Biomedical Engineering Reference
In-Depth Information
due to variation in the structural features that affect their mass transfer rate from bulk solution
onto γ-PGA.
4.1.2. Mass Transport Mechanism
An adsorption process involves three consecutive mass transport steps such as (i) film
diffusion, (ii) intraparticle or pore diffusion and (iii) adsorption onto interior sites [70].
Among these three steps, the last step is considered negligible as it is assumed to be rapid and
hence the rate of adsorption should be controlled by either film or particle diffusion. From the
practical point of view, it is essential to determine the rate-determining step of an adsorption
process. Therefore, the kinetic data were further analyzed using a particle-controlled diffusion
expression proposed by Boyd et al. [78,79], which is given below
61
∞
∑
2
F = 1-
exp[-n Bt]
(9)
2
2
π n
n=1
B = π
2
D
i
/r
o
2
(10)
where r
o
(cm) denotes the radius of the γ-PGA particle determined by sieve analysis, D
i
(cm
2
/s) is the effective diffusion coefficient and B is the time constant. The Bt values
calculated for each value of F were plotted against time t and the plots obtained were
shown to be linear (plots not shown), but did not pass through the origin, confirming that
film diffusion or external mass transport mainly governs the uptake of cationic dyes by γ-
PGA [70]. This tendency also suggested that intraparticle resistance is negligible during
the initial period of adsorption. Assuming γ-PGA particles to be spherical in nature, the
effective diffusion coefficient (D
i
, cm
2
/s) was determined using the Eq.10 to be 1.54 x 10
-
4
and 1.55 x 10
-4
for MB and MG dye adsorption, respectively. Similar D
i
values in the
order of 10
-4
were also reported for film-diffusion-controlled adsorption of MB dye by
mango seed kernel powder [80]. It was further reported that the film diffusion controls
adsorption process in a system with poor mixing, low solute concentration, small
adsorbent size and high solute/adsorbent interaction, whereas the opposite is true for the
particle diffusion-controlled adsorption process [80]. Apparently, the small-sized γ-PGA
particles (1-150 μm) employed for dye adsorption with poor mixing (120 rpm), and the
fast dye uptake rate implicating high dye/γ-PGA interaction ascertain that the ion
exchange reaction through film diffusion is the rate-controlling process for cationic dye
adsorption by γ-PGA.
4.2. Adsorption Isotherms
Adsorption isotherms are the basic requirements for designing an adsorption system as
an isotherm expresses the relation between the liquid phase solute concentration and the
mass of solute adsorbed at constant temperature per unit mass of adsorbent. Isotherm
curves obtained at three different temperatures (301, 318 and 333 k) and at natural pH
(without adjusting pH) were characterized by an increase in dye adsorption following a
