Mean free path of gas molecules

Figure 5 relates N j to collection efficiency particle diffusivity from Stokes-Einstein equation assumes Brownian motion same order of magnitude or greater than mean free path of gas molecules (0.1 pm at... 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

As described above, the magnitude of Knudsen number, Kn, or inverse Knudsen number, D, is of great significance for gas lubrication. From the definition of Kn in Eq (2), the local Knudsen number depends on the local mean free path of gas molecules,, and the local characteristic length, L, which is usually taken as the local gap width, h, in analysis of gas lubrication problems. From basic kinetic theory we know that the mean free path represents the average travel distance of a particle between two successive collisions, and if the gas is assumed to be consisted of hard sphere particles, the mean free path can be expressed as... 

X, the thickness of the boundary layer is approximately equal to the mean free path, , of gas molecules in air. 

The strict solution for the problem of the resistance to the motion of a small sphere moving through gas has been obtained by Baines et al. (1965). They considered both specular and diffuse reflection of the molecules at the surface of the sphere mass of which is large in comparison with the mean mass of gas molecules and the radius to be small compared with the mean free path of gas molecules. All these assumptions are applicable for circumstellar outflows. Fadeyev and Henning (1987) used these solutions for calculation of momentum transfer from silicate dust grains to gas molecules in cool 0-rich red giants... 

A the mean free path of gas molecules, m /t fluid viscosity, kg/m s pL liquid viscosity, kg/m s p density, kg/m3 Pp density of particles, kg/m3 t residence time, s r average residence time, s... 

When the mean free path of gas molecules becomes large relative to the distance between the walls of the... 

A final example of the application of effusive flow is found in the so-called absolute manometer designed by Knudsen for the measurement of very low pressures. If a disk is suspended near a heated surface at a distance which is small compared to the mean free path of gas molecules, then a molecular effusion will take place between the gas molecules in the space between the disk and surface and the rest of the gas (Fig. VII.8). The rate at which molecules enter this space will be proportional to PgTg, where To refers to the temperature of the gas and Po refers to the pressure. The rate at which molecules leave will be proportional to PsTr, where 5T, refers to the mean temperature of the space between disk and surface and... 

Considering at first transport mechanisms in porous membranes, viscous flow (Fig. 9), also called Poiseuille flow, takes place when the mean pore diameter is larger than the mean free path of gas molecules (pore diameter higher than a few microns), so that collisions between different molecules are much more frequent than those between molecules and pore walls. In such conditions, no separation between different molecules can be attained [45]. 

Equation (40) shows that the optimum hydraulic diameter decreases at lower temperatures. Thus, microscale effects may be more important in low temperature applications, such as in heat exchangers of cryocoolers. However, temperature has little effect on the relative importance of slip flow. The mean free path of gas molecules is given by... 

Perhaps the simplest basis for separation of two gases is molecular size. Gases of different molecular weights have different diffusion coefficients and will diffuse at different rates through the membrane. For membranes having pores whose diameter is comparable or smaller than the mean-free path of gas molecules, the diffusion coefficient is inversely proportional to the square-root of molecular weight ... 

The physical meaning of the above criteria is as follows. The external force acting on an aerosol is generally gravitation. This means that the lifetime of a particle in the system is determined by its sedimentation velocity. If the particle radius is greater than the mean free path of gas molecules, the vs falling velocity is given by the well-known Stokes equation ... 

It should be noted that deposition processes in manufacture of nanoparticles often take place in a regime very far from equilibrium conditions [1]. The model for description of the impurity molecule trapping by growing nanoparticles should be valid for high non-equilibrium conditions. It should also describe the deposition process for arbitrary relation between the mean free path of gas molecules and the particle radius and take into account the trapping of non-condensable molecules. It is known that the gas-to-particle conversion can be realized by ordinary condensation (physical deposition) and by chemical deposition. Further we will consider the trapping of molecules by a small aerosol particle in physical deposition. 

Pressure, type of gas flow and mean free path of gas molecules are phenomena which can be described with the aid of the well known kinetic theory of gases. The theory is based on the following idealized assumptions. ... 

Size effects in the particle growth by deposition from the gas phase are related in particular to the Kelvin effect that decreases the saturation pressure near the particle surface with the reduction of the particle size and dependence of the sticking (condensation) coefficient on the particle size. Transfer of vapor molecules to the particle surface in the general case also depends on the particle size through the Knudsen number Kn that is equal to the ratio of the mean free path of gas molecules to the particle radius. Further we consider the free-molecular gas flow when Kn l. The particle growth rate is proportional to the trapping coefficient /i that is defined as the ratio of the resulting flux of vapor molecules into the particle to the flux of vapor molecules incident on the particle... 

Aerosol particles of dimensions comparable with the mean free path of gas molecules (about 0.06 pm) recognize their gaseous surroundings as composed of individual molecules, and every collision of a particle with a gas molecule changes its kinetic energy and direction of motion as a result, the particle moves at random through the gas (Brownian motion or diffusion). The random displacement a particle covers by this transport increases with time and with decreasing particle diameter. It is independent of the particle density. 

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