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�A study of Osmotic Distillation.

Miles Rzecho= wicz and Richard M. Pashley*.

University of New South Wales, Australian Defence Force Academy, Canberra, Australia. E-mail: [email protected]

 

Graphical Abstract:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 1. Schematic representation of water penetration int= o a hydrophobic pore, within a hydrophobic membrane. The liquid water (phase A) will not readily enter a vapour-fi= lled pore or channel (phase B) in a hydrophobic material, such as Teflon or polypropylene, due to the high water contact angle, θ, on the hydrophobic surface.� Although liquid water will not enter th= e fine hydrophobic porous network, water vapour will easily pass through the pores, into dry air or a vacuum.

The Laplace equation (1) gives the pressure differ= ence (D= ) across any curved fluid interface:

<= ![endif]>��������������������������������������������������������������� = (1)�������������������������������������������������= ����������������� ���� (1)

is the surface tension of the liquid and r is the radius of curvature of the water-air interface, which is usually assumed to be spherical.� If rc is the radius of a capillary tube or pore, it follows from simple geometry (again assuming that the meniscus is spherical and that q>900) that the radius of the meniscus, r, is given by:

����� <= ![endif]>�������������������������������������������������= ������������ (2)������������������������������������������������= ���������������������������������������������������������������������������= ��������������

and hence t= he Laplace pressure (positive by definition) is given by the equation (for q >900):

�<= ![endif]>����������� ���������������������������������������� (3)������������������������������������������������= ��������������������������������������������������������������������������

This is the minimum pressure required to force liquid water into the pores, where the pore walls have a water contact angle of q.

 

Figure 2. This graph gives the magnitud= e of the Laplace pressure, in atm, required to force liquid water through a 1 mi= cron pore, for porous materials with a range of different water contact angles.<= span style=3D'mso-spacerun:yes'>� A hydrophilic pore material, with a con= tact angle below 90o, will draw water through the pore, while a hydrophobic material, with a contact angle greater than 90o, will require the application of a substantial pressure. �Teflon, with a contact angle of about 11= 0o, will require a pressure of about 1atm for 1 micron pores.<= /span>

 

m diameter is about 1atm4.� Pores of this size (or less) will therefore allow the pressure in the water to be at 1atm, with a vacuum,� or water vapour (at a pressure of about 20mm of Hg at 200C) on the other side, without allowing liquid water to flow through the pores.� This method works because water has a h= igh surface tension (73mJm-2) and Teflon has a very low tension (of about 18mJm-2).� The water-Teflon interfacial tension is also high at about 45mJm-2 a= nd hence the water contact angle on Teflon is very high, at about 1100.

Teflon and polypropylene porous membranes are al= so used commercially to concentrate wine and fruit juice for export5,6. These processes are referred to as membrane distillation and osmotic distillation (OD)7.� In = each of these processes, the solution to be concentrated is flowed around the exteriors of porous hollow fibres of these materials, while a vapour pressu= re gradient is used to draw vapour from the solution into the interiors of the fibres.� In the case of membrane distillation, this is achieved either by applying a vacuum to the fibre interiors, or by circulating through them a solvent at a lower temperature = than that of the feed solution.� In the = case of osmotic distillation, concentrated brine is used as the low vapour press= ure fluid.� In these processes it is important that the high contact angle be maintained and so the membranes are regularly washed to prevent adsorption of surface active agents.=

�The concentrative effect of osmotic distillation occurs due to the effect of solutes on the chemical potential of the water.� For ideal mixtures, the chemical potential of the water depends upon= the mole fraction of water in the solution, according to the relation:

 

<= ![endif]>�� = ���= ����������� (4)�������������������������������������� ���������������������������� �����������������������������<= /span>

mwl<= ![endif]>�w*= l<= ![endif]>xw<= ![endif]>�wv, <= /span><= ![endif]>�wl <= ![endif]>xw=3D pwpw*<= ![endif]>������������������������������������= ������������������������������ (5)��������� ������������������������������������������������= ������������������������������������������������������������������

pw<= ![endif]>pw*= <= ![endif]>μwP+= Π=3D= μw*= P+PP+= ΠVmwdp<= ![endif]>��� (6)����������������������� ������������������������������������������������= �������

V<= /span>mw<= ![endif]>�is the molar volume of wate= r, P is the standard pressure and Π is the additional, applied (osmotic) pressure.� Using equation (4) and equating the change in chemical potential cau= sed by the applied pressure with the change produced by adding solute, gives the relationship:

<= ![endif]>� (7)

assuming that the solvent is incompressible.� For dilute solutions <= ![endif]>xs<= ![endif]>l= n(xw)= Vm*<= ![endif]>nsV<= ![endif]--><= ![endif]>ns<= ![endif]> �<= ![endif]>��������������������������������� (8)��������� ���������= ���������������������������������� ������������������������������������������������ where Рis the osmo= tic pressure, V is the water (solve= nt) volume and nS is the number of moles of solute.� Applying Raoult's law to equation (7), we obtain the result:

<= ![endif]>��������������������������������������� (9)

ln<= span style=3D'font-size:14.0pt;mso-ansi-font-size:14.0pt;mso-bidi-font-si= ze: 14.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cam= bria Math"; mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font= -style: normal'>pw<= /m:sSub>pw<= m:sup><= m:r>*=3D= -2γVmwrRT<= ![endif]>������������������������������������= ������������� (10)�������������������������������������������������= ������������������������������� ������������������������������������������������= ���������������������������� In the case of a salt solution, where the vapour pressure has been depressed according to Raoult's law, it may be increased back to its normal value by creating an interface with a positive radius of curvature,

�������������� <= ![endif]>������������������������������������������� (11)= Π=3D= -= RTln(xw)= Vmw<= ![endif]>������������������������������������= ������������������ (12)�������������������������������������������������= ������������������������������� �������������� ������������������������������������������������= ���������������� which leads us back to the van't Hoff equation, (9), demonstrating t= hat the hydraulic pressure applied to the concentrated phase required to equali= se the vapour pressures of the two phases is identical to the osmotic pressure.

ln(xw)= Vm*<= ![endif]>nsV<= ![endif]--><= ![endif]>Figure 3. This graph shows the measured8 and ide= al9 vapour pressure differences between pure water and varying NaCl solution concentrations, at 200C. The depression in vapour pressure predi= cted using Raoult's law is linear, whereas the experimental data shows non-linear behaviour.

 

a= w= ,<= ![endif]>�= wl=3D = �= w*<= /m:r>l+ RTln(a<= /m:r>w<= /m:r>)<= ![endif]>���= � �������������� (13)��������������������� �����������= �������������������������������� ���������������������������������������������

�QUOTE <= ![if gte msEquation 12]>a= w=3D pwpw* <= ![endif]>��� <= ![endif]>

<= ![endif]>ϕ=3D-<= m:num>nwnslneaw <= ![endif]>ϕ=3D-<= m:num>nwnslne= a= w= <= ![endif]>Π=3D-<= m:num>RTVmwlne= a= w= <= ![endif]>Π=3D<= m:num>RTVmw<= m:num>nsnwϕ<= ![endif]>Π=3D<= m:num>RTVmw<= m:num>nsnw∙ϕ <= ![endif]>1.2. Limits = of Conventional Methods of Determining Solution Osmotic Pressures

2.� Methods and Materials=

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Figure 4. Schematic diagram of the experimental apparatus u= sed in this study. The apparatus consisted of a peristaltic pump, which drew solutions from two measuring cylinders, at equal flow rates, circulated them through the hollow-fibre cartridge, and returned them to their respective cylinders.� One cylinder contained de-ionised water, which was passed over the hollow-fibre exteriors (shellsi= de), while the other contained aqueous NaCl solutions, of various concentrations= , which was passed through the fibre interiors (lumenside).� The transfer of water through the membr= ane was measured by observing the solution levels in the measuring cylinders.

 

3D"Description:Figure 5. Experimentally measured flow rates across the hol= low fibre membranes, from pure water into salt solutions, as a function of the = salt concentration. The experimental results are compared with the ideal, linear prediction from Raoult�s law. The experimentally measured rate of transfer = of water vapour, by osmotic distillation, was found to vary with solution concentration in a non-linear manner.� The measured flux follows a greater than proportional relationship w= ith the concentration difference between the dilute and concentrated feed solutions.� The shape of this curve= is very similar to that of the published experimental vapour pressure data, as shown in Fig. 3.

 

4.� Analysis and Discussion

4.1. Compari= son of Observed Transfer Rate with Industrial Membrane Processes

 <= /o:p>

4.2. Compari= son of Observed Results with Theoretical Predictions

The experimental results obtained f= rom this study showed a non-linear increase in the water transfer rate across hydrophobic hollow fibre membranes, as the concentration difference was increased, as shown in Fig. 5.� Whe= n a direct comparison is made between the shapes of the curves of the transfer = flux data and the vapour pressures10, in Fig. 3, an almost perfect ma= tch was observed.� Interestingly, the o= smotic pressure curve also deviates from the linear van�t Hoff prediction in a sim= ilar manner, as shown in Fig. 6.

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

 <= /o:p>

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Figure 6. �Ideal9 and measured8 osmotic pressures of various concentrations of NaCl solutions. The osmotic pressures of a variety of aqueous NaCl solutions can= be theoretically predicted using the van't Hoff equation and are compared with values calculated from experimentally determined, published practical osmot= ic coefficient data8. Significant differences occur at concentratio= ns above about 3M, for aqueous NaCl solutions.

A plot of the difference between th= e vapour pressures of the salt solution and pure water, against the process flux yie= lds a straight line (Fig. 7), which is consistent with the above-mentioned correspondence between the shapes of the vapour pressure and flow rate curves.� The slope of this curve ca= n be used to predict the rate of vapour transfer across a membrane, for a known pressure difference. This dependence can, in theory, be applied to any situation where a partial pressure differential exists across a hydrophobic membrane.� As an example, this can = be used to calculate the loss of water vapour into a vacuum system or sweep ga= s, in the case of a hollow-fibre degassing arrangement, by combining the slope= of the curve, or partial pressure of water in the sweep phase or vacuum, the m= embrane surface area, the membrane porosity, and approximate feed temperature.� This may be of value in the design of commercial degassing systems, using vacuum pumps capable of tolerating the condensable vapours. The slope will depend on membrane type, feed compositi= on and feed flow rate.

 

 

 

 

 

 

 

 

 

 

Figure 7. Experimental vapour transfer flux rates are compa= red with the calculated difference in vapour pressure between the two feed liqu= ids. The rate of transfer of water through the hollow fibre membranes has a direct linear relationship with the vapour pressure difference between the two solutions8.� The equation of the trendline could be = used to predict the flow rate of the process for a known vapour pressure differe= nce, generated by any means, e.g. by application of a vacuum, by temperature differential, or by osmotic pressure.

V<= /span>mw<= ![endif]> QUOTE = V= m=3D Vm* <= ![endif]>�� The two sets of data that = were calculated agreed to 3 significant figures, indicating that the practical osmotic coefficients were derived from vapour pressure values, and calculat= ed using the same assumption.

5.� Conclusions

Appendix

Nomencl= ature

a������������ Act= ivity

c������������ Con= centration (moles/m3)

l������������� Li= quid

n������������ Num= ber (moles)

P����������� Pressure (Pa)

p������������ Vapour pressure = (Pa)

R����������� Gas constant (J/K mol)

r������������ Radius (m)

T������������ Temperature (K)

v������������ Vapour phase

x������������ Mole fraction

V����������� Volume (m3)

 <= /p>

Greek Symbols

����������� Surface tension (N/m)

����������� Difference

����������� Contact angle (�)

����������� Chemical potentia= l

����������� Osmotic pressure (Pa)

����������� Practical osmotic coefficient

 

Superscripts

*������������ Pure component

w����������� Water

 <= /p>

Subscripts<= /i>

1,2�������� Components 1, 2=

c������������ Capillary

m����������� Molar

s������������ Solute

w����������� Water

References

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4. Rzechowicz, M;, 2006, 298(1), 321-326=

5. Jiao, B.; Cassano, A.; Drioli, E.� J. Food Eng. 2004, 63, 303�324.

6. Diban, N.; Athes, V.; Bes, M. J. Membr.=  Sci.<= /i>,=  2008, 311(1-2), 136-1= 46.

7. Curcio, E.; Drioli, E. Sep. Purif. Rev.<= /span>, 2005, 34, 35-86.

8. Colin, E.; Clarke, W.; Glew, D.E.� J. Phys. Chem., 1985, 14(2), 489-610.

9. Wolf, A.V.; = Brown, M.G.; Prentiss, P.G. CRC Handbook of Chemistry and Physics 68th Edit= ion, R.C. Weast (ed.), 1988, CRC Pr= ess, pp D253-D254.��������������������� <= /span>

 

10. Robinson, R.A.� Trans. R. Soc., N. Z. 1945, 75, 203�217.

�=

11. Partanen, J.I.; Covington, A.K.� J. Chem. Eng. Data, 2009, 54, No. 2.

 

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13. Fact Sheet, SWRO HR Series, Form No. FS1289EN.doc Feb-09, General Electric Company, 2009.

&nbs= p;

14. Ander= son, G.M.; Crerar, D.A. Thermodynamics in geochemistry: the equilibrium model, 1993, Page 215.� Oxford University Press,= UK.

 

15. Perron, G.; Roux, A.; Desnoyers, J.E. Can. J. Chem., 1981, 59, 3049-3054.

 

16. Garcia-Castello, E.M.; McCutcheon, J.R.; Elimelech, M. �J. Membr. Sci., 2009, 338(1-2), 61-66.

 

17. B�lafi-Bak�, K.; Koroknai, B.� J. Membr. Sci., 2006, 269, 187�193.  <= /o:p>

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All Res. J. Chem, 2011, 2, 1-10

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