Knudsen chemical reactions

Pipe Lines The principal interest here will be for flow in which one hquid is dispersed in another as they flow cocurrently through a pipe (stratified flow produces too little interfacial area for use in hquid extraction or chemical reaction between liquids). Drop size of dispersed phase, if initially very fine at high concentrations, increases as the distance downstream increases, owing to coalescence [see Holland, loc. cit. Ward and Knudsen, Am. In.st. Chem. Eng. J., 13, 356 (1967)] or if initially large, decreases by breakup in regions of high shear [Sleicher, ibid., 8, 471 (1962) Chem. Eng. ScL, 20, 57 (1965)]. The maximum drop size is given by (Sleicher, loc. cit.)... 

Numerical Model for the Effect of a Spatial Temperature Gradient on Chemical Reactions in a Knudsen Gas... 

We derive a numerical model for the effect of a spatial temperature gradient on the local equilibrium of a chemical reaction in a low--density gas (Knudsen regime). The gas consists of two constituents and the chemical reaction is assumed to take place at the walls of the container. The numerical results are compared with experimental results on the equilibrium 2Na - Na2. From the comparison it follows that the chemical accommodation coefficient for a Na2 wall collision is essentially equal to 1. 

When mass transfer to the catalyst surface is fast compared to chemical reaction, the reaction rate may still be limited by the rate of diffusion in the catalyst pores. Bulk diffusion (i.e. the same process as for mass transfer to the external surface) occurs when the mean free path between molecular collisions is small compared to the pore radius. Knudsen diffusion occurs when the mean free path is large... 

In many problems of mass transfer in a solid porous medium with a large specific surface area (as with catalysts), with or without a chemical reaction, the solutes are considered to be carried only by diffusion (molecular, superficial or Knudsen diffusion), the molecular barycentric velocity being... 

Onifer, L.G. and Knudsen, J.G., 1983, Modelling chemical reaction fouling under sub-cooled body conditions - Atlanta A.I.Ch.E. Symposium Series, Vol. 89, pages 308 - 313. 

The analysis in this section focuses on the appropriate dimensionless numbers that are required to analyze convection, axial dispersion and first-order irreversible chemical reaction in a packed catalytic tubular reactor. The catalytic pellets are spherical. Hence, an analytical solution for the effectiveness factor is employed, based on first-order irreversible chemical kinetics in catalysts with spherical symmetry. It is assumed that the catalytic pores are larger than 1 p.m (i.e., > 10 A) and that the operating pressure is at least 1 atm. Under these conditions, ordinary molecular diffusion provides the dominant resistance to mass transfer within the pores because the Knudsen diffusivity,... 

The TAP reactor is very well suited for kinetic studies. At low pressure, all transport of gas-phase species is by (Knudsen) diffusion, thus ruling out any external mass transfer limitations. The diffusion as a random movement also eliminates all radial concentration gradients. Very low amounts of reactants are pulsed into the reactor, which are on the order of a few nanomoles. Thus, the amount of heat generated is very small even in the case of strongly exo- or endothermic reactions. Therefore, the reactor is operated isothermally and no heat transfer limitations occur. Concentration profiles inside the pores for transient experiments might arise even in the absence of chemical reaction. If significant diffusion of reactants and products inside the catalyst pores occurs, it will be revealed by the transient response and then needs to be addressed correctly by a modeling approach. This is often the case for microporous materials [26,27,72]. 

Gaseous media neeir a surface is perturbed by the scattering and adsorption-desorption processes, as well as the surface chemical reactions (see Figs. 1,2). This perturbation may be taken into account via a kinetic boundary condition (KBC) at z = Zt h (in the scale of the gas phase kinetic parameters the value z, can be set to zero) for the distribution function Qc- The kinetic boundsuy problem (Knudsen layer problem) for the distribution function 9c(b,r,t) is formulated in the following way... 

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