An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

Flow through Porous Media XVI: Electrokinetic Transport Coefficients of Aqueous Solutions of Mercuric Chloride and Glycine through a Sintered Disc Impregnated with a Cellulose Acetate Membrane under a Magnetic Field

The effect of the magnetic field on the electrokinetic transport coefficients (permeability coefficient and electro-osmotic permeability coefficient) of water and aqueous solutions of mercuric chloride and glycine through a sintered disc impregnated with cellulose acetate at different potentials, concentrations, and magnetic fields varying up to 21 kg/cm² are reported at 308.15 K. The phenomenological coefficients characterizing the electro-osmotic flow and the membrane characteristics are also estimated for the various solutions with the object of determining the efficiencies of electrokinetic energy conversion and ζ potential. The effect of magnetic field has been attributed to the molecular orientation of dipoles in solutions and to the change in the structure of the membrane.     

The Additive Influence of Propane-1,2-Diol on SDS Micellar Structure and Properties

Micellar systems are colloids with significant properties for pharmaceutical and food applications. They can be used to formulate thermodynamically stable mixtures to solubilize hydrophobic food-related substances. Furthermore, micellar formation is a complex process in which a variety of intermolecular interactions determine the course of formation and most important are the hydrophobic and hydrophilic interactions between surfactant–solvent and solvent–solvent. Glycols are organic compounds that belong to the group of alcohols. Among them, propane-1,2-diol (PG) is a substance commonly used as a food additive or ingredient in many cosmetic and hygiene products. The nature of the additive influences the micellar structure and properties of sodium dodecyl sulfate (SDS). When increasing the mass fraction of propane-1,2-diol in binary mixtures, the c.m.c. values decrease because propane-1,2-diol is a polar solvent, which gives it the ability to form hydrogen bonds, decreasing the cohesivity of water and reducing the dielectric constant of the aqueous phase. The values of ΔGm0 are negative in all mixed solvents according to the reduction in solvophobic interactions and increase in electrostatic interaction. With the rising concentration of cosolvent, the equilibrium between cosolvent in bulk solution and in the formed micelles is on the side of micelles, leading to the formation of micelles at a lower concentration with a small change in micellar size. According to the ¹H NMR, with the addition of propylene glycol, there is a slight shift of SDS peaks towards lower ppm regions in comparison to the D₂O peak. The shift is more evident with the increase in the amount of added propane-1,2-diol in comparison to the NMR spectra of pure SDS. Addition of propane-1,2-diol causes the upfield shift of the protons associated with hydrophilic groups, causing the shielding effect. This signifies that the alcohol is linked with the polar head groups of SDS due to its proximity to the SDS molecules.     

A critical reappraisal of recent communications on the hydrodynamic characterization of silica (aerosil) hydrosols

Different results from recent communications on the hydrodynamic characterization of ultrasonicated silica (®Aerosil) hydrosols led to a critical reappraisal of the data.It can be concluded that the degree of dispersion achievable in pyrogenic (Aerosil) hydrosols by ultrasonication is highly sensitive to the detailed parameters of the dispersion process. Characterization in terms ofabsolute numbers of a limiting particle morphology, corresponding to minima of aggregate size, porosity and number of primary particles in the aggregate is not possible.The most straightforward approach for hydrodynamic characterization seems to be a combination of sedimentation and diffusion data.Other approaches using a combination of sedimentation and viscosity data underestimate the particle dimensions. Moreover, they are quite arbitrary since the final result depends upon the proper choice between several equations for fitting the viscosity concentration dependence; the most rigorous approach seems to be an extended Einstein equation which has recently been adapted to particle aggregates.     

Dynamic Light Scattering and NMR Studies of Napin

We analyze the structure of napin (BngNAP1), a storage protein (m.w. 14.5 kDa) from Brassica napus. On the basis of the results of ¹H NMR spectroscopy and dynamic light scattering (DLS) studies, the overall shape and secondary structure of the molecule are estimated.     

Thermocapillary Alignment of Gas Bubbles Induced by Convective Transport

The effect of a weak convective heat transfer on the thermocapillary interaction of two bubbles with an arbitrary orientation relative to an externally imposed temperature gradient is examined. Asymptotic analysis of the case of large separation distances, Z, suggests that the corrections to the bubbles' velocities are of (Pe/Z²), rather than (Pe²) previously found for an isolated bubble. Equal-sized bubbles are known to move with the same velocities, as if they were isolated, when heat conduction is the only transport mechanism. However, the convective transport results in a relative motion of the bubbles. The tendency of equal bubbles to line up in a plane perpendicular to the applied thermal gradient is shown analytically in the weakly nonlinear limit of small Pe numbers, and an interesting interaction behavior in the case of unequal bubbles is discussed.     

柱几何Rayleigh-Taylor不稳定性的数值模拟

给出了柱几何中流体力学方程组及其在数值模拟中采用的计算方法。对二维柱几何Rayleigh-Taylor不稳定性进行数值模拟,在线性阶段与线性理论符合得很好;不稳定性增长进入非线性区域的阈值依赖于界面的位置,并且明显不同于平面情况。     

Like‐Charge Attraction: A Combined Electrostatic–Hydrodynamic Approach

Abstract

This article discusses the like‐charge attraction of colloidal spheres close to a charged plate and compares results produced by an electrostatic and a hydrodynamic model with experimental data. Hydrodynamic coupling is shown to be the dominating effect, while the electrostatic influence may often be neglected. Some observations, however, can be explained only by means of a combined electrostatic–hydrodynamic model, which is derived in this work. The combined model is able to predict not only the attractive force between particles of similar charge close to a charged plate but also the change to a purely repulsive force once the sphere‐plate distance is further reduced. This prediction matches qualitatively results of experiments reported in the literature.