Membrane and Desalination Technologies - TCE Moodle Website

Adsorption Desalination: A Novel Method 395
Moles Adsorbed
Moles Adsorbed
Type I
0 P/Ps 1
0
Type III
P/P s
Moles Adsorbed
1
Here, Rp denotes the average radius of an adsorbent particle and F0 is a constant depending
on the adsorbent shape. The surface diffusivity Ds is expressed as
Ds ¼ Dso exp
0 P/Ps 1
Ea
RT
Type II
; (4Þ
where D so is a pre-exponential term, E a denotes activation energy, R denotes the universal gas
constant, and T stands for temperature.
In the linear-driving force (LDF) method, the key parameter is the determination of the
overall particle mass transfer coefficient. Ruthven (5) reported that both the diffusion time
constant and the overall mass transfer coefficient can be estimated by tracking the experimental
vapor-uptake behavior using the solution of a diffusion equation where the particle mass
transfer coefficient (ksap) could be determined. There exits a constant relationship between the
overall mass transfer coefficient to the particle shape (e.g., described by the radius) and local
concentration profile within the adsorbent. Liaw et al. (11) show that a parabolic concentration
of the form, w(t,r) ¼ a0 þ a2r 2 , as prescribed within the spherical particle, led to the wellknown
LDF model. Li and Yang (12) have demonstrated a general profile of the LDF model
Moles Adsorbed
Moles Adsorbed
0 P/P s
Type IV
0 P/Ps 1
Type V
Fig. 9.1. Five different Brunauer adsorption isotherms (8).
1