Electrokinetic energy conversion through cylindrical microannulus with periodic heterogeneous wall potentials

In microfluidic electrokinetic flows, heterogeneous wall potentials are often required to fulfill some functions, such as increasing dispersion and mixing efficiency. In this paper, we study the pressure-driven electrokinetic flow through microannulus with heterogeneous wall potentials in circumferential direction. The streaming potential induced by the ions accumulating in downstream of the microannulus is considered and the electrokinetic energy conversion efficiency is further investigated. Interestingly, based on the method of Fourier expansion, the analytical solutions of fluid velocity, streaming potential and energy conversion efficiency are derived for arbitrary peripheral distribution of the small wall potential for the first time. Four specific patterned modes of the heterogeneous wall potential, i.e., constant, step, sinusoid with period 2π and sinusoid with period π/2 are represented. The distributions of the electric potential and the velocity for four different modes are depicted graphically. Furthermore, the variations of the streaming potential and the electrokinetic energy conversion efficiency with related parameters are also discussed. Results show that when these integral values from -π to π associated with the wall potentials are identical, the streaming potential and the electrokinetic energy conversion efficiency corresponding to different modes are the same. Additionally, the amplitude of fluid velocity peripherally reduces with the increase of the wavenumber of wall potential distribution in θ-direction.

Sheath collapse at critical shallow angle due to kinetic effects

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.

Plasma sheath and presheath development near a partially reflective surface

This work addresses one-dimensional evolution of a collisionless plasma next to a solid surface that is immersed into the plasma instantaneously. In particular, we consider how the self-similar rarefaction wave (Allen & Andrews, J. Plasma Phys., vol. 4, 1970, pp. 187–194) establishes dynamically and how the electron reflection from the surface modifies the structure of the rarefaction wave and the Debye sheath. We demonstrate that a sufficiently strong reflection eliminates the Debye sheath and changes the wall potential and the plasma flow parameters significantly. The paper presents numerical results that illustrate the developed analytical theory.

Perturbation of One-Dimensional Time Independent Schrödinger Equation With a Symmetric Parabolic Potential Wall

The first author has recently investigated a type of Hyers-Ulam stability of the one-dimensional time independent Schrödinger equation when the relevant system has a rectangular potential barrier of finite height. In the present paper, we will investigate a type of Hyers-Ulam stability of the Schrödinger equation with the symmetric parabolic wall potential.

Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a nonminimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the nonrelativistic limit of the system, we investigate the effects of the Lorentz symmetry violation on thermodynamic aspects of the system.

Noninertial effects on a scalar field in a spacetime with a magnetic screw dislocation

We investigate rotating effects on a charged scalar field immersed in spacetime with a magnetic screw dislocation. In addition to the hard-wall potential, which we impose to satisfy a boundary condition from the rotating effect, we insert a Coulomb-type potential and the Klein–Gordon oscillator into this system, where, analytically, we obtain solutions of bound states which are influenced not only by the spacetime topology, but also by the rotating effects, as a Sagnac-type effect modified by the presence of the magnetic screw dislocation.