Temporal and Steady State Transition Probabilities for Molecules Interacting with Oscillating and Static Electric Fields and Surfaces

1988 ◽  
pp. 453-460 ◽  
Author(s):  
William J. Meath ◽  
R. A. Thuraisingham
Keyword(s):  
Steady State ◽  
Electric Fields ◽  
State Transition ◽  
Transition Probabilities ◽  
Static Electric Fields

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

scholarly journals Functionalized Silicon Electrodes Toward Electrostatic Catalysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Long Zhang ◽  
Xiaohua Yang ◽  
Shun Li ◽  
JianMing Zhang
Keyword(s):  
Electric Fields ◽  
Silicon Surfaces ◽  
Double Layers ◽  
External Electric Fields ◽  
Space Charges ◽  
Surface Models ◽  
Solid Liquid ◽  
Static Electric Fields ◽  
Mediator Catalysis

Oriented external electric fields are now emerging as “smart effectors” of chemical changes. The key challenges in experimentally studying electrostatic catalysis are (i) controlling the orientation of fields along the reaction axis and (ii) finely adjusting the magnitudes of electrostatic stimuli. Surface models provide a versatile platform for addressing the direction of electric fields with respect to reactants and balancing the trade-off between the solubility of charged species and the intensity of electric fields. In this mini-review, we present the recent advances that have been investigated of the electrostatic effect on the chemical reaction on the monolayer-functionalized silicon surfaces. We mainly focus on elucidating the mediator/catalysis role of static electric fields induced from either solid/liquid electric double layers at electrode/electrolyte interfaces or space charges in the semiconductors, indicating the electrostatic aspects is of great significance in the semiconductor electrochemistry, redox electroactivity, and chemical bonding. Herein, the functionalization of silicon surfaces allows scientists to explore electrostatic catalysis from nanoscale to mesoscale; most importantly, it provides glimpses of the wide-ranging potentials of oriented electric fields for switching on/off the macroscale synthetic organic electrochemistry and living radical polymerization.

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