Inversion of the transverse force on a spinning sphere moving in a rarefied gas

The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Features of the Flow of a Model Liquid Into a Medium with a Variable Degree of Rarefaction

Experimental results of observing ethanol micro-jets expiring into a highly rarefied medium (vacuum) through a nozzle are presented. The study of the process was carried out both at the horizontal and vertical liquid stream from the source compared to the direction of gravity The residual background gas pressure in the vacuum chamber was maintained at a level much lower than the saturated vapor pressure of the working fluid at a given outlet temperature. The possibility of modeling complex processes of micro-fluids expiring into a medium with a given rarefied atmosphere on a compact vacuum gas-dynamic stand is shown. It is established that the long-term flow from a thin capillary or a small-diameter hole into a vacuum or a highly rarefied gas medium differs significantly from the well-studied flow modes into a dense gas medium, as well as from the pulsed flow modes into a vacuum. The paper describes the main features of the flow and the conditions for the occurrence of instability. It is shown that the long-term flow of a liquid micro-jet in a vacuum has a high degree of surface instability, with a large number of sudden changes in the direction, structure, and observed density. An explanation of the reasons for the destruction of the micro-jet is proposed. The formation of surface gas caverns causing explosive destruction of the micro-jet with the release of vapor-liquid droplets is established.

Method for investigating rarefied gas flow around a cylindrical surface at arbitrary Knudsen numbers

A moment method for solving the linearized kinetic Boltzmann equation for arbitrary Knudsen numbers is presented. The isothermal flow of a rarefied gas around a cylindrical surface (the limiting cylindrical Couette problem) is investigated. The moments of the collision integral are calculated for the hard sphere model. The moment of resistance force acting per unit length of the surface, the profile of the gas flow velocity in the transient regime, and the gas velocity on the surface are calculated.

A Review on BGK Models for Gas Mixtures of Mono and Polyatomic Molecules

We consider the Bathnagar–Gross–Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties and entropy inequality). However, in practical applications, one often has to deal with two additional physical issues. First, a gas often does not consist of only one species, but it consists of a mixture of different species. Second, the particles can store energy not only in translational degrees of freedom but also in internal degrees of freedom such as rotations or vibrations (polyatomic molecules). Therefore, here, we will present recent BGK models for gas mixtures for mono- and polyatomic particles and the existing mathematical theory for these models.

Non-isothermal rarefied gas flow in microtube with constant wall temperature

In this paper, pressure-driven gas flow through a microtube with constant wall temperature is considered. The ratio of the molecular mean free path and the diameter of the microtube cannot be negligible. Therefore, the gas rarefaction is taken into account. A solution is obtained for subsonic as well as slip and continuum gas flow. Velocity, pressure, and temperature fields are analytically attained by macroscopic approach, using continuity, Navier-Stokes, and energy equations, with the first order boundary conditions for velocity and temperature. Characteristic variables are expressed in the form of perturbation series. The first approximation stands for solution to the continuum flow. The second one reveals the effects of gas rarefaction, inertia, and dissipation. Solutions for compressible and incompressible gas flow are presented and compared with the available results from the literature. A good matching has been achieved. This enables using proposed method for solving other microtube gas flows, which are common in various fields of engineering, biomedicine, pharmacy, etc. The main contribution of this paper is the integral treatment of several important effects such as rarefaction, compressibility, temperature field variability, inertia, and viscous dissipation in the presented solutions. Since the solutions are analytical, they are useful and easily applicable.