ore industrial applications of dialysis have been developed within the last three years than in the previous hundred. The prime limitation on large scale dialysis has always been the membrane. Synthetic plastics have shifted this limit so far that many additional processes can be performed by dialysis. Separations now being used on a commercial scale are beyond the range of assumptions made in developing the theory. This does not result only in lack of king accuracysometimes material transport occurs in the opposite direction to that expected. Until recently, dialysis was limited to removal of low molecular weight solutes from colloids. Only one large scale application had been found-recovery of sodium hydroxide from viscose steep Liquor or mercerizing baths. This is performed most often with a plateand-frame dialyzer using parchmentized paper membranes, which possess little burst strength, gradualIy deteriorate in alkalime solutions, and cannot withstand chemicals such as acids. Greatly improved membranes, recently introduced in commercial quantities (2, 73), have already resulted in new applications of dialysis (77). The new membrane, described by Nalco as a vinyl type of plastic, has a high burst strength and a long useful life, even when used with strongly acid solutions. Present expectations are that the membrane will last up to two years.
M
DIALYSIS A SLE,EPER? Thc factors affecting d@usiml transport of dissoiz-ed substances thrmrgh a membrane give us a wider range of possibilities in practical dialysis than hos b a n realized, both in improving transport rates and in carrying out not too obvious separations. A complete thepry of the phenomena involved cannot be given, but it as important to be aware of the existing efects and of the possibilig of matching the membrane to the applicatron. The advent of good synthetic plastic membranes ha^ made this a definite possibili/y.
B.
n.
VROMEN
Typical dialyst separations, impossible a few years ago, are: -Recouning sulfuric acid in copper rcf;ncric. At least four industrial plants are now on stream -Recoucring mineral acidsfrom synthetic organic compounds -Treating spent stainless steel pickle liquor for rccouey of nitric and hydrojuoric acids -Purifying pharmaceuticals -Extiding useful life of a polymer by remouing low molecular Wright contaminants, both organic and.inorganic It is now necessary to re-evaluate the theoretical basis for dialyzer design. New applications have come under scrutiny where a partial separation of solutes of not too greatly different mobilities through the membrane is desirable, requiring a careful evaluation of the rate of transport of all components of the solution. Investigation of these possibilities showed that the existing theoretical treatments of dialysis (4, 8, 9) do not always explain satisfactorily the observed transport rates and separations. Until a complete quantitative treatment of dialysis becomes available, experimental data must be used in process design. However, one of the experimental techniques, long used, does not give information that can be readily used for the evaluation of industrial processes. 20
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
This technique involves a stirred cell with a dilute solution on one side of the membrane and water on the other. For many separations, reliable data can only be obtained by duplicating flow rat- and concentrations as closely as possible, in a laboratory-scale model of an industrial dialyzer. One such piece of equipment available for experimental studies is a model Hi-Sep dialyzer of Graver Water Conditioning Co. It was used to gather the data presented here (Figure 1). The experiments reported illustrate the phenomena encountered with a number of electrolytes. The results are related to theories not before applied to dialysis, but found to be highly relevant to it. As shown in the following pages, the membrane is still the all-important factor in dialysis, and is still the major limitation, even with the best membranes available today. The interaction found between membrane
Demlopmmt of impoucd mmbmncs h brought about the fdlowing i m p o w e n t s in equipment de&: --Use of M W m a h i a h of combnotion, mainly plnstics, resistant Lo the mmc cmrosivr liquors that are now heated - T h i m frmncs and goskels mnkc for easier handling and more compact equipment
-
-Operation with slighf c x c m pressure on the diffusate side ir now possible. This eliminates separatorr in the water-d@uate frames, as the mmbrarus ore pressed snugly on the separators in the l i p didyrntc frames. Pollution in thc cost of r? membrane leak is also minimiad.
PORTS FOR WATER
WATER
GASKET AND
FRAME
MEMBRANE
UQUOR FRAME WITH SEPARATOR
GASKET AND WATER FRAME
Ass(MEMBRANE OMITTED)
ssible to improve dialysis perand s o h formance by an appropriate membrane. Thus a new item is added to the list of traditional membrane requirements: high porosity suitable pore size good swelling mechanical strength chemical stability
chemical compatibility In the dialysis of acids and bases, using two of the new membranes, the dialysis process generally gave much better separations than would be predicted by present dialysis theory. In addition, =me of the conclusions were entirely unexpected : -Dialysis coefficient can be concentration dependent. Coefficients of strong acids show a very steep rise with concentration, with a decrease in water transport.
-Dialysis coefficients in mixtures of electrolytes are variable and unpredictable. In the case of an acid and a salt, the transfer of the acid will often be increased, while that of the salt is decreased. This double effect greatly assists in separating a salt from its acid. These coefficients are particularly sensitive to flow rates and concentration. In some cases, the diffusate may become more concentrated in acid than the feed liquor. -Water transport is an important and unpredictable quantity; it should be determined experimentally in all cases. In one case given below, negative water transport occurred, although the membrane possesses no demonstrable ion exchange properties, and is not usually regarded as a charged membrane. This has not been observed before. -Dialysis coefficients of several materials were found to increase with flow rates. (carinunlon mxfj q e ) VOL 5 4
NO. 6 JUNE 1 9 6 2 21
DIALYSIS-HOW
IT WORKS
For dialyzer design, composition of the liquor and two product streams must be related to the material transport and the membrane area. This is accomplished by ,using an over-all dialysis coefficient. The present methods for calculating these coefficients consider only the mechanical or “sieving” effect of membranes, and thus over simplify actual membrane separations. The lack of a complete theory for the prediction of dialysis rates makes it imperative to base dialyzer design on data from an experiment that duplicates conditions of the application rather than on predictions based on theoretical models. In all dialysis applications at least two dissolved substances are present, and each may influence the other (2). Any satisfactory treatment must consider the complexity of transport phenomena in a membrane. No quantitative method can be attempted at present. But full advantage should be taken of certain qualitative conclusionsdrawn from transport mechanisms. Dialysis Coefficients
A relation has been derived (6) for each solution component in terms of the over-all dialysis coefficient, U., of this component. Then for component x:
U, = W./AACl., ~
I
(1)
AC,,,,is the logarithmic mean concentration diffennce for x acrom the membrane., Equation 1 assumes that no volume changes take place on either side. of the membrane as a result of the process, and that mass transfer coefficientsareconstant along thedialysispath (9). The over-all dialysis coefficient can be considered as a combination of two transfer coefficients, the membrane dialysis coefficient (Urn);and the combined liquid film transfer coefficient ( U J . Over-all dialysis coefficient can be determined from the performance of an actual dialyzer. The membrane dialysis coefficient can be measured using a mrchanically stirred dialyzer. Then 1/u. = 1/u, -I-vu,
(2)
Mechanical Theory of Dialysis
For the theoretical evaluation of the three coefficients,
U,, Urn,and V I ,a treatment based on elementary assumptions has been worked out that leads to simple equations [equations 5 and 6 in the article by Lane and Riggle
I I
(9)]. Coefficients can be evaluated from knowledge of some membrane properties (swollen thickness, pore size, pore volume) and two solute properties-diffusivity [adjusted to the prevailing temperature and concentrations (7)] and molecular weight. This treatment assumes that the material transport through a membrane resembles diffusion in a free solution in every respect except the following: - O n l y that fraction of the membrane volume that is not iaken up by membrane material is available for solute transport. 22
1
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
-The irregular shape of the pores will force the diffusing material to follow a tortuous path. -In general, pore size is not very large compared to the particle size of the material dialyzed. The resulting restraining force exerted by the wall is a function of the ratio of particle diameter to average pore diameter only. Steps toward a Mer Theory DIFFUSION IN FREE SOLUTION AND THROUOH A MEMBRANE
Eucn in the sirnpljficd model, neglecting interaction behuccn membrane and solution, it is possible to describe d@uion of one dissolved substawe though a rnmbranc ody by means of kuo indcpmdml co@cimls, neither of which is usually nuailable in thc chnnical literahcrc. The diffusivity, or diffusion coefficient,of a substance links its diffusional flux through a plane with a concentration gradient perpendicular to that plane:
x is the coefficient that
(3)
The plane through which the diffusional transport takes place must be fixed by an appropriate convention. For free solutions (without membranes) there are two convenient ways to fix the reference plane : -The first system adopts a reference plane that is fixed in relati.on to the containing vessel. This plane has a constant volume of liquid on each side. The diffusion coefficient is called the mutual diffusion coeficient Dl;. -The second system uses a reference plane that separates fixed quantities of solvent. The solvent-fixed dzyusion coeficient is written 0;. -These coefficients are not identical and become increasingly different with increasing concentration of x. Using either system of reference, it is possible to describe all diffusional transport in a free binary solution by one coefficient only ( 3 ) ,because D, zz 0,”and DyY = 0 In dealing with dialysis, no freedom exists in choosing the reference plane-results can be related only to diffusion through the plane of the membrane. The membrane separates two solutions whose volumes and solvent quantities are bound to change as a result of the dialysis process, so it is obviously not justified to use either Dl; or DP in Equation 6 of Lane and Riggle ( 9 ) . I t is necessary to define a new set of membrane dzffusion coeficients 0’3 and : DY. Neither DY nor DY can be readily calculated from available values of the mutual or the solvent-fixed diffusion coefficient, except at extremely low concentrations of x. For the ideal case, some general observations ( 79) can be made on the relationship between D”and D” : -D: is smaller than D,”, and the difference will be large for high concentrations of x and low D:. -DY is larger than DJ,and this difference will become pronounced at high concentrations of x. -Exceptions are the few substances that have an extremely high mutual difiusion coefficient (3 X 105 sq. cm. per second at room temperature, or higher) where this relationship is reversed. A s a result, if two dissolved substances show a considerable difference in their dzyusion rates in free solution, they will often show an even more pronounced dzfference in dzffusion rates through a membrane, independent of the restraining force exerted by the membrane pores. OSMOTIC TRANSPORT RATE
In dialysis, the transport of solvent through a membrane is called osmotic transport. For dilute nonelectrolyte solutions, the osmotic transport rate might be expected to be in good agreement with the method of Lane and Riggle, whereas in concentrated solutions the limitations mentioned above should apply. However, when a colloid solution is contacted with the solvent through a membrane impermeable to the colloid, the osmotic transport rate exceeds by one or more orders of magnitude the rate predicted, even when the solution is dilute ( 7 7). T h i s finding should be more generally applicable: Existing theory correctly predicts a low transport rate of solute particles with a diameter comparable to the average pore diameter. A n exceptionally high osmotic transport should also be predicted.
CHEMICAL INTERACTION
Most useful dialysis membranes consist of a loose network of long chain molecules or fibers. They have a high, and often variable, degree of swelling-Le., certain sections of the long chain molecules interact strongly with the solution or with one of its components. The transport through the membrane of any solution component x and of solvent y can be written : vx = M:.C:.E, and ‘pu = M:.C?.E, (4) The driving force E is proportional to the difference in chemical potential on the two sides of the membrane; it may be considered as independent of the membrane properties. Chemical interactions influence M“ and C”. Consider the case where solute x is negatively absorbed in the membrane-Le., that at equilibrium the ratio, Cz/CF, inside the membrane is smaller than C,/C, in the surrounding solution. Only in rare cases will the mobility in the membrane M $ be larger than its mobility in the free solution. Negative absorption of component x will thus result in a flux that is smaller than the flux calculated for a chemically inert membrane. At the same time, the flux of solventy will be larger than anticipated, unless its mobility is impaired, which is not likely. In the case of positive absorption of component x, it is impossible to predict the resulting change in flux because concentration C: will increase while mobility M $ may decrease. The concentration of chemically active groups in the membrane material can often be very large, and even a relatively weak interaction can cause a large increase in Cf. The concomitant decrease in M,” may not be very considerable. The flux of component x will be larger than anticipated, while the flux of the solvent will be decreased. In the case of a strong interaction, influence on the mobility may be considerable and total net effect on the flux of component x may become small, or even negative. ELECTRICAL INTERACTION
A particular case of interaction between solution and membrane occurs when the solution contains an electrolyte, and the membrane contains fixed electric charges such as ion exchange groups. When the cation and the anion have different ionic mobilities, this rule applies : If the membrane has a net charge of the same sign as the more mobile ion, then the water transport through the membrane from the dilute to the more concentrated electrolyte solution is depressed, and water may even be transferred from the concentrated to the dilute electrolyte solution. When the net charge on the membrane has the same sign as the less mobile ion, then the osmotic water transport from the dilute to the concentrated solution is enhanced. These modified water transport rates are called anomalous osmosis. Negative osmosis was apparently observed in 1854 by Graham; anomalous osmosis was studied by Bartell (7) and by Sollner (75). The theoretical explanation has been the subject o i a lively discussion ( 7 4 ) . I t i s therefore amazing that implicafions of anomalous osmosis f o r dialysis have not been poznted out. An anomalous water transport will be accompanied by anomalous solute transport. The rule is: An anomalously small or negative water transport will coincide with a fast transport rate of the dissolved substances, whereas with an anomalously large positive water transport the opposite occurs. In an extreme case, “incongruent” electrolyte transport may occur, that is, transport of the electrolyte from its dilute to its more concentrated solution. (Continued on next page) VOL. 5 4
NO. 6
JUNE 1962
23
NEW DATA FROM DIALYSIS SEPARATIONS Apparatus ond R o e d u n
A Graver laboratory Hi-Sep dialyzer (Figure 1) was used. A 3-inch head of water CONTINUOUS DIALYZER.
I
was maintained in -the diffusate frames relative to tlie dialyzate frames in order to make the membranes press against the separators. The liquor and water were delivered to the dialyzer by adjustable diaphragm pumps. Material balances were within 3%. Dialysis coefficients were determined two to eight times at each liquor concentration. Experiments were performed at room temperature (ZOO to 27' C.). DIALYSIS CELL FOR BATCH EXPERIMENTS. Two 2-inch borosilicate glass elbows were used as half cells. This arrangement and its use were described by Mindick and Oda (73). The apparatus with the membrane in position was conditioned for 1 hour with the liquor to be dialyzed. Dialysis times were exactly 1 hour. MEMBRANES USED. The Graver Hi-Sep 70 membranes, corresponding to Nalfilm D-30 (73) used for the acids, were 0.0132 cm. thick. The No. 70 membranes used for the sodium hydroxide solutions were 0.0112 em. thick. This membrane had a relative pore volume of 67%, found by determining weight loss after drying for 8 hours at 90" C. The Graver ' Hi-Sep E-97 experimental membrane was obtained from Nalco Chemical Co. It is a highly porous membrane with cation exchange properties: Its exchange capacity is 0.23 meq. per 100 sq. cm. Absorption in Membranes
A membrane square was' steeped in an acid (or .alkaline) solution for an hour,, wiped dry with filter
E I 24
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
paper, introduced into a beaker with distilled water, and then titrated. Calculations
The over-all dialysis coefficient was calculated by Equations 1 and 2. Whenever possible, care was taken to adjust flow rates in such a way that ACbuam equaled ACmp so that the method of averaging the concentration difference had no influence on U.. For the stirred batch experiments, the membrane dialysis coefficientwas calculated by:
where W'= (in grams per minute) is the mean transport rate of solute through the membrane from the beginning to the end of the experiment, and AC',,,,is the logarithmic mean value of the concentration differences between the two half-cells at the start and end of the test. Water transport can be expressed in terms of an over-all transfer coefficient U0.,, analogous to the coefficients calculated for other solution components. In practice, it was more useful to calculate water transport as grams of water transported per gram of dissolved substance dialyzed. This ratio is called water transport number, T. It is positive when water moves from the more dilute to the concentrated solution. Efhsl of Flow Rams
Using Hi-Sep 70 membranes, the following acids were tested : nitric, hydrochloric, hydrofluoric, sulfuric, phosphoric, and chromic. All but chromic acid have over-all dialysis coefficientsthat are independent of the flow rates, provided feed concentration is constant.
1.1
0
2
f
20
I
I
I
I
I
30
40
50
60.
70
i
80
I
90
I H
J
PER CENT Figure 2. Dtfmin cocfiicicnt of NaOH imcmm slightly with incrcaring pow rates. The co@cicnt con be relded sdisfrztmiy *-
1.0
4
the relotint reconny
For instance, sulfuric acid, 3.9M, flow rate through a dialyzer was varied between 22 and 120 ml. per minute at a constant water rate of 80 ml. per minute. U. was found to be 2.26 X 10" cm. per minute with a mean deviation of 0.07 X lo-' for a set of seven measurements. An equally large variation in water flow rates does not influence the over-all dialysis coefficient. The over-all dialysis coefficient of sodium hydroxide demnds somewhat on flow rates (Figure 2).
TABLE 1.
Electrolyte
HCI "01
HWI EW
of Feed Concanhation
The strong acids show a marked increase of the over-all dialysis coefficient with increased liquor concentration (Figure 3). For the weaker acids, HF and HIPO,, the dialysis coefficient is not strongly dependent on acid concentration. Figure 4 shows the influence of concentration on U. of sodium hydroxide for two different membranes. The values plotted correspond to a recovery level of 75%.
pmkm Hi-Sep E-97 showed consistently higher dialysis
Type of
coefficients for sodium hydroxide than Hi-Sep 70 (Figure 4), but the opposite was true for sulfuric acid. For 4.5M acid:
2.4 X lo-' cm. p n min.
With Hi-Sep 70
U.
With Hi-Sep E-97
U. = 1.1 X lO-'cm.pnmin.
=
Water transport numbers for different liquor concentrations and membranes are tabulated in Table I. The membrane dialysis coefficient U, was measured for a number of cases and the combined liquid film transfer coefficient calculated by Equation 2 (Table 11).
HF
HIP08 NaOH
NaOH HYSO.
WATE R TRANSPORT NUMBERS Fad COm,. Woln Tmnrport No., Mda/Litm G./G.
Membrane, Hi-Sep 70 2.5 4.4 6.6 2.5 4.75 6.6 2.0 3.8 4.5 2.1 5.0 3.0 6.25 14
-0.25 -0.09 +0.12 +0.10 +0.14 +0.18 +0.45 +0.60 4-0.63 +1 .o +0.77 +1.1 +5.2
+3.4
Membrane, Hi-Sep E-97 1.2 6.3 15.3 4.5
-7.1 -0.40 +0.55 +8.0
TABLE II. COMPARING LIQUID F I L M AND MEMBRANE COEFFICIENTS
(Membrane: Hi-Sep 70) Hectrolytc
HCI
HISO, Ha04 NaOH
corn.,
Mole/Lifm
0.56 2.45 4.45 6.5 0.212 4.24 0.20 3.20 0.5 7.5
u. x l@, u,"x
7@,
u, x
103,
Ctn./Min.. Cm./Min.. Cm./Min.k
1.8 2.7 3.4 3.9 1.25 2.3 0.60 0.70 1.3 0.9
3.2 3.9 5.3 5.8 2.5 2.9 1.04 0.88 2.0 1.9
4.1 6.8 9.0 11.6 2.3 10.8 1.8 3.5 3.4 1.7
V O L 5 4 NO. 6 JUNE 1 9 6 2
25
Effect of Common Ions
YI
k
1.8
f
5
In mixtures of electrolytes common ion effects may be expected to influence the behavior of the electrolytes in dialysis. Two cases are given h e r m n e where the common ion effect is not noticeable and the other where it is considerable.
HI SEP E 97
6 1.4
e
Care I. A mixture of hydrofluoric and nitric acid (5N in HF and 3.5N in "0s) was dialyzed. The following results were:
z
n
1 .o
x
2
0.8J 0
2 4 6 CONCENTRATION
I I 1 0 1 2 1 4
8
iMOLES/LITER1
Figurt 4. Dialysis of $odium hvdroxide solution
HF HA'03
U. = ,155 U.
= 2.6
f
0.30 X 10" c m . p e r min.
* 0.4 X
10-1 cm. per min.
Within limits of the experimental error the presence of the strong nitric acid does not appreciably influence the dialysis coefficientofthe much weaker hydrofluoric acid. Care II. An example of two dialysis experiments on a solution containing 0.0288 gram per ml. of iron as ferric nitrate and 0.0242 gram of free nitric acid is given in Table 111. When thr dialysis coefficientsare calculated,the results are:
Expt. I : Fe, U. = 0.55 X "03, U, = 6.6 X Expt. 2: Fe, U, = 0.56 X "03, U. = 41 X (the comparable value for pure
c?0
E F 0.75
'
z3
I
i.2
1
0.5
I
,
I
Membrane Propertier
3 4 5 6 7
2
CONCENTRATION OF HCI
iMOLES/LITERI
Figurc 5. Hi Scp No. 70 absorbs adds
-?
u 4.5 4.0
4.0
3.5
3.5
n
'2 3.0 x
f
-
3.0 x
251 0
I 1
I 2
I 3
I 4
CONCENTRATION
I
I
I
5
6
7
1
. 0
IMOLES /LITER1
Figurc 6 26
= 1.6
These results illustrate a general experieqce about this type of system: the dialysis coefficient of the acid is very high but it is no longer a constant at a given liquor concentration; it is extremely dependent on the flow rates of the liquor and the water in the dialyzer. In a number of cam at low flow rates acid concentration in the diffusateis higher than in the feed liquor; computing the dialysis coefficient for the acid by Equation 1 is then impoasible.
1.0
$+ EZ
HNO,, U.
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Swollen, Thickness. The swollen thickness of the Hi-Sep 70 membrane used for most experiments was 0.0132 cm. Thia thickness was measured in acid, caustic, and salt solutions in a wide range of concentrations and was found constant and independent of the solution used. This is an important difference from most membranes based on natural products (9). When dried, the membrane shrinks and shrivels considerably and its dry thickness is approximately 0.009 cm. Absorption. The Hi-Sep 70 membrane absorbed acids from their aqueous solution (Figure 5). It showed negative absorption for sodium hydroxide. Equilibrium is established extremely quickly-about 1 minute was apparently sufficient. The negative absorption of sodium hydroxide was determined at only one concentration: 1N NaOH where the concentration of NaOH in the imbibed solution was only 72% of the bulk concentration. The behavior of the Hi-Sep 70 membrane did not indicate the presence of ion exchange groups. All ionic constituents absorbed from aqueous solutions were removed completely by distilled water in a few washings. The E97 membrane showed the opposite behavior: It has a moderate cation exchange capacity, but acids and alkali are present in the imbibed solution in the same concentrations as in the bulk solution.
RELATING THEORY AND PRACTICE The results show clearly that the membrane material plays an important role in dialysis performance. Hi-Sep 70 gives a high material transport per unit area for acids, whereas for caustic it is mediocre. The steep rise in dialysis coefficient w+th increasing concentration, shown by the strong acids (Figure 4) is remarkable. .4 priori, the dialysis coefiient of most substanceswould be expected to decrease because: -The higher viscosity found at higher concentrations spells lower diffusivity. -The higher water transport will cause lower solute transport; this agrees with the large difference between DZ and D: predicted for high concentrationsof x . I t is therefore of interest to attempt an explanation of the exceptional behavior of the acids in the system investigated. One factor involved may be an increase in diffusivity with increasing concentration. Data are available from literature for only two of the acids usedhydrochloric (16) and phosphoric acid (5). The best basis of comparison is bemeen the membrane dialysis coefficient U, and the published integral diffusion coefficient 0:. In Figure 6, these two are compared for hydrochloric acid. The diffusivity does indeed increase with increasing concentration, but not at a rate comparable to the much steeper increase of Urn. A possible explanation is that hydrochloric acid is one of the exceptional substances having high diffusivity that should have > D:. The difference should become more pronounced the higher the concentration. There is at present no way to evaluate quantitatively the difference between the two diffusivities, and the divergence between the Urn and Dl curves remains unanswered. The observed water transports for hydrochloric acid are partly negative, partly abnormally low: They cannot be explained by the high value of D: only. The absorption of acid by the membrane is an important clue in this respect. Such an absorption may cause an increased acid transport through chemical interaction, accompanied by a lower water transport. Negative mater transpat through a mtmbranc that possesses no dnnonstrable ion exchange popmties and that is not usually rcgorded' as o charged
-
e
mnnbranc has not btm reported fiediously.
F h Rols, sweanl
MI./Mk
Water Liquor Dialyzate Diffusate
70 58
In the case of phosphoric acid, the following comparison is found between U, and D'(5):
H a , 0.2 M Urn= 1.04 X 10-a cm./m,. = 0.94 X IOd sq. cm./sec.
D'
H8043.2M -Uk = 0.88 X 10" cm./min. F = 0.88 X 104 sq. nn./sec With increasing concentration, U, decreases slightly faster than D,as expected when comparing diffusion in free solution and through a membrane. For phosphoric acid, the water transport through the membrane is the highest among the acids tested (Table I), but it is still less than the amount anticipated by conventional theory (9). Again, the interaction between acid and membrane is probably the reason. The high water transport encountered with sodium hydroxide and Hi-Scp 70 is l i e d with the negative absorption of this substance. The behavior of sodium hydroxide is thus the opposite of hydrochloric acid. The experiments on the E-97 membrane show one way to influence water transport-by an appropriate choice of membrane. No strong membrane was available that would absorb sodium hydroxide. Therefore, a cation exchange membra ne^ was' chosen, giving the expected negative or anomalously low water transport kith caustic solutions (and, of course, a high water transport with acid). These eHects are qualitatively in agreement with those predicted from the electrical interaction between membrane and solution. Importonce of Wakr Tmnsporl
Detailed consideration should be fiven to wacer transport because of its importance in dialysis practice. A high positive water transport increases the membrane area required to effect a predetermined material transport from a given feed liquor because it dilutes this Liquor on its passage through the dialyzer, and thus reduces the driving force for dialysis. Where the dialyzate is a waste stream, its dilution is an additional burden on the waste disposal system. It is therefore of great economic importance to select a dialysis membrane that shows low or negative water transport for the solution in
TABLE 111. DIALYSIS EXPERIMENT9 Iron Gmn., Free Acid Comn.,
G./MI.
G./MI.
Irm Rote,
G./Min.
Acid Rote, C./Min.
1.67 1.28 0.389
1..41 0.29 1.16
0.825 0.023 0.795
Expt. 1 66 62
0.0288 0.0193 0.00627
0.0242
0.0044 0.0188
Expt. 2
Water
Liquor Dialyzate Diffusate
42 34 42 34
0.0288 0.0159 0.0097
0.0242
0.980
0.00055
0.667
0.0234
0.330
Membrane area 3350 69. un. VOL. 5 4
NO. 6 JUNE I962
27
question. Results in Table I show that Hi-Sep 70 is especially suitable for the dialysis of acids hecause of the negative or low positive water transport numbers. Liquid Film Resistance
Talde I1 shows that the resistance to material transport resides predominantly in the membrane and not in the liquid films, and this is in particular true for concentrated acids. Ui increases with increasing concentration, even when U,,, decreases. This indicates that the relation between the niemixane dialysis coefficient and the combined liquid film coefficient LTLis more complex than has been suggested ( 9 ) . Apparently factors exist that improve material transport through the liquid films at high concentrations; these factors do not operate inside the membrane, or at least not to the same extent. The most probable explanation is that at higher liquor concentration dialysis creates higher concentration differences in the immediale vicinity of the membranes. The local concentration differences, accompanied by density differenccs, producc convection currents reducing the thickness of the unstirred film. Any local heat of dilution will have the same effect. Two facts emerge from these olxervations : -The over-all dialysis coefficient is more favoralile for concentrated solutions than might be calculated from batch tests only, using a fixed apparent liquid film thickness and Equation 5 of reference (9). -Most resistance to material transport resides in the membrane, even in the best membranes available now for technical use. Improved membrane performance should further increase the liquid film transfer coefficient because of the stronger convection currents that result. Sodium hydroxide behaves in a different way (Table 11). The liquid film transfer coefficient decrea..Ces more strongly than the membrane dialysis coefficient, although local convection currents would tie expected to occur here as well. Extremely high water transport may be connected with this behavior because it creates a dilute solution layer on the dialyzate side of the mernhrane, rcducing the concentration drop. If this is correct, it adds to the importance of a low water transport number. However, more work is required. Where two substances are dissolved, the varia hility of the acid dialysis coefficient in the presence of a salt has been observed in a great number of cases. The higher the ratio of salt to acid, the greater the variability of the acid dialysis coefficient. The case o f simultaneous diffusion of a salt and an acid has been treated for a free niembraneless solution Iiy Vinograd and McBain (78) and the experiments on dialysis are qualitatively in agreement. As noted previously, this effect yreatly assists in separating a salt from its acid. AUTHOR B . H. Vromen was a Group Leader zn Research and Detelobment f o r Graver Wafer Condztionzng Co., A‘. Y., when this artzcle was wrztten. He zs now a membei o f Technzcal Stqf of Bell Telephone Lnboratmes, Murray Hzll,
1’.
