UNIVERSITY OF MINNESOTA DULUTH
DEPARTMENT OF CHEMICAL ENGINEERING
ChE 3211-4211
ULTRAFILTRATION
OBJECTIVE
The objective of this experiment is to determine the affects of pressure and flow rate on the
rejection (or recovery) of solute in a spiral wound ultrafiltration (UF) membrane separator.
INTRODUCTION
Ultrafiltration1 (UF) is a pressure-modified, convective process that uses semi-permeable
membranes to separate species by molecular size and shape. It separates solvents from solutes of
various sizes, independent of solute molecular size. UF is far gentler to the solutes processes than nonmembrane processes. It does not require a phase change which often denatures labile species and can
be performed at room temperatures.
Figure 1. Cross section of an anisotropic UF
membrane. UF “skin” is invisibly thin at the
very top. Open Cell structure is highly
permeable. Electron mcirograph (650X).
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Rreview of Ultrafiltration and figures are taken in part from the Amincon Membrane
Filtration and Chromatogratphy Catalog.
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UF membranes generally have two distinct layers: A thin (0.1 - 1.5 µm), dense skin with a pore
diameter of 10-400 D and an open substructure of progressively larger voids, largely open to the
permeate side of the UF (Figs 1,2). Any species capable of passing through the pores of the skin
(whose size is controlled in manufacture) can therefore freely pass through the membrane.
Retention (or rejection) by an UF membrane relates to the solute quantity allowed to pass or held
back. At any point in the process, the rejection of the membrane is expressed by:
R = 1 − Cp Cr
(1)
where R is the rejection coefficient, Cp is the solute concentration in the solution going through the
membrane (permeate), and Cr is the solute concentration upstream of the membrane (retentate).
Figure 2. Anisotropic UF
The average rejection of a membrane is expressed by:
R=
ln ( Cf Co )
ln ( Vo Vf )
(2)
where Cf is the final solute concentration in a sample, Co is the initial solute concentration
in a sample, Vo is the initial process volume, and Vf is the final process volume.
When a solute is totally retained by a membrane, its rejection equals 1. Concentration proceeds in
direct proportion to volume reduction, i.e., solute concentration doubles at 50% volume reduction. At
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40% rejection (R = 0.4), doubling of concentration requires 82% volume reduction. At R = 0 (for
freely permeating material), the concentration of solute in the retentate and permeate will be equal (Fig.
3).
Figure 3. Recovery of solutes with membranes of
various degrees of retention, as a function of volume
reduction.
Equation 1 assumes complete mixing of retentate, seldom accomplished (due to concentration
polarization). The apparent rejection coefficient depends on factors affecting polarization, including UF
rate and mixing.
Under pressure, solvent and solute are forced onto the membrane surface, resulting in
accumulation of rejected solute. Called concentration polarization, this eventually leads to formation of
a gel layer, or secondary membrane (Fig. 4). The flux of solvent through the membrane can be
expressed as:
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J=
( ∆P − ∆π )
(R
g
+ Rm
)
(3)
where ÄP is the transmembrane pressure (TMP) drop, Äð is the osmotic pressure difference of the
solution across the membrane, Rg is the hydraulic resistance of the gel layer, and Rm is the hydraulic
resistance of the membrane.
Figure 4. Concentration gradient during gel
polarization. CB = bulk fluid concentration. CG = gel
concentration.
Since the osmotic pressure for macrosolutes in solution is very low, the equation is
simplified to:
J=
(R
∆P
g
+ Rm
)
(4)
At moderate to high concentrations of retained solutes, the resistance of the gel layer is significantly
greater than that of the membrane and flux becomes independent of membrane permeability. Under
continuing pressure, Rg will increase as solute accumulates at the membrane/liquid interface. Greater Rg
reduces flux. Resistance will continue to grow until net transport of solute toward the membrane (due
to convection by solvent flow) equals back diffusion if solute toward the bulk solution caused by the
pressure gradient. Any further increase in TMP will cause the gel layer to thicken and flux will remained
unchanged.
When the concentration of the solute in the permeate is low, the steady state flux of solvent through
the membrane may be expressed as
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J ( C ) + D s ( dC / dy ) = 0
(5)
where Ds is the diffusivity of the solute. The solution to the equation is
(
J = K ln Cg / Cs
)
(6)
where K is the mass transfer coefficient, Cg is the concentration of the gel, Cs is the bulk concentration
of the solution. The mass transfer coefficient is a measure of the flow of solute away from the
membrane surface. It is primarily controlled by fluid flow conditions and temperature.
In spiral wound membrane cartridges (Fig. 5) a "sandwich" of membrane layers is wrapped spirally
around a permeate collection tube (Fig. 6). Layers are separated by a mesh flow spacer which
maintains retentate flow channels at 0.8 mm. It also enhances turbulence in the process stream to
reduce fouling and gel formation. The edges of the membranes are bonded so that process solution
cannot enter the channel where permeate is collected. Permeate moves spirally inside the membrane
sandwich to the central collection tube, then exits through the header assembly.
Figure 5. End-View of spiral cartridge; Amicon cartridges
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Figure 6. Spiral wound cartridge construction
All experiments are performed in semi-batch mode. The retentate is returned to the feed vessel
mounted above the peristaltic pump (Figure 7,8). The permeate is collected in a mixed vessel for
sampling. The flow rate and pressure on the retentate side of the membrane is controlled with the
peristaltic pump and the back pressure valve.
Figure 7. UF device
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Figure 8. Schematic of Amicon membrane separator.
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TABLE 1. Terminology of Ultrafiltration
Batch Process
A fixed volume of solution contained in a tank to which the concentrate is returned during
the process.
Concentration Polarization
Accumulation of rejected solute on the membrane surface. Depends on interactions of
pressure, viscosity, crossflow (tangential) velocity, fluid flow conditions, flow channel
conditions and temperatures.
Crossflow (Tangential Flow)
Solution flows across (tangential to) a membrane surface. Facilitates back diffusion of
solute from that surface into the bulk solution, counteracting concentration polarization.
Cut-off (MW Cut-off)
The molecular weight at which at least 90% of a globular solute of that MW is retained by
the membrane.
Nucleotide cut-off is the number of nucleotides in a DNA fragment (single- or doublestranded) at which 90% of the fragment is retained by the membrane.
Feed (Sample)
The starting solution (sometimes the solution remaining upstream of the membrane).
Fluid Velocity
The flow rate of solution across the membrane surface in cross (tangential) flow. Related to
hydraulic pressure drop.
Flux
The filtration rate through the membrane per unit area.
Fouling
Irreversible decline in membrane flux due to deposition and accumulation of submicron
particles and solutes on the membrane surface. Also: Crystallization and precipitation of
small solutes on the surface and in the pores of the membrane. Not to be confused with
concentration polarization.
Hydraulic Pressure Drop
In a flowing system, the pressure difference between inlet and outlet. The higher the liquid
flow through the device, the higher the pressure drop. It increases with solution viscosity
at a given fiuid velocity. Relationship between fluid flow and pressure drop is determined
empirically at various solute concentrations.
Permeate
(Filtrate, Ultrafiltrate)
The solution passing through the membrane, containing solvent and solutes not retained
by the membrane.
Plugging
Accumulation of debris in the fluid flow path, restricting or blocking flow.
Rejection
The fraction of solute held back by the membrane. Can be measured at any point in the
process or averaged over the run.
Retentate
(Reject Stream, Concentrate)
The solution containing the retained (rejected) species.
Transmembrane Pressure (TMP)
The driving force in ultrafiltration. In a stirred cell, equivalent to gas pressure. In
centrifugal devices, it is related to g-force. In a flowing system, TMP decreases as the
stream moves from inlet to outlet.
Average TM P = [(Pin + Pout) /2]1 - Ppermeate
Yield
Amount of species recovered at the end of the process as a percentage of the amount
present in the feed solution.
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REFERENCES
ChE 3230 Textbook: McCabe, et al, Unit Operations of Chemical Engineering. 5th ed.
Perry's Chemical Engineering Handbook: 6th ed.
EQUIPMENT
1. Genesys 2 UV-Vis spectrophotometer
2. 10 ml cuvettes
3. 50 mL E-flasks
4. Magnetic stirrer and stirring bar
5. 1 L beaker
CHEMICALS/MATERIALS
1. Aqueous Dextran Blue
2. Aqueous Riboflavin
3. Deionized water
SUGGESTED EXPERIMENTAL PROCEDURES
1. Perform an absorption spectra scan for the peak wavelengths of dextran blue and riboflavin
with the spectrophotometer.
2. Construct standard curves for dextran blue and riboflavin using absorption data from a uvvis spectrophotometer.
3. Determine the recovery as a function of volume reduction. Use a magnetic stirrer to mix the
permeate collected in a large container.
4. Determine the flux as a function of transmembrane pressure (TMB). Control the TMB with
the back pressure valve and flow rate.
5. Determine the flux as a function of flow rate through the membrane for a constant TMB.
SAFETY NOTES
1. Before starting the experiment, review the Material Safety Data Sheet (MSDS) on Dextran
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Blue and Riboflavin. These sheets are found in the MSDS notebook located in the
laboratory.
2. Personal protective equipment shall include safety glasses. Disposable nitrile gloves should
be worn when handling chemical solutions.
3. Check all hoses and connections before starting the experiment. If a spill occurs, turn off the
pumps (if possible without injury) and immediately get in touch with the Laboratory Services
Coordinator or faculty member.
WASTE DISPOSAL PROCEDURES
There is very little waste generated from this experiment. The aqueous solution of dextran blue
and riboflavin should be stored in the original container for reuse. Mix the permeate back into the feed
stock. Collect all waste chemical solutions in containers marked ULTRAFILTRATION WASTE.
Clean the membrane by flushing with clean DI water. Prepare the membrane for storage by running a
dilute alcohol solution through the cartridge, leaving the solution in the system.
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Department of Chemical Engineering
Stockroom Checkout slip
Ultrafiltration
ChE 4211
Name:
Group No.:
Date:
(print name)
Lab 2 Tuesday Thursday
Lab No.: Lab 1 Tuesday Thursday
(circle one)
Equipment
Out
In
Equipment
2 magnetic stirbars
7 - 10 mm cuvettes
6 - 50 mL E-flasks
1 - 1 liter beaker
4 - 10 mL vol flasks
Pasteur pipets
1 - 5 mL transfer pipet
Pipet bulb
2 - 100 mL beakers
1 - 100 mL grad cylinder
Stopwatch
Name:
(Signature)
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Out
In
APPENDIX A
BASICS OF UV/VIS SPECTROSCOPY
The electromagnetic spectrum extends from the high energy, short wavelength cosmic rays,
through ultra-violet light (UV), visible light, to low energy radio waves. Energy and wavelength are
inversely related:
E = hc / λ
(7)
where h is Planck's constant, c is the speed of light and ë is wavelength. Thus, shorter wavelengths
correspond to higher energy radiation, and longer wavelengths correspond to low energy radiation.
Atoms or molecules absorb electromagnetic radiation through electronic transitions between
different energy levels. There are a variety of possible transitions resulting from molecular vibrations
and rotations that affect the absorption spectra. The result is a broad absorption band (Fig. 9).
Figure 9. Typical absorption spectrum.
Beer's law is the starting point for quantifying absorption spectra. According to Beer's law,
absorption is a linear function of concentration:
A = εbC
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(8)
where A is absorbance, å is the molar absorptivity (determined from calibration), b is the path length of
a beam of light through a sample (usually the width of the sample cell), and C is the molar concentration
of the sample.
Absorption spectra are additive. The effects of the solvent are eliminated by subtracting the
absorbance of the solvent from the solution absorption spectra. This is usually done by using pure
solvent in a "blank" cell to zero the spectrophotometer.
Deviations from Beer's law may be caused by solute-solvent interaction (e.g., hydrogen bonding or
chemical reaction), high solute concentrations, pH, etc. In this case, it may be necessary to use a
non-linear calibration curve.
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