Mean free path of a gas

Mean Free Path. The mean free path of a gas moiecuie I and the mean time between coiiisions T are given by... 

For polyatomic gases in porous media, however, the relaxation rate commonly decreases as the pore size decreases [18-19]. Given that the relaxation mechanism is entirely different, this result is not surprising. If collision frequency determines the Ti, then in pores whose dimensions are in the order of the typical mean free path of a gas, the additional gas-wall collisions should drastically alter the T,. For typical laboratory conditions, an increase in pressure (or collision frequency) causes a proportional lengthening of T1 so the change in T, from additional wall collisions should be a good measure of pore size. 

Forces acting on a particle as a result of a temperature gradient in a gas (thermophoresis) or nonuniform radiation (photophoresis) are known as radiometric forces. For a particle diameter much larger than the mean free path of a gas, the force due to the temperature gradient is given by [Hettner, 1926]... 

The mean free path of a gas molecule is the average distance it will travel before colliding with another gas-phase molecule. Conceptually, this will be equal to the velocity divided by the frequency of collisions. The frequency of collisions between like molecules, Z, is given as... 

From Eq. 3.24 we see that X. 1/P, i.e., the mean free path of a gas molecule is inversely proportional to pressure. This fact is of tremendous importance in vacuum systems. It should be borne in mind that at 1 atm pressure, X is very small compared with the macroscopic dimensions (such as 1 cm) which implies that the molecules collide with one another far more frequently than they collide with the walls of the container and that a molecule moves a distance of several molecular diameters before colliding with another molecule. 

The viscosity of a suspension of nonsettling spherical particles larger than the mean free path of a gas increases linearly with the volumeiric concentration, 0, expressed as volume fraction of the particles according to a relation first given by Einstein ... 

Under viscous flow (Poiseuille flow), the mean free path of fluid molecules is small compared to the pore diameter, and molecules undergo many more collisions with each other than with the walls of the membrane. The molecules in a mixture do not behave independently in viscous flow and no separation is possible. Thus, viscous flow is not desirable. As the pressure is lowered, the mean free path (A.) of the molecules becomes longer than the pore diameter (Figure 9.2(a)). As a result, the molecules undergo far more collisions with the pore walls than with each other, and the molecules flow through the pores independently from each other. The mean free path of a gas molecule can be calculated as kT... 

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms ... 

When the pressure is lowered or the pore radius is small, (he mean free path of a gas molecule becomes comparable to that of the pore radius. In this situation, called the Knndsen diffusion regime, collisions between gas molecules and the wall are as impottant as those among molecules. The Knndsen diffusion coefficient is given by the expression ... 

Unfortunately, even though (9.5) provides valuable insights into the dependence of X.BB on the gas concentration and molecular size, it is not convenient for the estimation of the mean free path of a pure gas, because one needs to know the diameter of the molecule ob, a rather ill-defined quantity as most molecules are not spherical. To make things even worse, the mean free path of a gas cannot be measured directly. However, the mean free path can be theoretically related to measurable gas microscopic properties, such as viscosity, thermal conductivity, or molecular diffusivity. One therefore can use measurements of the above gas properties to estimate theoretically the gas mean free path. For example, the mean free path of a pure gas can be related to the gas viscosity using the kinetic theory of gases... 

Mean Free Path of a Gas in a Binary Mixture If we are interested in the diffusion of a vapor molecule A toward a particle, both of which are contained in a background gas B (e.g., air), then the description of the diffusion process depends on the value of the Knudsen number defined on the basis of the mean free path Tab- The mean free path X.ar is defined as the average distance traveled by a molecule of A before it encounters another molecule of A or B. Note that because ordinarily the concentration of A molecules is several orders of magnitude lower than that of the background gas B (air), collisions between A molecules can be neglected, and the collisions between A and B are practically equal to the total number of collisions for an A molecule. The Knudsen number in the case of interest is given by... 

To obtain the mean free path Xp, we recall that in Section 9.1, using kinetic theory, we connected the mean free path of a gas to measured macroscopic transport properties of the gas such as its binary diffusivity. A similar procedure can be used to obtain a particle mean free path A,p from the Brownian diffusion coefficient and an appropriate kinetic theory expression for the diffusion flux. Following an argument identical to that in Section 9.1, diffusion of aerosol particles can be viewed as a mean free path phenomenon so that... 

Mean free path of a gas molecule (cm.), which is the average distance a molecule travels between intermolecular collisions. 

At constant pressure, the mean fi-ee path (A) of a gas molecule is directly proportional to temperature. At constant temperature, A is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, A is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Rnjp, like the ideal-gas constant) and define units for Pmfy. 

When the total pressure is very low or pore diameter is small, mean free path of a gas molecule, A, becomes smaller than the pore diameter, 27 p. 

As the mean free path of a gas is in the order of 100 nm, Kn is small for the carbon paper GDL and the Knudsen effect can be neglected. But pore sizes inside the MPL are of the same order of magnitude as the mean free path of the gas and thus Knudsen effects have to be taken into account. The Knudsen diffusion effect in the MPL was investigated by Becker et al. by applying Bosanquet s formula " ... 

In porous media, the mechanism of permeation of fluids is dependent on the pore size. If the pore diameter is much larger than the mean free path of a gas, the mechanism of flow is governed by viscous flow. In this mechanism, permeability is inversely proportional to the pressure and proportional to the temperature. 

Each of these thermal conductions mechanism is shown in Figure 13-3. Here, the thermal conduction through the air can be regarded as a transport phenomenon with kinetic energy driven by the collision of gas molecules in the air imder a temperature gradient. Therefore, the thermal conductivity of a gas depends on the mean free path of the gas, and the mean free path of a gas (If) enclosed in a narrow space can be given by equation (13-2), from the mean pore size (I,) and the mean free path of the gas in free space (Lg), and this can be transformed as in equation (13-3) (Takahama, 1995 Takita,... 

Debye length (3.1.10b), mean free path of a gas molecule (3.1.114), filter coefficient (7.2.187), parameter for a dialyzer (8.1.399), parameter for a distillation plate/stage (8.3.38), latent heat of vaporization/condensation molecular conformation coordinate (3.3.89c) electrode spacings (7.3.18) retention parameter for species i (7.3.213), ionic equivalent conductance of ion i (3.1.108r) value of Xi for a cation value of A, for an anion value of A, at infinite dilution (Table 3.A.8) defined by (5.4.100) equivalent conductance of a salt (an electrolyte) (3.1.108s)... 

The kinetic molecular theory also allows us to predict the mean free path of a gas particle (the distance it travels between collisions) and relative rates of diffusion or effusion. 

From the kinetic theory of gases we know that tiie mean free path of a gas particle is given by ksTIQ pa), where ks is the Boltzmann constant, T is the absolute terrqierature, p is tiie pressure (in Pa) and cr is die collision cross section (in m ). A reasonable estimate of the collision cross section between a small molecular ion and N2 or O2 is 50 = 5 x 10 m, and thus... 

Xx. magnetic snsceptibility of solidri A eqnivalent condnctivity X mean free path of a gas molecnle X wavelength of radiation Xx mnltiplying coefficient of step k p chains mnltiplying factor p rednced mass... 

A much better approach to this quantity is possible if special Knudsen cells are used the cover of these has an orifice (10-100 pm) whose size is comparable with the mean free path of a gas molecule. When the system is maintained under high vacuum (p < 0 mm Hg) and constant 7 , the release of the volatiles occurs at a constant rate and the relevant heat flux attains a constant level. Thus both DSC and DTG traces are horizontal straight lines the DSC/DTG ratio gives therefore the vaporization enthalpy at any moment of the weight-loss process [117] ... 

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