Mean free path experiment

Knudseci s very careful experiments on a long uniform capillary show that N L/ Pj -p ) passes through a marked minimum when plotted as a function of (P +P2)/2, at a value of the mean pressure such that the capillary diameter and the mean free path length are comparable. At higher values of the mean pressure, N L/(pj " 2 rises linearly, as in the case of a porous medium. 

As a consequence of these simple deductions, Graham s experiments c effusion through an orifice came to be regarded as one of the earliest direct experimental checks on the kinetic theory of gases. However, a closer examination of his experimental conditions reveals that this view is mistaken. As mentioned earlier, his orifice diameters ranged upwards from 1/500 in., while the upstream pressure was never very much less thai atmospheric. Under these circumstances the molecular mean free path len ... 

Xps is a surface sensitive technique as opposed to a bulk technique because electrons caimot travel very far in soHds without undergoing energy loss. Thus, even though the incident x-rays penetrate the sample up to relatively large depths, the depth from which the electron information is obtained is limited by the "escape depth" of the photoemitted electrons. This surface sensitivity of xps is quantitatively defined by the inelastic mean free path parameter which is given the symbol X. This parameter is defined to be the distance an electron travels before engaging in an interaction in which it experiences an energy loss. 

The functional relation ia equation 53 or 54 cannot be determined by dimensional analysis alone it must be suppHed by experiments. The significance is that the mean-free-path problem is reduced from an original relation involving seven variables to an equation involving only three dimensionless products, a considerable saving ia terms of the number of experiments required ia determining the governing equation. 

The LEED experiment relies on the duality of electrons, which have both particle and wave character. Electrons of primary energy, p, somewhere in the minimum of the mean-free path curve (Eig. 4.7) possess a wavelength, 1, that is comparable with the distance between atoms in a lattice ... 

Collisions of molecules with the walls of the passage provide the resistance to diffusion when the mean free path, A, is appreciably greater than the diameter, d, of the passage. In experimental work the ratio, A/d, is taken as 10 or more to isolate the Knudsen effect. That investigator did experiments with small capillaries and deduced the equation... 

When the mean free path is small compared with pore diameter, the dominating experience of molecules is that of collision with other molecules in the gas phase. In that respect, the situation is much the same as that which exists in the bulk gas. The appropriate diffusion coefficient Dm may be obtained from published experimental values, or calculated from a theoretical expression. For molecular diffusion in a binary gas, the Chapman and Enskog equation may be used, as discussed by Bird, Stewart and Lightfoot(32). This takes the form ... 

In the Knudsen effusion method a substance is enclosed in a sealed container into which a very small hole is drilled. This hole must be knife-edged and the mean free path of the vapour must be 10 times the diameter of the hole. In its simplest form an experiment proceeds as follows. The Knudsen cell, with sample in it, is carefully weighed and then heated in a vacuum at the requisite temperature for a set time. The cell is then re-weighed and the weight loss is measured. However, it is now more usual to continuously measure the weight of the cell. If the molecular weight and surface area of the sample is known the vapour pressure can be found. 

Model concept Gas Is pourable (fluid) and flows In a way similar to a liquid. The continuum theory and the summarization of the gas laws which follows are based on experience and can explain all the processes in gases near atmospheric pressure. Only after it became possible using ever better vacuum pumps to dilute the air to the extent that the mean free path rose far beyond the dimensions of the vessel were more far-reaching assumptions necessary these culminated in the kinetic gas theory. The kinetic gas theory applies throughout the entire pressure range the continuum theory represents the (historically older) special case in the gas laws where atmospheric conditions prevail. 

The light-scattering experiment showed that the particle size was on the order of 50 nm, significantly smaller than the gas mean-free path. In this limit the thermophoretic velocity is [136]... 

Fig. 5 dotted lines). The overall spectra shapes are qualitatively reproduced, except for the peak of the 50 nm spectra which is noticeably different from the experimental data. At large Ln, the predicted mini-gap is clearly smaller than in the experiment. Changing the s values or introducing a small interface resistance in the calculation did not improve the fit. We tried to take into account the dependence of the elastic mean free path with the normal metal thickness Ln, and hence the related variation of the characteristic length n... 

---