Page 351 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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286 Membranes, Synthetic, Applications

the first power of the shear rate at the membrane surface Combined surface modification and management of fluid
2
and the square of the particle size, viz., D S = 0.03d γ o . dynamics at the membrane surface are effective tools for
p
For example, the shear-induced diffusion coefficient for fouling avoidance.
a1-µm diameter particle at a shear rate of 1000 sec −1
2
−7
is 3 × 10 cm /sec—more than two orders of magnitude
2. Sorption-Diffusion Separation Mechanisms
higher than for simple Brownian diffusion of such a par-
ticle in water at ambient temperature (Belfort, Davis, and Asthesizedifferencebetweenpenetrantsdecreases,mole-
Zydney, 1994). Under such conditions, the steady state cular sorption and diffusion phenomena control their rel-
permeation flux is expected to be proportional to the shear ative permeation rates across the ideal rate-limiting layer
rate and to increase with particle size, consistent with ac- in Fig. 2. As noted earlier, so-called nano porous me-
˚
tual data. Shear-induced diffusion is a factor for parti- dia (e.g., pores ∼1–2 nanometers or 10–20 A diame-
cles in the range of 0.5–30 µm, which comprises much ter) are usually felt to exist at this limit. Dialysis, elec-
of the practically important size range for microfiltration trodialysis, and nanofiltration processes operate in this
(Belfort, Davis, and Zydney, 1994). complex region to perform a selective sorting of electro-
The so-called “inertial lift” phenomenon is another lytes and other small molecules under mild concentration
factor opposing membrane fouling for microfiltration or electrical driving forces. Recent reviews of membrane-
(Belfort, Davis, and Zydney, 1994). If the conditions are related aspects of electrodialysis and hemodialysis are
such that the inertial lift velocity is sufficient to offset availablefortheinterestedreader(Baker,Cussler,Eykamp
the opposing permeate velocity, then the particles are et al., 1991; Nakao, 1994). The greatest difficulty and am-
not expected to be deposited on the membrane. Inertial biguity in defining pore sizes occur as pores approach mi-
˚
lift arises from nonlinear interaction of a particle with cromolecular dimensions on the order of 5–10 A and less.
the surrounding flow field under conditions where the Low salt rejection RO membranes (e.g., R < 0.5 for
Reynolds number based on the particle size is large NaCl) are sometimes classified as “nanoporous” and al-
enough to cause the nonlinear inertial terms in the low retention of sugars and large molecules while perme-
Navier–Stokes equations to be significant (Belfort, Davis, ating small electrolytes. In this case, a hindered transport
and Zydney, 1994). The inertial lift increases with the description of the process would be appropriate with the
cube of the particle size and the square of the tangential water and nonrejected electrolytes being treated as a single
shear rate. “fluid” and the rejected sugar considered the solute.
Besides the above subtle effects, simple crossflow- Good quality RO membranes can reject >95–99% of
induced drag of the deposited cake toward the filter exit the NaCl from aqueous feed streams (Baker, Cussler,
can also help prevent excessive cake accumulation. The Eykamp et al., 1991; Scott, 1981). The morphologies of
tangential drag force can be estimated, but the rheology these membranes are typically asymmetric with a thin
of the cake may be complex, so prediction of this an- highly selective polymer layer on top of an open sup-
tifouling force is difficult. Nevertheless, maximizing these port structure. Two rather different approaches have been
velocities is useful, since all the above fluid dynamic ef- used to describe the transport processes in such mem-
fects help prevent fouling under high crossflow conditions. branes: the solution-diffusion (Merten, 1966) and sur-
Such antifouling measures come as an expense of me- face force capillary flow model (Matsuura and Sourirajan,
chanical energy input in the form of pump work, and 1981). In the solution-diffusion model, the solute moves
hence operational costs for the system. Ongoing work within the essentially homogeneously solvent swollen
seeks to optimize the use of such mechanical energy in- polymer matrix. The solute has a mobility that is de-
puts to reduce solute accumulation. Unsteady and sec- pendent upon the free volume of the solvent, solute, and
ondary flows can also be used to help prevent bound- polymer. In the capillary pore diffusion model, it is as-
ary layers stabilization even at relatively low Reynolds sumed that separation occurs due to surface and fluid
numbers. Taylor and Dean vortex flows, rough channels, transport phenomena within an actual nanopore. The pore
flow reversals, rotating flows, torsional oscillating flows, surface is seen as promoting preferential sorption of the
and even internally moving wipers have been used in ex- solvent and repulsion of the solutes. The model envisions
treme cases with pastes, pulps, foods, pulp, and other a more or less pure solvent layer on the pore walls that
difficult to process feeds (Belfort, Davis, and Zydney, is forced through the membrane capillary pores under
1994). pressure.
In addition to fluid dynamics, surface modification of For truly high rejection reverse osmosis membranes,
the membrane can reduce the attractive forces or even the “solution-diffusion” description of this process is
create repulsive ones between potential fouling solutes the most popular and probably the most realistic. In this
and the membrane (Belfort, Davis, and Zydney, 1994). case, the high osmotic pressure difference between the