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396 K.C. Ng et al.
but modified with an exponent index n, where n is an integer 2. They commented that the
parabolic profile of Liaw et al. (11) is one of the many possible local solutions. An article of
Sircar and Hufton (13) highlighted that as long as the local concentration profile of the
adsorbent is continuous, a constant relationship exits between ksav and the diffusion time,
Ds/R 2 , which is given by Eq. (3). This relationship was originally derived by Glueckauf (10),
where F0 is 15 for spherical shapes of adsorbents. El-Sharkawy et al. (14, 15) measured the
adsorption rate of ethanol onto activated carbon fiber (ACF) of type A-20 using a thermogravimetric
analyzer (TGA) unit over a wide range of adsorption temperatures, typically from
27 to 60 C, a region of operation which is useful for the processes of adsorption chillers. They
have proposed a novel local concentration profile, w(t,r) ¼ a0 þ a2r 2þk , which is effective in
attributing the higher ethanol uptake due to the presence of meso- and micropores within the
ACFs (see Fig. 9.2). The value of k in the local concentration profile has been independently
validated using the measured data and it is found to be about 1.5 when F0 is 11. The value of k
is also valid for the wide range of adsorption temperatures and it is much higher than the
conventional value of 8. By combining the values of k and the diffusion time constant, Ds/R 2 ,
the LDF model is proposed to be of the form
dw
dt
ð8 þ 3kÞDs
¼
R2 ðW wÞ; (5Þ
p
which is valid for a cylindrical adsorbent. The numerical values of k and D s/R 2 are valid over
a wide range of adsorption temperatures (27–60 C) as well as the adsorbent surfaces with
Vapor Phase
w = W
w(t) =
1 R
v ∫ w (r,t)dv
o 0
w(r,t)
dr
∂w
∂r
Adsorbent phase
= 0
r
R
w(r,t) = a o + a 2 r 2+k
Uniform micro-pores
Meso-pores
Surface diffusion
w(r,t) = a o + a 2 r 2
Fig. 9.2. Local concentration profiles for uniformly distributed micro- and mesopores structures in
ACF (14).