By Hassler J.W.
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Additional info for Activated Carbon
10. Shrinking Core Behavior The “shrinking core” model has been widely used to account for diffusion and reaction in solid-gas systems (such as combustion of coal) as well as for adsorption in macroporous adsorbents when the equilibrium isotherm is highly favorable. Under these conditions all adsorption occurs at the adsorption front and the adsorbed phase concentration profile assumes the form of a shockwave penetrating into the adsorbent at a rate that depends on both the adsorbent capacity and the pore diffusivity.
Vϕ )= ∇ • (D∇ρα . ) ∂t (18) where D is the mutual diffusion coefficient. The reference frame is given by (19) The result is the appropriate diffusion equation and its boundary and initial conditions. The total mass is any sample is M For a system (a film of thickness L, the limiting long time solution for the mass pick-up yields a straight line solution with time, as below: (21) At short times, the solution is a function of the square root of time: ADap ρα 2 dM =− dt 2 Dap t π (22) For virtually all polymer systems, the diffusion coefficient is a very strong function of solute concentration.
25) flux (relative to fixed frame of reference surface rate coefficient (Eq. 26) file length; parameter defined in Eq. 28 dimensionality of lattice flux (relative to center of mass of diffusing species) partial pressure adsorbed phase concentration saturation limit of q crystal radius gas constant; particle radius time absolute temperature u species velocities (Eq. 11) x z l mole fraction distance coordinate half-thickness of slab D D Greek letters E T P W O Hp U parameter in Eq. 25 fractional loading (q/qs) chemical potential time interval (Eq.
Activated Carbon by Hassler J.W.