The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces

In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier–Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.

The Dekel-Zhao profile: a mass-dependent dark-matter density profile with flexible inner slope and analytic potential, velocity dispersion, and lensing properties

ABSTRACT We explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark-matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the Numerical Investigation of a Hundred Astrophysical Objects cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centres. We show that the profile parameters are correlated with the stellar-to-halo mass ratio Mstar/Mvir. This defines a mass-dependent density profile describing the average dark-matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite–galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20 per cent decrease of the concentration parameter for Mstar/Mvir = 10−3.5–10−2, corresponding to $M_{\rm star} \!\sim \! 10^{7-10}\, \mathrm{ M}_\odot$. The accuracy by which this profile fits simulated galaxies is similar to certain multiparameter mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.