Schneider and Smith have measured the diffusivity of propane–helium mixtures in silica gel with a pore diameter of 2.2 nm. While helium is completely inert, propane is adsorbed at the silica surface. In this case, the overall transport of propane occurs as a result of two mechanisms in parallel: diffusion in the pores and diffusion along the pore surface. The overall diffusivity of propane (A) is given by:

where  is the diffusivity in the pores,  is the surface diffusivity, and Kc is an equilibrium constant describing the ad-sorption of propane. Based on the data in Schneider and Smith, at 50°C and 1 atm absolute pressure,  = 0.0106 cm2/s and Kc = 1,040:

(a) Estimate the pore diffusivity  at this temperature and pressure. Note that the pores are small enough that Knudsen diffusion should be considered.

(b) From your result in (a)
estimate the surface diffusivity  and the fractional contribution ofsurface diffusion to the overall transport.

Transcribed Image Text:

DA, D A,pore + KD A,s