Knudsen diffusion regime

These descriptions apply to diffusion processes inside a pore, but on a longer time scale (interpore regime), the diffusion of solutes will be controlled by the shape of the porous network itself (which can be treated as a Knudsen diffusion regime). The description of Knudsen diffusion is beyond the scope of this paper, but we can recollect that the tortuosity of the medium, besides the pore diameter, is an important parameter that can slow down interpore diffusion and hence diffusion-controlled reactions. ... 

For a circular capillary of radius r and length I, the molar flux of component i in the Knudsen diffusion regime is given by ... 

An equimolar mixture of feed gas, di ffusing across a membrane in the Knudsen diffusion regime, will have a separation factor /Mi when the permeate side is at vacuum. 

Otherwise, the separation factor will be smaller. The narrow pore-size distributions and the small pores of ceramic and glass membranes allow separation due to Knudsen diffusion (for the appropriate pressure range) by preferential diffusion of the lighter component through the membrane. In composite membranes, the thin permselective layer can be in the Knudsen diffusion regime and thus be responsible for all the separation. The support layers, with their larger-diameter pores, are usually in the viscous-flow regime. 

Separation by Knudsen diffusion has some limitations because only the lighter component can be preferentially removed. The best separation in the Knudsen diffusion regime is thus obtained for H2. When the molecular weight difference between components to be separated is small, an economical separation probably cannot be obtained by Knudsen diffusion. 

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

However, the specific features of the TAP system are demonstrated in pulse-response experiments under vacuum conditions in the Knudsen-diffusion regime, in which the diffusion process is well defined. This means that—unlike the molecular diffusion coefficient—the Knudsen diffusion coefficient does not depend on the composition of the gas mixture. 

When the mean free path of the components is much larger than the pore dimensions, the momentum transfer mainly results from collisions with the pore walls. This is the Knudsen diffusion regime, encountered at pressures below 5 bar and with pore sizes between 3 and 200 nm. The flux of i is then written as ... 

As a first approach to calculate the combined bulk and Knudsen diffusive flux using a Fickian flux formulation, the Bosanquet formula [11] has been suggested in literature [11,70,151]. In this approach, the Fick form formulation uses a diffusivity computed as the reciprocal additivity of the diffusion coefficients in the ordinary and Knudsen diffusion regimes. 

This type of diffusion is known as Knudsen diffusion. In the Knudsen diffusion regime, the equation for the flux is... 

---