Page 350 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN009K-419 July 19, 2001 20:57

Membranes, Synthetic, Applications 285

1950;Bessarabov,1999).Withadequatecrossflowpastthe TABLE III Relationship between Molecular Weight
membrane face, the boundary layer thickness is reduced and Hydrodynamic Diameter Estimated Using In-
◦
trinsic Viscosity Measurements at 25 C for Essen-
greatly, so for dilute solutions j v approaches (n A ˆv A ) o , the
tially Monodisperse PEGs
puresolventflux.Increasingfeedpressureincreases j v and

C , which can cause the solute to form a precipitated cake PEG sample M w (g/mole) d s ( ˚ A)
B

or gel at the membrane face. The C value tends to be a
B 400 376 12.2
constantcharacteristicoftheprecipitatedlayer,andfurther
1,000 1,025 19.6
pressure increases produce no increase in flux. Excessive
1,500 1,569 24.2
feed pressures may not only fail to provide additional flux,
2,000 2,052 27.8
but also may complicate subsequent cleaning due to seri-
3,000 2,971 33.8
ous occlusion of pores, so operating at pressures leading
4,000 3,872 38.8
to limiting flux behavior is generally not recommended.
6,000 6,375 51.0
Qualitatively similar polarization responses are appar-
12,000 12,000 81.0
ent for both microfiltration and ultrafiltration processes,
35,000 35,000 133.4
but for microfiltration, additional more complex can occur
as is discussed below (Belfort, Davis, and Zydney, 1994;
Segre and Silberberg, 1962). The “rejection” parameter
mentioned earlier can be written as either an “observed,” dynamical effects. Early modules maximized membrane
R o , or an “intrinsic,” R i , value: packing density without much attention to fluid dynamics,
and suboptimal performance resulted (Belfort, Davis, and
C B n B
R o = 1 − bulk = 1 − bulk (8a) Zydney, 1994). With suspensions, shell-fed hollow fiber
C C
B B j v and even spiral wound modules have a tendency to clog,
and while flat sheet and tubular designs show the least ten-
dency to clog under crossflow filtration. Turbulent cross-
C B n B
R i = 1 − = 1 − . (8b) flow velocities are required to avoid serious polarization

C C j v
B B and fouling with domestic wastewaters and cell culture
The observed rejection [Eq. (8a)] is clearly the important media that tend to form compressible cakes that compli-
one for a practical separation operations, but it includes the cate operation.
confounding effects of concentration polarization. Since Early predictions of suppression of fouling were based

C bulk ≤ C , the observed rejection is less than the intrinsic only on Brownian back-diffusion of large colloids and
B B
rejection and can be determined by estimating the solute particles. These predictions failed to account for addi-
wall concentration with Eq. (7). tional factors opposing particle deposition. New phenom-
As the name implies, R i characterizes the intrinsic abil- ena were suspected when experimental data showed that
ity of the membrane to reject the solute. Molecular weight flux increased with increasing suspension particle size,
and size correlate roughly for high molecular weight so- rather than showing a greater tendency for cake deposi-
lutes, and although imprecise, it is common to characterize tion as expected. Moreover, the flux increased with shear
the intrinsic “cutoff molecular weight” of a given mem- rate to a higher power than one third, which was predicted
brane.Amembranecanbe“calibrated”bydeterminingthe for molecular diffusion-dominated boundary layers in the
molecular weight of a series of standard solutes at which traditional Leveque solution (Belfort, Davis, and Zydney,
roughly 90% rejection occurs under conditions with neg- 1994). Several factors explain this “flux paradox” for par-
ligible concentration polarization. Monodisperse solutes ticles >0.5 µm diameter, including (i) shear-induced dif-
such as polyethylene glycol (PEG) of known molecular fusion, (ii) inertial lift, and (iii) surface transport. These
weight are useful for this purpose. Table III gives typical mechanisms are described in detail in a recent review
◦
values for PEGs in water at 25 C (Segre and Silberberg, on crossflow microfiltration (Belfort, Davis, and Zydney,
1962; Miller, 1992): The effective size of a macromolecule 1994) and are only summarized here.
depends upon the quality of the solvent used, so in a non- The simple form in Eq. (7) can be maintained by repla-
aqueous solution, reevaluation of the effective size of the cing the Brownian diffusion coefficient in the expression
PEG’s would be necessary (Segre and Silberberg, 1962; k c = D eB /δ by the shear-induced hydrodynamic diffu-
Miller, 1992). sion coefficient for the particles, D S . Shear-induced hy-
In microfiltration, especially for larger particles (>1– drodynamic diffusion of particles is driven by random
20 µm typically), molecular diffusional phenomena have displacements from the streamlines in a shear flow as
little impact. In these cases, deposition on the membrane the particles interact with each other. For particle volume
surface is prevented primarily by exploiting various fluid fractions between 20 and 45%, D S has been related to