Livermore National Laboratory Report UCID-205 87. [Pg.512]


See other pages where Solutal model is mentioned: [Pg.132]    [Pg.134]    [Pg.457]    [Pg.285]    [Pg.5]    [Pg.249]    [Pg.252]    [Pg.483]    [Pg.59]    [Pg.20]    [Pg.229]    [Pg.295]    [Pg.301]    [Pg.305]    [Pg.290]    [Pg.880]    [Pg.283]    [Pg.828]    [Pg.513]    [Pg.53]    [Pg.390]    [Pg.293]    [Pg.403]    [Pg.5]   
See also in sourсe #XX -- [ Pg.303 ]




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A Model for Chemical Reactions in Solution

A Qualitative Physical Model for Photochemical Reactions in Solution

A closed-form solution for the PARAFAC model

APPROXIMATE ANALYTICAL SOLUTIONS FOR MODELS OF THREE-DIMENSIONAL ELECTRODES BY ADOMIANS ECOMPOSITION METHOD Keith Scott and Yan-Ping Sun ntroduction

Activity Coefficient Models for Electrolyte Solutions

Activity coefficient models regular solution

Adsorbents Vacancy Solution model

Adsorption from electrolyte solutions Surface complexation models

Advection-diffusion modeling of solute transport in tissues

Analytical Solution of the Simplified Symmetric Model

Analytical Solutions of the Ideal Model

Analytical and Numerical Solutions of the Kinetic Models

Application of Flexible-Chain Models to Solutions

Application of an Interstitial Model for Water to Aqueous Solutions

Application of the blob model to aqueous solutions

Aqueous solutions modeling

Associated Solution Model

Associated Solution Model for the Liquid Phase

Associated solution model, domain

Associated-solution model application

Associated-solution model assumptions

Atomistic solution models

Automata Models of Aqueous Solution Systems

Born-Onsager solvent-solute model

Carreau model solution

Cell model of solution

Chemical models of electrolyte solutions

Classical solution model

Classical solution model molecule

Clustering in dilute solutions and Pitzer models

Concentration, polymer, model chain solution conformations

Confined model systems solutions

Conformal solution model

Conformal solution model anisotropic

Debye-Hiickel/Boltzmann model, solution

Definition of the ideal solution model

Direct model solution

Discussion of the Model and Numerical Solution

Dispersed Medium Model of Micellar Solution

Dispersed plug flow model solutions

Electrode-solution interface model

Electrolyte solutions model

Electrolyte solutions primitive model

Electrostatic solute-solvent interaction models

Equilibrium and Quasiequilibrium Solutions to the LG Model

Equilibrium-dispersive model numerical solution

Explicit model steady-state solution

First-order absorption models solution

Florys athermic solution model

Fowler and Guggenheims quasi-chemical model of the solution

General Closed Solution by Combined Model (Approximation)

General rate model numerical solution

Hamiltonians model solutions

Heat transfer model solution procedure

Hildebrand solution model

Hollow Nanoshell Formation and Collapse in One Run Model for a Solid Solution

Information Obtained from Model Solutions

Initial model solution

Instantaneous absorption models solution

Intermolecular interactions, model chain solution conformations

Kinetic model analytical solution

Kinetic model numerical solutions

Lattice model for ideal and regular solutions

Lattice models for solutions

Linear Isotherm Systems—Solution to the General Model

Liquid lattice model ideal solution

Liquid lattice model polymer solution

Liquid phase associated solution model

Liquid solutions activity-coefficient models

Lower critical solution temperature Model

Lumped pore diffusion model numerical solution

Macromolecular models polymer solutions

Many-body Hamiltonians model solutions

Markov model solution techniques

Mass balance equations, setup and solution model

Mass transfer model, solution

Mathematical modeling solution method specification

Mathematical modeling solution process

Mathematical models concentrated solution theory

Mathematical models dilute solution theory

Membrane model solution

Membrane permeability modeling solute effect

Metal-solution interphase model

Micellar solutions models

Model Solutions for the Motion of a Hypothetical Economy in Ideal Time

Model analytical solution

Model and Solution Robustness

Model ideal adsorbed solution

Model phases solid solution

Model solute mass recoveries, concentrated

Model solutions

Model solutions

Model solutions analytical solution

Model solutions validation

Modeling advanced solution methods

Modeling of the Oxide-Solution Interface

Modelling polyelectrolyte solutions

Models for ionic solutions

Models for solution reaction dynamics

Models many-body Hamiltonian solutions

Models polymeric solutions

Models solution systems model

Modified Poisson-Boltzmann models electrolyte solutions

Molecular Models for Solutions

Multiplicity modelling solutions

Nonequilibrium stage model solution

Nonporous membranes solution-diffusion model

Numerical Solution of Chemical Transport Models

Numerical Solution of the Column Reactor Model

Numerical Solution of the Lumped Pore Diffusion Model

Numerical Solution of the Model Equations

Numerical Solution of the Model System

Numerical Solution of the Two-dimensional Model

Numerical Solutions for Diagenetic Models

Numerical Solutions of the Equilibrium-Dispersive Model

Numerical modelling 5% NaCl solution

Numerical modelling solution

Numerical solution of model

Numerical solution, of complex flow models

Numerical solution, of model equations

Numerical solutions fluid model equations

Numerical solutions mass transfer model equations

Optimization of Reaction Models With Solution Mapping

Oxide-solution interface constant capacitance model

Oxide-solution interface diffuse double layer model

Oxide-solution interface electrostatic models

Oxide-solution interface model

Oxide-solution interfaces, theoretical model

Particulate flow model solution

Pervaporation solution diffusion model

Polymer solution properties, model

Polymer solution properties, model interactions

Process Model and the Solution Method

Quasichemical solution model

Random walk model, molecule solution

Reactive transport model numerical solution

Regular Solution model application

Regular solution model defined

Regular solution model for a two sub-lattice system

Regular solution model general

Regular solution model mixing enthalpy

Regular solution model mixing entropy

Regular solution model temperature

Regular solution modelling

Regular solution modelling phase diagrams

Results for HR solute in dilute solutions of the primitive cluster model

Reverse osmosis solution-diffusion model

Rigid solutions, partially, model

Robustness, model/solution

Segregation model solution

Selectivity solution-diffusion model

Semidilute polymer solutions Blob model

Simple Models for Nonideal Solutions

Simple model for mixed surfactant solutions

Simple solution diffusion model

Simple solution model

Simplified solute model

Soil solution model

Solid-solution Model

Solute Orientation The Shape Model

Solute Partitioning Model

Solute clusters model steel

Solute model

Solute model

Solute retention displacement model

Solute transport model

Solution Kinetic Models

Solution Properties of Model Branched Polymers

Solution Techniques for Models Producing PDEs

Solution diffusion model

Solution diffusion model assumptions

Solution diffusion model multicomponent

Solution diffusion model single-component

Solution diffusion model solubility, permeants

Solution diffusion model sorption isotherms

Solution diffusion model sorption process

Solution diffusion model transport equation through membrane

Solution lattice model

Solution models Bragg-Williams

Solution models Flory

Solution models Redlich-Kister

Solution models ideal

Solution models quasi-chemical

Solution models quasi-regular

Solution models reciprocal ionic

Solution models regular

Solution models solutions

Solution of Stochastic Model

Solution of the Model

Solution of the Model Equations

Solution of the Robust Model

Solution phase models

Solution phase models Aqueous solutions

Solution phase models cellular model

Solution phase models central atom model

Solution phase models complex’ model

Solution phase models dilute solutions

Solution phase models ideal solutions

Solution phase models interstitial solutions

Solution phase models line compounds

Solution phenomenological models

Solution systems model

Solution systems model aqueous solutions modeling

Solution systems model dissolution application

Solution systems model hydrophobic effect

Solution systems model probability

Solution systems model rules

Solution systems model solute

Solution systems model structure

Solution theory modeling

Solution, athermal models

Solution, concentrated lattice model

Solution-Diffusion Model for Single Gas Transport

Solution-Diffusion Model for the Transport of Binary Gas Mixtures

Solution-Precipitation Model for Creep

Solution-diffusion imperfection models

Solution-diffusion model for

Solution-diffusion model relationships

Solution-diffusion model relationships development

Solution-diffusion transport model

Solution-phase reactions, surface complexation models

Solutions of model

Solutions of the Brusselator Model

Solutions of the effective-particle model

Solutions robust model

Solutions, Mixtures, and Models

Solvation parameter model solute descriptors

Solvent-solute descriptor models

Solvent/solute partitioning models

Some Practical Hints on Application of UNIQUAC Solution Model

Sphere-Model for the Solution of Iodine in Ethanol

Steady-State Model Solution

Surface complexation models oxide-solution interface

Surface complexation models solid-solution interface

Surfactant solutions, thermodynamics mass action model

Surfactant solutions, thermodynamics pseudo-phase model

Surfactants in Solution Experimental Observations and Models

Temperature field, solutal model

The Information Obtained from Model Solutions

The Interaction Between Simulation and Models for Solution Reaction Dynamics

The Model and Its Solution

The Molecular Model and Its Solution

The One-Dimensional Model of Solutions

The Pauling model and its solution

The Solution of Stochastic Models with Analytical Methods

The Solution-Diffusion Model

The ideal solution model

The microscopic model of a perfect solution

The quasi-chemical method of modeling solutions

Theoretical models for individual surfactant solutions

Thermodynamic Modeling of Supercritical Fluid-Solute Phase Behavior

Thermodynamic model ideal solution

Thermodynamic model regular solution

Thermodynamic model, polymer solution

Transition-state model, for solution reactions

Transport model solution-diffusion imperfection

Tube model in concentrate solutions and melts

Turbulent solutal convection model

Two-Zone Model Solutions

UNIQUAC model extended to ionic solutions

Vacancy Solution Model

Vapor transport, solution-diffusion model

Zero-order absorption models solution

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