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Transient sorption rates of allene and methylacetylene in synthetic faujasite (Linde 13X) powder and self-bonded pellets are studied in a constant-volume, constant-pressure system at three temperatures. The intracrystalline diffusion coefficients are found to be in the order of 10−11 cm2/s and the activation energy for diffusion is 4.0 kcal/g-mole. A simple bipore distribution model for transient diffusion in macropores and micropores is presented. It agrees well with the experimental data and quantitatively predicts the macropore diffusion coefficients. The flow in the macropores is found to be in the Knudsen flow regime.

In connection with improving the retention of solid fission products in gas-cooled high-temperature reactor fuels, the vaporization of Ba from UO 2 model nuclear fuel particles with and without a pyrocarbon coating was studied by high-temperature mass spectrometry using a Knudsen cell. The UO 2 kernels of the particles were doped with BaO. In addition, some of them contained Al 2 O 3 . Whereas BaO mainly evaporated from the surface of the kernels as BaO, only Ba could be observed over the coated particles. Moreover, the BaO vapor pressure over kernels with and without the addition of Al 2 O 3 was determined. From this it was determined that the BaO vapor pressure could be diminished by approximately two orders of magnitude by the admixture of Al 2 O 3 . Finally it was proved that the diminution of the BaO vapor pressure was caused by the formation of the compound BaAl 2 O 4 .

The thermodynamic properties of the system LiH were investigated by the mass spectrometric Knudsen effusion method in the “plateau region” between 700 and 873°K. The enthalpy of the reaction LiH(s. sat. with Li) = Li(l. sat. with LiH) + 12H2(g) was determined. The resulting equilibrium pressure for hydrogen in the “plateau region” defined by this temperature range is given by the equation: logp(torr=−(1·040±0·021)×104T+13·30±0·26. The average standard enthalpy, and free energy of formation of LiH are: ΔH0298−21·8±0·5kcal/mole ΔH0298−16·77±0·5kcal/mole.

A method has been outlined for the calculation of the pressure gradient that can exist within the reacted shell when a spherical pellet reacts with a gas and undergoes a transport controlled topochemical reaction. It is known that pressure gradients can arise because of Knudsen flow existing in the reacted shell with small pores and the reactant gas having a different diffusivity than that of the product gas. The phenomena can be represented by a boundary value problem involving a set of partial differential equations with a moving boundary, incorporating time and positional dependence of diffusivities of the reactant and product gases. In the present work, the resulting equations have been solved numerically. A study has been made of the influence of the relevant parameters like total and Knudsen diffusivity ratios of the reactant and product gases, the porosity to tortuosity ratio of the reacted shell, the Biot modulus, the equilibrium constant of the reaction and the viscous flow parameter on the pressure build up inside the reacted shell.

An experimental study of the L cathode is presented, including the chemistry of carbonate decomposition and barium generation, the origin of BaO in the evaporant, the barium transport mechanism through the porous plug, and the factors determining cathode life. Carbonate decomposition is accompanied in low porosity cathodes by the deleterious reaction BaCO3+13W=13Ba3WO6+CO. Barium is generated in the cavity at an equilibrium pressure by the reaction 2BaO+13W=13Ba3WO6+Ba and is transported continuously through the porous tungsten predominantly by Knudsen flow. During transport the barium acquires oxygen from the tungsten, producing in the evaporant a large BaO content which helps to activate the surface. Termination of life coincides with completion of the BaO–W reaction and onset of the subsequent reaction 23Ba3WO6+13W=BaWO4+Ba, which is accompanied by release of a poisoning agent. Material decrease in evaporation rate and a corresponding increase in cathode life may be gained by addition of SrCO3.

Chambre has shown that the diffusion and reaction in a catalyst whose relevant dimensions are much smaller than the molecular mean free path are determined by the Clausing–DeMarcus integral equation for internal free‐molecule flow. A rigorous upper bound on the reaction rate for the irreversible reaction A → B occurring on the internal surfaces of such a catalyst is formulated from a variational inequality due to Kourganoff and DeMarcus. The bounds are evaluated for two pore models, a bed of randomly over‐lapping solid spheres and a right circular cylinder.

The rate of iodine permeation through graphite has been studied and the following results were obtained:(1) The process of iodine permeation through graphite has been found to consist mainly of a simple gas flow through the pore volumes, just as in the case of inert gases. The chemical interaction between iodine and graphite has been observed to be negligibly small.(2) At tempeatures ranging from 90 to 160°C, and under a corresponding pressure of iodine vapor below 400 mmHg the rate of iodine permeation has been observed to be almost linearly proportional to the pressure of iodine. It has been concluded that the Knudsen flow was the predominant element of the total flow.(3) The ratio of the flow rates for air and iodine, which were interpolated to the value under the same conditions, has been calculated to be 2.68∼2.85, close to the value 2.96, namely (MI2/Mair)1⁄2, as was expected from the Knudsen flow model.(4) The rate of iodine permeation has been observed to decrease in the presence of argon gas, eve...

Knudsen limiting law in free molecular gaseous flow in various capillaries with temperature gradient

Flow and self-diffusion of xenon through Morgan EY9-166 graphite has been studied in the pressure range 10–400 torr, by a tracer technique using xenon—133. This pressure range covers the transition region from viscous to Knudsen flow. The permeability coefficient K and the effective diffusion coefficient D eff differ markedly at high pressure but tend to the same value at low pressure. The precision of the low pressure results is not sufficient to determine if there is a significant difference between K and D eff in the Knudsen region.

The evaporation rate of barium from a sintered nickel cathode and the diffusion rate of barium through it have been measured using 140Ba and tracer techniques. Confirmation of the evaporation rates thus determined have been obtained by comparison with measurements made by a method due to Becker. The activation energy of evaporation is 2.2 to 2.5 eV. Two diffusion processes operate, one predominant in the range 875 to 1020° C and one below 875° C. The activation energies are 2.5 and 0.5 eV respectively. The mechanism of diffusion at the higher temperatures appears to be Knudsen flow following evaporation from the inner surfaces, and that for the lower temperatures probably by surface diffusion.

An apparatus for measuring the leak rates and angular distributions of the molecular flux from multichannel sources was constructed. Four types of beam sources were tested: A single capillary, a crinkly foil stack, an electron‐beam milled quartz membrane, and two sources constructed by fiber optics techniques. The leak rates of the sources were compared to the predictions of Knudsen flow. The angular distributions were characterized by a ``peaking factor,'' defined as the ratio of the center‐line beam intensity from the source to that from a cosine emitter of the same total flow rate. The measured peaking factors agreed with the theoretical predictions of free molecule flow at low source pressures and approached the limit for isentropic flow at high source pressures.

A theory of gas flow in porous media is presented. The flow regime includes Knudsen flow, slip flow, and Poiseuille flow. The basic model is developed from a solution for flow in capillary tubes of any cross-sectional area. Analysis of several flow studies on natural rocks exhibiting different pore size distributions and variations in pore geometry are presented.

Experimental investigation of the flow rates of normal paraffins in porous Vycor glass shows that there are deviations from the viscosity dependence required by Poiseuille's law. A discussion of the application of capillary models to describe flow in porous media in terms of the measured porosity and surface‐to‐volume ratio points out that such models are not generally applicable, though they give useful results for some purposes. An estimate of the permeability predicted by Poiseuille's law is made by an empirical method which uses gas flow measurements in the Knudsen flow region. The equations of slip flow as derived for gases do not explain the experimental deviations from Poiseuille flow. The concept of a slipping adsorbed layer of molecular thickness at the wall of a capillary is combined with the usual Poiseuille treatment for the interior to give a result which is compatible with experiment.

Emission and evaporation characteristics of a porous tungsten cathode impregnated with the composition 5BaO·2Al2O3 are presented and are interpreted in terms of the cathode mechanism. Barium necessary for activation is generated by the reaction, 23 Ba3Al2O6+13 W=13 BaWO4+23 BaAl2O4+Ba, and is transported through partially clogged pores, the length of which increases with time, predominantly via Knudsen flow. During transport, oxygen is acquired from the tungsten, leading to a substantial content of BaO in the evaporant. The BaAl2O4 component of the impregnant is inert. Emission is substantially lower than that of an L cathode, presumably because of release of a poisoning agent accompanying the activator.

As part of a general study of Knudsen flow in porous media, three special cases have been analyzed using Monte Carlo simulation. Steady flow through cylindrical tubes has been studied, the results indicating the range of validity of the analytic short and long tube formulas. Transient flow in tubes with adsorption on the walls has been analyzed. The results indicate that the diffusion equation adequately describes the flow, provided ( L / r 0 ) ⩾ 50. The response of short tubes, ( L / r 0 ) ∼ 1, to a point source pulse illustrates special characteristics which might be useful for an experimental determination of wall adsorption times. Lastly, the flow in a converging-diverging tube has been studied, and the results indicate that significant reductions in the flow rate can occur for channels having the same average diameter but varying degrees of curvature in the direction of flow.

Reciprocal variational principles are used to formulate upper and lower bounds on the low‐pressure (Knudsen) flow rate of a gas through a channel of arbitrary geometry. The upper bound is equivalent to one obtained earlier by DeMarcus, but we believe the lower bound to be new. Explicit calculations are given for a short parallel‐plate channel. The variational principles discussed here may be applied to a wide range of problems involving linear inhomogeneous integral equations.

Computer simulation of real experiment by Monte Carlo techniques has been used to study the behavior of particulate fluxes in Knudsen cell orifices. Two types of interaction with the interior and exterior surfaces of the cell lid and with the orifice wall have been predicted to cause deviations from Knudsen flow. The first is concerned with low-angle specular reflection in cylindrical orifices. The second perturbation results when a particle, upon striking a surface, is momentarily adsorbed and migrates to another location before being reemitted. Effects arising from these two types of perturbations have been analyzed as a function of the length-to-radius ratio of the orifice. Precise steady-state values were obtained for transmission coefficients, flux gradients on the surface, and spatial distributions of effusate.

The transport equation is discussed for neutron density in a non- multiplying medium assuming the initial neutron density distribution is known. The characteristics of both the medium and the neutron sources are considered to be a function of time. The existence and the uniqueness of the initial problem were proved and some of the earlier results obtained by the author were generalized. The behavior is briefly discussed of Knudsen's gas in a thermal bath. (auth)

A theoretical model has been developed for gas flow through long square tubes. The continuum differential equation is solved with noncontinuum slip boundary conditions and the “self-diffusion” or normal molecular transport effect is obtained by numerical integration. Specific flow rates as predicted by this theoretical model are compared with experimental data which were obtained using a 0.0985-in-square tube with argon as the test gas. In addition, a comparison is made using a “hydraulic radius” in the equation which Weber developed for rarefied gas flow through cylindrical tubes. Good agreement between theory and experiment give a high confidence level to the theoretical model.

A numerical technique has been developed to study the behavior of the flow conductance through a cylindrical channel for various types of rarefied particles. The present method has the characteristics of being accurate and more efficient than the conventional Monte Carlo. In comparison with Clausing and DeMarcus's approaches of solving integral equations, the method is superior by being both versatile and flexible. The channel obstruction effects are characterized by a dimensionless parameter K which is computed in TUBNOF code. Some of the effects investigated are the specular reflection, adsorption, and absorption. The finite molecular mean free path effect on the rarefied particle flow is also considered. The technique can be very useful in studies involving sublimation, molecular beams, cold gas jets, and radiation streaming.