A perturbation solution to the problem of Wien dissociation in weak electrolytes

1978 ◽  
Vol 359 (1698) ◽  
pp. 303-317 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Applied Electric Field ◽  
Pair Distribution Function ◽  
Infinite System ◽  
Perturbation Technique ◽  
Relative Increase ◽  
Ion Pair ◽  
Legendre Transform ◽  
Weak Electrolytes

The problem of Wien dissociation of a weak electrolyte in the presence of a uniform applied electric field, X , is analysed by using a perturbation technique. The partial differential equation for the ion-pair distribution function is first reduced to an infinite system of ordinary differential equations by taking the Legendre transform . Explicit expressions for the relative increase in the dissociation constant, K ( X )/ K (0), due to the applied electric field, are calculated to second order in the expansion parameter 2 βq , where β is proportional to X and q is the Bjerrum association distance. Further, by induction, the m th term of this expansion is derived. The infinite series obtained in this way for K ( X )/ K (0) is convergent for all values of βq , and when summed, agrees with a formula in terms of an ordinary Bessel function of order one, given by onasager (1934) whose derivation has been published in full.

Ion trajectories in weak electrolytes

1980 ◽  
Vol 371 (1746) ◽  
pp. 413-427 ◽  
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Applied Electric Field ◽  
Numerical Quadrature ◽  
Average Flow ◽  
Recombination Processes ◽  
Weak Electrolytes ◽  
The Mean ◽  
Charged Ions ◽  
Oppositely Charged

The equations of the mean relative trajectories of neighbouring oppositely charged ions in a weak electrolyte that has attained a steady state in a uniform applied electric field are determined analytically. Both the dissociation and recombination of ions are considered and the mean relative trajectories are defined in terms of the ensemble average flow patterns of the ions participating in these processes. For recombination of ions, the equation of the boundary of ionic attraction is also derived. The mean times involved in the dissociation and recombination processes are determined by using numerical quadrature. The results obtained are consistent with the Bjerrum (1926) theory of weak electrolytes.

Stokes’s stream functions for ion association and dissociation in weak electrolytes

1987 ◽  
Vol 413 (1845) ◽  
pp. 465-496
Keyword(s):  
Distribution Function ◽  
Stream Function ◽  
Pair Distribution Function ◽  
Ion Association ◽  
Ion Pair ◽  
Order Partial Differential Equation ◽  
Ion Dissociation ◽  
Method Of Solution ◽  
Stream Functions ◽  
Weak Electrolytes

The brownian motion theory of ion flow in a weak electrolyte that has attained a steady state in the presence of a uniform applied electric field is reformulated in terms of a Stokes stream function. The Stokes stream function describing the process of ion association is first derived and the equation of the streamlines and the association constant are obtained. The Stokes stream function describing the process of ion dissociation is then calculated with the aid of the solution of Onsager ( J . Chem . Phys . 2, 599-615 (1934)) for the ion-pair distribution function and the equation of the streamlines and the dissociation constant are found. An alternative derivation of the Stokes stream function for ion dissociation is presented by solving directly the second-order partial differential equation for the stream function. This derivation of the Stokes stream function yields the ion-pair distribution function in the process of the analysis and therefore provides an alternative method of solution for the ion-pair distribution function.

LIQUID CRYSTLASLIGHT SCATTERING BY FLUCTUATIONS INDUCED BY AN APPLIED ELECTRIC FIELD IN A NEMATIC LIQUID CRYSTAL (APAPA)

1972 ◽  
Vol 33 (C1) ◽  
pp. C1-63-C1-67 ◽  
Author(s):  
M. BERTOLOTTI ◽  
B. DAINO ◽  
P. Di PORTO ◽  
F. SCUDIERI ◽  
D. SETTE
Keyword(s):  
Liquid Crystal ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Applied Electric Field

Improved technique for measuring mechanical deformations induced by an applied electric field to an organic insulator

2012 ◽  
Vol 15 (2-3) ◽  
pp. 127-139
Author(s):  
Tung Tran Anh ◽  
Laurent Berquez ◽  
Laurent Boudou ◽  
Juan Martinez-Vega ◽  
Alain Lacarnoy
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Mechanical Deformations ◽  
Improved Technique

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

Synergistic use of electroosmotic flow and magnetic forces for nucleic acid extraction

The Analyst ◽  
2020 ◽  
Vol 145 (6) ◽  
pp. 2412-2419 ◽  
Author(s):  
Rachel N. Deraney ◽  
Lindsay Schneider ◽  
Anubhav Tripathi
Keyword(s):  
Nucleic Acid ◽  
Electric Field ◽  
Microfluidic Chip ◽  
Applied Electric Field ◽  
Electroosmotic Flow ◽  
Acid Extraction ◽  
Nucleic Acid Extraction ◽  
Magnetic Forces ◽  
Extraction And Purification

NA extraction and purification utilitzing a microfluidic chip with applied electric field to induce electroosmotic flow opposite the magnetic NA-bound bead mix.

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