Thermal slip of Fermi gases

A kinetic equation which describes the behavior of Fermi gases in a half-spatial problem of thermal slip has been deduced for the first time. For the problem, an analytic solution has been found and the function of distribution of particles flying to a wall has been obtained in explicite form. It has been analyzed how the slip equation and velocity depend on the parameter that is defined as the ratio of the chemical potential to the product of Boltzmann’s constant by the absolute temperature. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 11–17, July, 2006.     

Slip velocity during the flow of a liquid over a solid surface

An equation is derived for the slip velocity when a nonequilibrated drop is spreading over a solid surface. This velocity is obtained as the product of the force induced by the gradient of the chemical potential along the surface with Einstein’s expression for the mobility of the molecules. A similar approach was applied to the flow in a capillary. In that case, the surface diffusion coefficient evaluated by comparing the obtained theoretical expression with experiment is orders of magnitude larger than expected. For this reason, one concludes that the observed slip is apparent and is caused by the formation of a gap of gas separating the flowing liquid from the solid surface.     

Variation of multiplicities of the secondary charged particles on the geometry of collision

The total charge of the projectile spectator fragments, Q_pf is taken as a measure of the degree of centrality of collision thus defining the collision geometry. In this paper the mean multiplicities of the different charged secondaries emitted in the interaction of ²⁴Mg-Em at 4.5A GeV have been investigated as a function of the total charge Q_pf of the projectile spectator fragments. It has been observed that the average number of the produced particles, 〈N^s〉 and the heavily ionizing particles, 〈N_h> decreases exponentially with the increase of Q_pf showing strong correlation with the geometry of the collision. An attempt has also been made to compare these results with ⁸⁴Kr-Em interaction at 0.95A GeV.     

Prediction of ultrasonic velocity and intermolecular free-length and their correlation with interaction in binary liquid mixtures

The ultrasonic velocities of binary liquid mixtures of 1,1,2,2-tetrachloroethane with benzene, toluene,p-xylene, acetone and cyclohexane have been evaluated at 298.15 and 308.15 K using Schaaff’s collision factor theory (CFT), Jacobson’s free length theory (FLT), Nomoto’s relation and Van Dael ideal mixing relation. The ideal mixing relation gives the minimum deviation for all the systems except with acetone. The intermolecular free length has also been evaluated using ultrasonic and thermodynamic methods and the limitations of both the methods have been discussed. The deviations in ultrasonic velocity and intermolecular free length are discussed in terms of weak interaction between unlike molecules.     

The impact of collisions on platelet distribution in the blood flow

The impact of platelet collisions on their distribution in a viscous liquid flow has been analyzed. It has been shown that platelet distribution in the flow perpendicular to current lines resulting from their collisions can be described as “shear” diffusion. In the wide physiological range of shear velocities specific for blood, the coefficient of “shear” diffusion is much larger than the coefficient of “Brownian” diffusion. For a parabolic fluid velocity profile (Poiseuille flow) in cylindrical vessel “shear” diffusion causes uneven radial distribution of platelets over the vessel radius. “Shear” diffusion causes platelet concentration to grow from the wall toward the center (vessel axis). This effect appears to be a consequence of the specific distribution of platelet collision frequency reaching its maximum at the vessel wall.     

Barnett slip of the Fermi gas

A half-space problem of the Barnett slip of the quantum Fermi gas is solved analytically. A formula for calculating the velocity of the Barnett slip of the Fermi gas along a plane surface and a distribution function of particles moving toward a wall are derived in an explicit form. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 44–49, October, 2007.     

A high resolution X-ray crystal spectrometer to study electron and heavy-ion impact atomic collisions

We have studied fast ion-atom and electron-atom collision processes using a reconditioned high resolution X-ray spectrometer. The X-rays, generated by the collisions, are dispersed by a curved ADP crystal (Johansson geometry) and detected by a gas proportional counter. A self-written LabVIEW based program has been used to give precise and controlled movement to the crystal and for data acquisition. The performance was tested by detecting the Kα diagram and satellite lines of several elements. The Kα satellite lines of Al have been studied in collision with 3–12 keV electrons and 40 MeV C⁴⁺ ions. In ion collisions as large as four L-vacancies are created simultaneously with the K-vacancy, compared to two satellites in case of the e-impact. In addition, we have measured the X-rays from H-, He- and Li-like Si ions which arise due to the electron loss/capture process in highly charged 80 MeV Si⁷⁺ ions in collision with thin carbon foil. Approximate charge state distribution has been obtained using this new technique.      

Influence of heterogeneous chemical reactions on the slip velocity of an inhomogeneous multicomponent gaseous mixture

In constructing a theory of thermal diffusiophoresis of volatile aerosol particles it is necessary to have boundary conditions for the tangential velocity component which allow for the presence of heterogeneous chemical reactions. Conditions of this sort have been obtained by a number of authors [R. N. Gupta et al., Technical Papers, AIAA 22nd Aerospace Science Meeting, AIAA 19th Thermophysics Conference, New York (1985), pp. 465–490; D. V. Kul’ginov, Tech. Phys. 63, 940 (1993); A. V. Bogdanov et al., Preprint No. 1051, Fiz-Tekh. Inst. Akad. Nauk. SSSR, Leningrad (1986)]. The results of Gupta et al. are in the form of analytical expressions, but their computations actually used Maxwell’s method, which is of low accuracy. Kul’ginov et al. and Bogdanov et al. used the method of matched asymptotic expansions, which did not permit them to get simple analytical expressions. In the present paper the slip velocity is calculated by the Loyalka method. Analytical expressions are obtained for the slip coefficients, and the results of numerical calculations are presented. It is shown that in the presence of concentration gradients of the components of the gaseous mixture along the surface of an aerosol particle, the slip velocity can acquire new terms due to the change in the sticking coefficient along the catalytic surface. Expressions in final form are given for these terms. Zh. Tekh. Fiz. 67, 29–33 (May 1997)     

On the Relaxation of Energetic Electrons in Plasmas

The impact of individual collision processes on the relaxation of the velocity distribution function of a group of electrons, initially localized in a narrow region at relatively high energies, has been studied. By having recourse to solutions of the non-stationary Boltzmann equation and to corresponding Monte-Carlo simulations, the temporal behaviour of electrons in CO₂ plasmas, both in the absence and the presence of an external dc field, has been investigated. A microphysical interpretation of observed relaxation phenomena, based on the data relevant to the individual collision processes, is also given.     

Monte Carlo solution of the Boltzmann equation via a discrete velocity model

A new discrete velocity scheme for solving the Boltzmann equation is described. Directly solving the Boltzmann equation is computationally expensive because, in addition to working in physical space, the nonlinear collision integral must also be evaluated in a velocity space. Collisions between each point in velocity space with all other points in velocity space must be considered in order to compute the collision integral most accurately, but this is expensive. The computational costs in the present method are reduced by randomly sampling a set of collision partners for each point in velocity space analogous to the Direct Simulation Monte Carlo (DSMC) method. The present method has been applied to a traveling 1D shock wave. The jump conditions across the shock wave match the Rankine–Hugoniot jump conditions. The internal shock wave structure was compared to DSMC solutions, and good agreement was found for Mach numbers ranging from 1.2 to 10. Since a coarse velocity discretization is required for efficient calculation, the effects of different velocity grid resolutions are examined. Additionally, the new scheme’s performance is compared to DSMC and it was found that upstream of the shock wave the new scheme performed nearly an order of magnitude faster than DSMC for the same upstream noise. The noise levels are comparable for the same computational effort downstream of the shock wave.     

Quenching of fluorescence from Na(32P) and K(42P) atoms following photodissociation of NaCl and KCl at 193 nm

 Quenching of fluorescence from Na(3² P) and K(4² P) atoms by various collision partners was studied at 973 and 1273K. Excited alkali atoms were produced photolytically by excimer laser light at 193nm. For each collision pair, the appropriate relative velocity was computed and used to evaluate the quenching cross-section from the measured rate constants. Cross sections for CO₂, O₂ and N₂ are large (10–60Ų) while for Ar, the values are <1 Ų. The results are compared with those of previous investigations as a function of relative velocity. Finally, implications for combustion diagnostics are briefly discussed. Received: 29 March 1996     

The effects of ion-neutral collision frequency on the plasma sheath dynamics for oblique entrance of ions into the sheath

Recently it has been shown that the magnetic field has significant effects on the characteristics of ions which enter the collisionless plasma sheath with an oblique incidence angle. Here, we have investigated these effects in collisional plasma sheath. Considering the ion-neutral collision, the basic equations of fluid model in a plasma sheath have been numerically solved in the presence of an external magnetic field where the ion collision frequency has a power law dependency to the ion flow velocity. The results show that the effects of magnetic field on the plasma sheath dynamics strongly depend on the ion-neutral collision frequency and its dependency to ion flow velocity.     

随机粗糙微通道内流动特性研究

采用计算流体动力学的方法, 研究了微通道内气体在速度滑移和随机表面粗糙度耦合作用下的流动特性. 其中, 利用二阶速度滑移边界条件描述气体的边界滑移, 利用分形几何学建立随机粗糙表面. 研究发现, 综合考虑二阶速度滑移边界条件和随机表面粗糙度在较大的平均Knudsen数范围内 (0.025-0.59) 得到的计算结果与实验数据符合得很好, 而一阶速度滑移边界条件只在平均Knudsen数较小时(<0.1)符合实验结果. 随机表面粗糙度对气体在边界处的滑移有显著影响, 相对粗糙度越大, 速度滑移系数越小. 并针对计算结果, 给出了滑移系数与相对粗糙度近似满足的关系. 随机粗糙表面对气体流动过程中的压强、速度、Poiseuille数也有显著影响. 关键词： 随机表面粗糙度 二阶速度滑移边界条件 分形 微通道     

微通道疏水表面滑移的耗散粒子动力学研究

了解疏水表面的滑移规律对其在流动减阻方面的应用至关重要.利用耗散粒子动力学(dissipative particle dynamics, DPD)方法研究了微通道疏水表面的滑移现象.采用固定住的粒子并配合修正的向前反弹机制,构建了DPD固体壁面边界模型,利用该边界模型模拟了平板间的Couette流动.研究结果表明,通过调整壁面与流体间排斥作用强度,壁面能实现从无滑移到滑移的转变,壁面与流体间排斥作用越强,即疏水性越强,壁面滑移越明显,并且滑移长度与接触角之间存在近似的二次函数关系.无滑移时壁面附近密度分布均匀,有滑移时壁面附近存在低密度区域,低密度区域阻碍了动量传递,致使壁面产生滑移.     

Converging shock waves in metals

Study of propagation of a spherically converging shock wave has been carried out by Whitham’s method. The variation of shock velocity and pressure along the radius of curvature has been calculated numerically for a number of metals. Attempt has also been made to compare the experimental results of velocity of detonation wave with those reported elsewhere by the application of Whitham’s method. A good agreement between experimental and theoretical results has been obtained in this study.     

适用于中等耦合等离子体的碰撞算子

完全电离等离子体中，当试探粒子分布函数f_α是关于试探粒子速度v_α的偶函数时，导出了一个新的动力学方程的碰撞算子.该碰撞算子同时包括了大角散射(库仑近碰撞)和小角散射(库仑远碰撞)的二体碰撞的贡献,因此，该碰撞算子同时适用于弱耦合(库仑对数lnΛ≥10)和中等耦合(库仑对数2≤lnΛ≤10)等离子体.而且经过修改的碰撞算子和Rosenbluth势有直接的联系，当试探粒子和场粒子满足条件m_αm_β(如电子-离子碰撞或Lor 关键词： 中等耦合等离子体 小角散射 大角散射 碰撞算子     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.     

ELECTRON DIFFUSION IN A NON-UNIFORM ELECTRIC FIELD AND A UNIFORM MAGNETIC FIELD

A Monte Carlo simulation technique has been used to model the electron transport beharlot, especially the electron diffusion motion, in the cathode fall region of a glow discharge under the influence of a non-uniform electric field and a transverse magnetic field perpen-dicular to the cathode sheath electric field. Three types of collisions (elastic, excitation and ionization) are taken into account in our model. The electron free flying time is determined by the electron-neutral atom collision frequency. We focus attention on the electron diffusion distance and velocity. The electron-neutral atom collision processes and the electron drift velocity are also studied. The results indicate that with the increase of the magnetic field the electron diffusion distance increases and the electron diffusion velocity decreases. The results Mso show that the collision processes are enhanced by the magnetic field, this is in agreement with the experimental result. However, the axial magnetic field does not affect the electron transport behavior.     

Interaction of second sound with acoustic waves in solids

An expression has been derived for the collision operator for phonons in a solid, which is valid at very low temperatures. The set of coupled equations for the elastic deformation and the phonon density or second sound has been reduced to a simple tractable form and the dispersion equation for the coupled waves consisting of the acoustic modes and second sound has been derived. It is shown that only the longitudinal mode interacts with the second sound. It is also shown that as a result of the interaction with the second sound, the longitudinal velocity along the principal axis acquires a correction term that is proportional to bothγ ² andT ⁴. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Multi electron capture processes in slow collisions between X<Superscript>7+</Superscript> (X = N,O and Ne) ions with C<Subscript>60</Subscript>

Electron capture processes in collision between slow X⁷⁺ (X = N, O and Ne) ions and C₆₀ fullerene have been investigated using coincident measurements of the number n of ejected electrons, the mass and charge of the multicharged C₆₀ ^r+ recoil ions and their fragments C_m ⁱ⁺ and the final charge state of the outgoing projectiles X^(q-s)+ ( ). The collision velocity is about 0.4 a.u. The partial cross-sections σ_r ^s , corresponding to r electrons transferred to the projectile with only s electrons stabilized, have been measured. Cross-sections for collisions “inside” and those “outside” the C₆₀ cage have been separated by analyzing the kinetic energy of the outgoing projectile. The mean final charge state for frontal collisions has been measured to 3.1, 2.6 and 2.5 for N⁷⁺, O⁷⁺ and Ne⁷⁺ respectively. These results show the importance of the core effect on the stabilisation processes of captured electrons.