Page 441 - Book Hosokawa Nanoparticle Technology Handbook

7.4 REMOVAL OF NANOPARTICLES FUNDAMENTALS
the diffusive back transport of particle. Thus, the per- × 10 3
meate flux u is given by 5
1
p = 98 kPa
⎛ C C ⎞ 4 Downward Upward
u ln ⎜ m p ⎟ (7.4.3) filtration filtration
k
1
⎝ C C p ⎠ Silica sol -3
b
(s/cm) 3 s = 5×10
BSA
where C p is the particle concentration in the permeate, s = 1×10 -3
k ( D/ ) the mass transfer coefficient, and D the dif- d /d 2
fusion coefficient.
The osmotic pressure model assumes that the devi-
ation from pure water flux occurs solely due to the 1
osmotic pressure difference across the membrane, and
thus the permeate flux u is given by
1
0
0 0.5 1.0 1.5 2.0
3
2

p {( C ) C ( )} v (cm /cm )
u = m p (7.4.4)
1
R m Figure 7.4.9
Permeate flux in dead-end upward ultrafiltration of silica
where is the osmotic pressure, which is a function of sol and BSA solution.
the concentration. Equation (7.4.4) means that the
effective driving force across the clean membrane is
p { (C ) (C )}. Replacing p { (C ) (C )} by
m
p
m
p
the hydraulic pressure at the membrane surface, p , dead-end inclined filtration, where the membrane is
m
equation (7.4.4) reduces to the cake filtration equation. inclined, can reduce the cake formation onto the
membrane in UF of nanoparticulate suspension and
7.4.3.2 Techniques for controlling membrane fouling protein solutions. In upward UF of silica sol (mean
To minimize the effects of cake buildup and concen- diameter 6.2 nm) and BSA solution, a sustained
tration polarization, membrane filtration is usually permeate flux is achieved, as shown in Fig. 7.4.9
conducted using the cross-flow geometry in which the [19, 20], because the filter cake overlying the mem-
feed flow is parallel to the membrane and perpendi- brane is exfoliated continuously under the gravita-
cular to the filtrate flow [8]. However, especially in tional force acting on the particles comprising the
MF the energy requirements associated with pumping filter cake.
the feed (plus any recirculation flow) along the mem-
brane surface are typically very high. Thus, there have 7.4.3.3 Hybrid operation with membrane filtration
been some innovations in recent years with cakeless Another approach for enhancing the permeate flux is
filtration. to employ external force fields. Electrofiltration, in
The rotating disk module in which the membrane which an applied electric field is used to drive
disk is stationary is suited for large-scale operation [9]. charged particles away from the membrane surface,
It is possible to enhance the permeate flux by using the has been developed. In electrofiltration, the accumu-
vibrating modules [10, 11]. In the rotating cylinder lation of the particles on the membrane surface is lim-
device with the membrane on the inner rotating cylin- ited by the imposed electrophoretic force. In addition,
der, counter-rotating Taylor vortices within the annular the permeate flux through the filter cake is dramati-
gap are available [12, 13]. Dean vortices that twist and cally enhanced due to electroosmosis as a secondary
spiral in the direction of flow inside a highly curved electrokinetic phenomenon. This method can be
channel, similar to vortices in rotary modules can applied to a broad combination ranging from MF of
result in enhanced flux [14]. These vortices, or flow particulate suspension such as bentonite [21] to UF of
instabilities, induce turbulence into the system. protein solution. Fig. 7.4.10 shows the reciprocal per-
Periodic removal of the formed filter cake is also meate flux (d /dv) versus the permeate volume per
effective for enhancing the permeate flux. Recently, unit membrane area, v, for various values of the
several methods have been investigated: back washing strength of the DC electric field, E [22]. The steady
using the filtrate or air pressurization [15], periodic permeate flux increases noticeably with the magni-
rotation of the cylindrical membrane [16], pulsatile tude of the imposed field strength. Also, a higher
flow [17], high-frequency transmembrane pressure electric field strength causes the permeate flux to
pulsing with a frequency around 0.1–1 Hz [18]. equilibrate more rapidly.
Dead-end upward filtration, where the filtrate A method has been developed for removing
flow is in the opposite direction to gravity, and humic substances by hybrid UF combined with both

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