PLENARY ACCOUNT
Concentration Polarization with Membrane Ultrafiltration Mark C. Porter Downloaded via UNIV OF NEW ENGLAND on July 12, 2018 at 15:26:40 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Arrdcon Corp., Lexington, MA 02173
^Vlthough ultrafiltration Mask 0. Porter ager of Amicon’s
is ManIndustrial
Separations Department ivith responsibility for applications research, development, and production of large-scale membrane process equipment. He has authored over 20 papers concerned ivith the theory and industrial application of ultrafiltration. Dr. Porter has been invited to give numerous seminars and short courses on ultrafiltration and related membrane processes, the most notable of which are the annual courses on industrial membrane techin collaboration with Sidney Loeb and nology given sponsored by the Center for Professional Advancement. Before joining Amicon in 1969, he was a senior research engineer and group leader at AVCO’s Scientific Systems Division. Dr. Porter earned BS, MS, and ScD degrees in chemical engineering at MIT.
234
Ind. Eng. Chem. Prod. Res. Develop., Vof. 11, No. 3, 1972
was only a laboratory curiosity prior to the sixties, it has now assumed prominence as a practical industrial process for the concentration, purification, or dewatering of macromolecular and colloidal species in solution. The rapid development of this process was made possible by the advent of anisotropic, high-flux membranes
(23) capable of distinguishing among molecular and colloidal species in the 10 A to 10 n size range such as those shown in
Table I. The high flux and excellent fouling resistance of the DIAFLO membranes (all noncellulosic) are largely attributed to the anisotropic membrane structure seen in Figure 1. The graded pore structure in such a membrane results in little resistance to flow and virtually no entrapment of solutes within the pore network. However, the development of anisotropic membranes is only half the battle. The high-flux characteristics of these membranes results in rapid convection of retained solutes to the membrane surface leading to the well-known phenomena of concentration polarization (23) schematically portrayed in Figure 2. This accumulation of solute at the membrane interface can severely limit the flux, leading to an apparent fouling of the membrane which some workers have interpreted as pore blockage. That this is not the case is demonstrated by the easy restoration of the initial flux simply by washing the surface of the membrane. (Back flushing is not required nor desirable.) In reverse osmosis, where the solutes retained can have significant osmotic pressures, concentration polarization can result in osmotic pressures considerably higher than those represented by the bulk stream concentration (38). Higher the osmotic pressure and pressures are required to overcome produce reasonable flux values (Figure 3). For ultrafiltration, the macromolecular solutes and colloidal species usually have insignificant osmotic pressures. In this case, the concentration at the membrane surface can rise to the point of incipient gel precipitation, forming a dynamic secondary membrane on top of the primary structure (Figure 4). This secondary membrane can offer the major resistance to flow. In a stagnant dead-ended system, the gel layer will grow in thickness until the pressure-activated convective transport of solute with solvent toward the membrane surface just equals the concentration gradient-activated diffusive transport away from the surface. Thus, the flux in stagnant dead-
Unusually high ultrafiltrate flux values have been observed by use of thin-channel ultrafiltration in the dewatering and purification of colloidal suspensions. Polymer latices, paints, metal oxides, starch, and even cellular suspensions have all exhibited higher flux values than would be predicted by the now recognized gel-polarization model. Theoretical reasons for these anomalies are discussed in conjunction with experimental data obtained with thin-channel devices utilizing anisotropic noncellulosic membranes.
ended systems is often so small as to be virtually nonexistent unless the bulk stream concentration is extremely low. Furthermore, by the very nature of the process, increased pressures will not help since the gel layer only grows thicker to offer more resistance to the increased driving force. Therefore, the second major hurdle to be overcome in the development of a practical industrial unit operation is con-
centration polarization. Various fluid management techniques have been applied to increase the back-diffusive transport of solutes away from the membrane surface. In laboratory devices, magnetically driven stirred cells have proved simple and effective. Figure 5 shows stirred cell flux vs. transmembrane pressure for various concentrations of protein and stirrer speeds. Note that the higher bulk concentrations and lower stirrer speeds lead to lower flux values because of lower mass-transfer rates from the membrane back into the bulk solution. In addition, there is a threshold transmembrane pressure above which no further increases in flux are achieved (other than transient increases which disappear quickly). The stirred cell data of Figure 6 demonstrate another consequence of the limiting flow resistance of the gel layerflux is independent of membrane permeability. Three membranes of widely differing permeabilities show virtually the same flux when operated above the threshold transmembrane pressure. For industrial plants, the more convenient but equally effective fluid management technique of simply flowing fluids past the membrane surface (usually in turbulent flow) has been demonstrated in flat-plate and open-tube designs (Figure 7). We have developed a more efficient fluid management technique (in terms of flux per unit horsepower) referred to in the literature (3, 4, 7, 15, 27-30, 33, 34) as thin-channel ultrafiltration. It consists of flowing the process stream channels (10-30 mils) at high velocities through narrow (5-25 fps) —schematically shown in Figure 8. The resulting hydrodynamic shear at the membrane surface controls the concentration polarization such that flux values are typically 2-10 times higher than those obtained with more conventional techniques. Plate and frame equipment based on spiral-flow thin channels (Figure 8) is shown in Figures 9 and 10. For larger industrial applications, disposable cartridges (Figure 11) based on linear thin-channel tubes (Figure 12) may be arranged in parallel or series (Figures 13-15). Gel-Polarization Model
If one assumes that the limiting resistance to flow is in the dynamically formed secondary membrane or gel layer, it is possible to calculate the transport rate of water through the membrane (flux) on the basis of the mass transfer of membrane-retained species (dissolved solutes or colloidal materials) from the membrane surface back into the bulk stream (4). This is so because the dynamic gel layer is assumed to have a fixed gel concentration (CG) but is free to vary in thickness or porosity (varying permeability or resistance to
Table
1.
Amicon Ultrafiltration Membranes and Filters Nominal moi wt cutoff
DIAFLO® UM 05 UM 2 UM 10 PM 10 PM 30 XM 50 XM 100 A XM 300 DIAPOR
Apparent
Water
pore0 diam A
flux, gsfd, at 55 psi
500 1000
10,000 10,000 30,000 50,000 100,000 300,000
DP 02 DP 045 DP 06
21
10
24 30 38 47 66 110 480
20 60 550 500 250 650 1300
2000 4500 6000
11,500 27,000
4000
flow). In such an analysis, the flux (J) will be independent of the pressure-driving force or the membrane permeability since the gel layer’s resistance to flow will adjust itself until the convective transport of retained species to the membrane surface (JC) by the solvent is just equal to the back-diffusive transport [D(dc/dx)] (Figure 16). Thus, at steady state:
JC
dc =
(1)
°dx
where
J
=
C
=
solvent flux through the membrane concentration of membrane-retained colloidal species
dc —
dx
=
solutes
or
concentration gradient
The gel-polarization model facilitates the integration of Equation 1 since the boundary conditions are specified; the gel concentration at the membrane surface is fixed at an upper limit (CG), and the bulk-stream concentration is known (CB)
J
D =
r
0
In
CG
/tfl
(2)
where 8 is the thickness of the boundary layer over which the concentration of the solute varies. Equation 2 shows that under conditions where the gelpolarization model holds (above the threshold pressure illustrated in Figure 5), the flux through the membrane is invariant with transmembrane pressure drop or permeability and is dependent only on the solute characteristics (D and CG) and the boundary layer thickness 8. Thus, fluid management techniques must be directed toward decreasing the boundary layer thickness or, put another way, toward increasing the mass-transfer coefficient K where: Ind. Eng. Chem. Prod. Res. Develop., Vol.
1
1, No. 3, 1972
235
(3)
J
=
C0
0.816
(7)
K
=
0.816
(8)
(4)
The validity of Equation 4 has been demonstrated for a large number of macromolecular solutes and colloidal species. The data of Figure 17 show the semilogarithmic variation of flux with concentration for two proteins and two colloidal suspensions. The slight tendency for these curves to be concave upward is due to variations in the channel velocity because of fluid viscosity increases during the concentration. Careful control of channel velocity invariably results in linear plots on semilog paper. Note that the gel concentration (Co), the concentration at which the flux drops to zero, is higher for colloidal suspensions (60-70%) than for protein solutions (25-45%). This is not without significance since in the case of colloidal suspensions, the gel layer would be expected to resemble a layer of closepacked spheres having 65-75% solids by volume. The slope of the J vs. In (CB) plot (i.e., the mass-transfer coefficient) is higher for colloidal suspensions than for protein solutions. More will be said about this later. The mass transfer-heat transfer analogies well-known in the chemical engineering literature make possible an evaluation of the mass-transfer coefficient K of Equation 4 (4,10,16) and provide insight into how membrane geometry and fluidflow conditions can be specified to optimize flux. Evaluation of Mass-Transfer Coefficient in Laminar Flow. The Graetz or Lev6que solutions (17, 22) for convective heat transfer in laminar flow channels, suitably modified for mass transfer, may be used to evaluate the mass-transfer coefficient where the laminar-parabolic velocity profile is assumed to be established at the channel entrance but where the concentration profile is under development dowm the full length of the channel. For all thin-channel lengths of practical interest, this solution is valid (4). Leveque’s solution gives
(d
where Q
=
w
=
the volumetric flow rate the channel width
More generally,
K
b
0.816
(9)
the fluid shear rate at the membrane surface 8 U for rectangular slits for circular tubes.
where y 6 U —r~
=
=
=
=
——
d
A review of Equations 5-9 shows that the flux (or masstransfer coefficient) may be increased by increasing the channel velocity (U or Q) or by decreasing the channel height (b). In more general terms, any fluid management technique which increases the fluid shear rate (y) at the membrane surface will increase the flux. Indeed, Equation 9 shows that in laminar flow at a fixed bulk stream concentration (CB), the flux should vary directly as the cube root of the wall shear rate per unit channel length. This has been confirmed for a large number of solutions ultrafiltered in a variety of channel geometries (Figure 18). In a few cases, a higher power dependence of flux on recirculation rate (channel flow rate) than that indicated by Equation 8 has been noted (Figure 19). When faced with anomolous data such as these, one is tempted to use correlations such as that presented by Grober et al. (18) for the special case in which velocity and concentration profiles are both developing down the full channel length. Sh
=
0.664
(10)
\°-33
Re Sc
Sc
=
or
K\nf Os
for 100 < Re
K
(5)
J
^
