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: r.pashley@adfa.edu.au

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 r_c 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 90^o, will draw water through the pore, while a hydrophobic material, with a contact angle greater than 90^o, will require the application of a substantial pressure.  Teflon, with a contact angle of about 11= 0^o, 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 110^0.

Teflon and polypropylene porous membranes are al= so used commercially to concentrate wine and fruit juice for export^{5,6. 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]>µw*= l<= ![endif]>xw<= ![endif]>µwv, <= /span><= ![endif]>µwl <= ![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 Π is the osmo= tic pressure, V is the water (solve= nt) volume and n_S 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]>µ= wl=3D = µ= 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>nsnw∙ϕ<= ![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.

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

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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.

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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)

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Greek Symbols

γ             Surface tension (N/m)

Δ            Difference

θ             Contact angle (°)

μ             Chemical potentia= l

Π            Osmotic pressure (Pa)

Φ            Practical osmotic coefficient

Superscripts

*             Pure component

w            Water

 <= /p>

Subscripts<= /i>

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