A simple perturbation method for electrolyte solutions

1989 ◽  
Vol 54 (11) ◽  
pp. 2872-2878
Author(s):  
Jan Sýs ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Helmholtz Free Energy ◽  
Osmotic Coefficients ◽  
Perturbation Expansion ◽  
Electrolyte Solutions ◽  
Simple Expression ◽  
Monte Carlo Data ◽  
First Order ◽  
Restricted Primitive Model ◽  
Heats Of Dilution ◽  
Perturbation Potential

The first order perturbation expansion of the Helmholtz free energy was used to calculate the thermodynamic properties of aqueous electrolytes. The restricted primitive model was used as the reference system. Its properties were determined using semiempirical formulae consistent with simulated Monte Carlo data. A simple expression with two adjustable parameters was chosen for the perturbation potential. Integral heats of dilution and osmotic coefficients of alkaline halides and tetraalkylamonium bromides were calculated. An excellent agreement with the tabulated data was found up to the concentrations of 2-3mol/dm3.

Heats of mixing of nonelectrolytes

1979 ◽  
Vol 44 (2) ◽  
pp. 313-318
Author(s):  
Jiří Rameš ◽  
Petr Kyselka ◽  
Karel Procházka
Keyword(s):  
Hard Sphere ◽  
Helmholtz Free Energy ◽  
Contact Point ◽  
Perturbation Expansion ◽  
Liquid Mixtures ◽  
Good Qualitative Agreement ◽  
First Order ◽  
Binary Liquid ◽  
Heats Of Mixing ◽  
First Order Perturbation

The first-order perturbation method is applied to a rapid estimation of heats of mixing of binary liquid mixtures containing molecules with a negligible polarity and approximately spherical symmetry. The calculation is based on the approximate perturbation expansion of the Helmholtz free energy up to first order and requires the knowledge of the radial distribution function of the hard-sphere reference system at the contact point. Generalized relations are used for estimating the molecular parameters. The calculated values are compared with experimental data on six mixtures. Good qualitative agreement was achieved in all cases investigated.

Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons

2009 ◽  
Vol 75 (5) ◽  
pp. 593-607 ◽  
Author(s):  
SK. ANARUL ISLAM ◽  
A. BANDYOPADHYAY ◽  
K. P. DAS
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Perturbation Expansion ◽  
Magnetized Plasma ◽  
Wave Number ◽  
First Order ◽  
Zk Equation ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.

Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water

1993 ◽  
Vol 37 (04) ◽  
pp. 354-383
Author(s):  
Willard J. Pierson
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Perturbation Expansion ◽  
The United States ◽  
Order Perturbation ◽  
Naval Academy ◽  
Third Order ◽  
First Order ◽  
Stokes Waves ◽  
Perturbation Solutions

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

Thermodynamics of electrolyte solutions: activity coefficients of NaCl in the NaCl–NiCl2–H2O system at 25, 35, and 45 °C

1990 ◽  
Vol 68 (2) ◽  
pp. 294-297 ◽  
Author(s):  
Ch. Venkateswarlu ◽  
J. Ananthaswamy
Keyword(s):  
Activity Coefficients ◽  
Silver Chloride ◽  
Osmotic Coefficients ◽  
Reference Electrode ◽  
Nickel Chloride ◽  
Electrolyte Solutions ◽  
Pitzer Formalism ◽  
Harned Coefficients ◽  
Silver Silver ◽  
Silver Silver Chloride

The activity coefficients of NaCl in the NaCl–NiCl2–H2O system were estimated at 25, 35, and 45 °C and total ionic strengths of 0.5, 1.0, 2.0, and 3.0 m by an EMF method using a Na-ion selective electrode and a silver–silver chloride reference electrode. The Harned coefficients were calculated at all the temperatures studied. At 25 °C the data were analysed using the Pitzer formalism. The osmotic coefficients and the excess free energies of mixing were also calculated at 25 °C. Keywords: activity coefficients, sodium chloride, nickel chloride, Pitzer equations, thermodynamics.

CHARACTERISTIC TEMPERATURES OF FIRST-ORDER FERROELECTRIC PHASE TRANSITION: EFFECTIVE FIELD APPROACH

2012 ◽  
Vol 02 (02) ◽  
pp. 1241007 ◽  
Author(s):  
C. L. WANG ◽  
C. ARAGÓ ◽  
M. I. MARQUÉS
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Ferroelectric Phase ◽  
Effective Field ◽  
Static Properties ◽  
Field Approach ◽  
First Order ◽  
Characteristic Temperatures ◽  
Ferroelectric Phase Transitions

The explicit expression of Helmholtz free energy has been obtained from the equation of state from effective field approach. From the Helmholtz free energy, four characteristic temperatures describing a first-order ferroelectric phase transitions have been determined. The physical meaning of coefficients in Landau-type free energy has been revealed by comparison with the expanding Helmholtz function. Temperature dependence of polarization under different bias, and hysteresis loops at different temperatures are presented and discussed. These results provide the basic understandings of the static properties of first-order ferroelectric phase transitions.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

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