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Determination of membrane thickness for emulsion liquid membrane macrodrops. A new approach
journal of MEMBRANE SCIENCE
ELSEVIER
Journal of Membrane Science 115 (1996) 129-132
Determination of membrane thickness for emulsion liquid membrane macrodrops. A new approach Runu Chakraborty
a,
Siddhartha Datta b,,
a Department of Food Technology and Biochemical Engineering, Jadavpur University, Calcutta 700 032, hzdia b Department of Chemical Engineering, Jadavpur UniL'ersity, Calcutta 700 032, India Received 20 September 1995; accepted 10 November 1995
Abstract The mass transfer rate through a liquid surfactant membrane based on a film model often relies on the correct evaluation of the thickness of the membrane forming a layer around the emulsion drop. The present study gives an equation which correlates membrane thickness with the volume fraction of the dispersed hydrocarbon phase in the emulsion. The proposed equation is in good agreement with the experimental data of Goswami and co-workers [J. Membrane Sci., 54 (1990) 119] where the equation proposed by Kataoka et al. [J. Membrane Sci., 41 (1989) 197] shows deviation at higher values of microdrop holdup. Keywords: Emulsion liquid membrane; Membrane thickness; Internal droplet holdup; Film model
1. I n t r o d u c t i o n Since they were first invented by Li [1] emulsion liquid membranes have demonstrated considerable potential as a selective method for a wide variety of separations. During the last few years various attempts have been made to develop mathematical models to describe the mechanism of mass transfer through liquid membranes. These models are generally categorised into membrane film and distributed resistance models. The first approach assumes that the resistance to mass transfer are lumped together in
* Corresponding author,
a hypothetical membrane of constant thickness between the external and internal phases. The second approach of the distributed resistance model takes into account the diffusional resistances throughout the emulsion globule. For the separation of hydrocarbons where no carrier facilitated transfer is involved, it has been found that the membrane film model gives a useful insight into the transfer mechanism and the calculation of the transfer rate based on this model relies on the correct evaluation of the thickness of the outer water layer around an emulsion drop. In the separation of hydrocarbons by liquid surfactant membranes several researchers attempted to determine the above mentioned thickness of the water membrane layer which separates the dispersed
0376-7388/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD10376-7388(95)00313-4
R. Chakraborty, S. Datta / Journal of Membrane Science 115 (1996) 129-132
130
feed mixture and the receiving oil phase. Cahn and Li [2] lumped this membrane thickness into a permeation rate constant in their model as they found it difficult to measure the membrane thickness for a liquid membrane system. On the other hand, Matulivicius and Li [3] fitted their experimental data with model predictions through a judicious selection of this film thickness. Casamatta et al. [4] approximated the mass transfer coefficient in the membrane layer as the ratio of diffusivity to the membrane thickness. They have also deduced an equation which gives the maximum thickness of the membrane for a given fraction of the dispersed hydrocarbon phase, Goswami and co-workers [5] have devoted considerable attention to the determination of this film thickness. They have found the variation of membrane thickness with dispersed phased holdup, qO, through experiments. Results show that at lower values of internal phase droplet holdup, the membrane thickness increases. This finding supports the views of Casamatta et al. [4] that in an emulsion the excess water which drains out from between the droplets under gravity spreads around these drops in a more or less uniform manner to form an outer layer of constant thickness. This thickness increases as more water drains out with decreasing hydrocarbon phase in the emulsion. Goswami and co-workers compared their results with the equation given by Kataoka et al. [6] and found wide deviations at higher values of qb. However, they did not suggest any correlation from which membrane thickness can be determined without going into experiments. Chakraborty and Datta [7] have checked the validity of the assumptions made by Casamatta et al. [4] by performing experiments for the permeation of hydrocarbons through emulsion liquid membranes. Based on their experimental results they have proposed an equation for the accurate prediction of membrane thickness. But this equation also does not correlate the variation of membrane thickness with microdrop holdup because it does not accommodate any holdup terms, Kataoka et al. [6] arrived at the following expression for the inter-microdrop distance in an emulsion: { A,.rr ~
1/3
where fi is the membrane thickness (m), R~, the radius of the rnicrodrop in the emulsion (m) and qb the volume fraction of dispersed phase in the emulsion. They used this distance as the thickness of the membrane. Though, until now, this is the only equation which can correlate thickness with internal phase droplet holdup; unfortunately, it is found to be not so satisfactory in the higher regions of internal phase droplet holdup. The failure, as pointed out by Goswami and co-workers [5] is due to the occurrence of size distribution of droplets at higher values of holdup while Kataoka et al.'s equation assumes a uniform droplet size. Thus, there is a clear need for developing an equation which can predict accurately the variation in membrane thickness with internal phase droplet holdup particularly for hydrocarbon separations where the liquid membrane offers the major resistance to mass transfer. Accordingly, the present study proposes an equation based on the experimental mass transfer data of Goswami and co-workers [5] and can predict the accurate value of membrane thickness in the case of non-facilitated transport through liquid surfactant membrane. The experimental work of Goswami and co-workers is based on a system consisting of an inner hydrocarbon mixture of benzenen-heptane (50:50 w / w ) and 0.2 wt% Hyoxyd X-200 surfactant in aqueous layer with kerosene as the receiving phase.
2. Discussion It is a fact of solid geometry that an assembly of spheres of equal radius can be placed in a position of densest packing when the spheres are found to occupy 74.02% of the total assembly volume, the remaining 25.98% being empty space [4,8]. Hence in an O / W emulsion, the maximum volume fraction of hydrocarbon that can be taken to form a stable emulsion is 0.74. The water layer of uniform thickness would exist in the periphery of the emulsion drop only when the volume fraction of the dispersed hydrocarbon phase, q~, is less than 0.74, so that excess water drains out of the emulsion and forms a uniform ring around it. Thus, theoretically, the thick-
R. Chakraborty, S. Datta / Journal of Mernbrane Science 115 (1996) 129-132
131
ness of the peripheral water layer can be taken to be zero or minimum when 4' is maximum, The above observation is true only in the case of monosized spherical particles. But this is not valid in case of liquid membrane systems where deformation of emulsion drop increases the stable hydrocarbon volume fraction significantly beyond this theoretical ~max" So even at maximum volume fraction of hydrocarbon some amount of water is always squeezed out due to deformation to form a ring of uniform thickness. In the case of liquid membrane systems, we can consider it to be the minimum membrane thickness (Smi,). Further decrease in • and a corresponding increase in the aqueous phase volume resuits in an increase in the thickness of the membrane, The experimental data of Goswami and co-workers [5] obtained while studying the permeation of benzene through a liquid surfactant membrane is in
and co-workers [5] and from the above concept of deformation of drop we propose an equation for the prediction of liquid membrane thickness for any value of an internal phase droplet holdup. The equation is:
close conformity with the explanations given above. But this concept of deformation of emulsion drops in the case of liquid membrane systems has not been taken into account by Kataoka et al. [6] for the calculation of the liquid membrane thickness, Based on the experimental results of Goswami
~min =
(2)
= C1 e - c J a + ~min
where 8 is the actual thickness of the membrane (m), C 1 is a constant in Eq. (2), C 2 is another constant in Eq. (2), • the volume fraction of the internal phase droplet holdup and 8mi. the minimum membrane thickness (m). The above equation was fitted through all the 8 vs. • data of Goswami and co-workers [5] by a least squares method and the following values were obtained by curve fitting: CI = 9.895 × 10 -4 , C 2 = 17.6 and 12.6 × 10 - 6 m
Fig. 1 shows the variation of membrane thickness, 8, with internal phase droplet holdup, qb, for the experimental data of Goswami et al. [5] and the theoretical predictions of both Kataoka et al. [6] and
! 30
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. . . . Theoretical ( Kataoka et at. ) J 0 0 Experimental (Goswami et 0.1,~ i
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internal droplet holdup,~b Fig. 1. Variation of membrane thickness with internal phase droplet hold up.
132
R. Chakraborty, S. Datta/Journal of Membrane Science 115 (1996) 129-132
the equation proposed in the present study. It is evident from Fig. 1 that Kataoka et al.'s equation fails to predict the actual membrane thickness particularly in the region of high internal droplet holdup. On the other hand, the equation proposed in this study is found to be in excellent agreement with the experimental results of Goswami and co-workers [5] in all regions of internal phase droplet holdup, It should also to be noted that the minimum membrane thickness, 6m~., in Eq. (2) can be evaluated independently. If an emulsion is prepared with ~m~x = 0.74 then the water content of an emulsion drop of radius R is given by Vm = 4 / 3 7 r R 3 ( 1 - ~bmax). (3) When the same emulsion is stirred in the external phase, deformation of the drops take place and q0 in the inner core becomes greater than ~bm~x. So some water drains out of the emulsion to form an outer membrane of minimum thickness, 6mi n. If we denote this ~b after deformation by ~bde f then the initial volume of water is distributed between the inner core and the outer aqueous layer so that Vm = (1 - ~def)4/37r( R -
~min)3
[ ) ] + 4/37r_ R 3 - ( R -- 6min 3. Eqs. (3) and (4) give ~min ] 3 (~rnax = 1 ff)def R )
(4)
(5)
where (~def is the volume fraction of hydrocarbon inside the emulsion drop when deformation has taken place, ~bmax the maximum volume fraction of hydrocarbon in the emulsion corresponding to the closest packing of the non-deformable spheres and R the radius of an emulsion drop (m). In this case the minimum value of membrane thickness (12.6 × 10 - 6 ) is obtained from the above
equation when the value of ~bd~f is equal to 0.84 which is obviously greater than ~bmax.
3, Conclusions An attempt has been made in the present study to develop an equation which would correlate membrane thickness, 6, with the volume fraction of dispersed hydrocarbon phase in the emulsion, ~b. Kataoka et al.'s equation fails to predict the correct membrane thickness in all regions of internal droplet holdup and Goswami and co-workers confined their work only within experimental limits. The proposed equation can predict satisfactorily the membrane thickness in all regions of internal phase droplet holdup and is found to be in excellent agreement with the experimental data of Goswami and coworkers.
References l I] N.N. Li, Separating Hydrocarbonswith liquid membranes, US Pat., 3,410,794 (1968). [2] R.P. Cahn and N.N. Li, Separation of organic compounds by liquid membrane process, J. Membrane Sci., 12 (1976) 129. [3] E.S. Matulivicius and N.N. Li, Facilitated transport through liquid membranes, Sep. Purif. Methods, 4(1) (1975) 73. [4] G. Casamatta, C. Chavarie and H. Angelino, Hydrocarbon separation through a liquid water membrane: modelling of permeation in an emulsion drop, AIChE J., 24 (1978) 945. [5] T.C.S.M. Gupta, A.N. Goswami and B.S. Rawat, Mass transfer studies in liquid membrane hydrocarbon separations, J. Membrane Sci., 54(1990)119. [6] T. Kataoka, T. Nishiki and S. Kimura, Phenol permeation through liquid surfactant membrane-permeation model and effective diffusivity, J. Membrane Sci., 41 (1989) 197. [7] R. Chakraborty and S. Datta, Prediction of membrane thickness in hydrocarbon permeation through liquid surfactant membrane, Sep. Sci. Technol., 29 (1994) 1967. [8] P. Becher, Emulsions, Theory and Practice, 2nd edn., Reinhold, New York, 1965, p. 101.
ELSEVIER
Journal of Membrane Science 115 (1996) 129-132
Determination of membrane thickness for emulsion liquid membrane macrodrops. A new approach Runu Chakraborty
a,
Siddhartha Datta b,,
a Department of Food Technology and Biochemical Engineering, Jadavpur University, Calcutta 700 032, hzdia b Department of Chemical Engineering, Jadavpur UniL'ersity, Calcutta 700 032, India Received 20 September 1995; accepted 10 November 1995
Abstract The mass transfer rate through a liquid surfactant membrane based on a film model often relies on the correct evaluation of the thickness of the membrane forming a layer around the emulsion drop. The present study gives an equation which correlates membrane thickness with the volume fraction of the dispersed hydrocarbon phase in the emulsion. The proposed equation is in good agreement with the experimental data of Goswami and co-workers [J. Membrane Sci., 54 (1990) 119] where the equation proposed by Kataoka et al. [J. Membrane Sci., 41 (1989) 197] shows deviation at higher values of microdrop holdup. Keywords: Emulsion liquid membrane; Membrane thickness; Internal droplet holdup; Film model
1. I n t r o d u c t i o n Since they were first invented by Li [1] emulsion liquid membranes have demonstrated considerable potential as a selective method for a wide variety of separations. During the last few years various attempts have been made to develop mathematical models to describe the mechanism of mass transfer through liquid membranes. These models are generally categorised into membrane film and distributed resistance models. The first approach assumes that the resistance to mass transfer are lumped together in
* Corresponding author,
a hypothetical membrane of constant thickness between the external and internal phases. The second approach of the distributed resistance model takes into account the diffusional resistances throughout the emulsion globule. For the separation of hydrocarbons where no carrier facilitated transfer is involved, it has been found that the membrane film model gives a useful insight into the transfer mechanism and the calculation of the transfer rate based on this model relies on the correct evaluation of the thickness of the outer water layer around an emulsion drop. In the separation of hydrocarbons by liquid surfactant membranes several researchers attempted to determine the above mentioned thickness of the water membrane layer which separates the dispersed
0376-7388/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD10376-7388(95)00313-4
R. Chakraborty, S. Datta / Journal of Membrane Science 115 (1996) 129-132
130
feed mixture and the receiving oil phase. Cahn and Li [2] lumped this membrane thickness into a permeation rate constant in their model as they found it difficult to measure the membrane thickness for a liquid membrane system. On the other hand, Matulivicius and Li [3] fitted their experimental data with model predictions through a judicious selection of this film thickness. Casamatta et al. [4] approximated the mass transfer coefficient in the membrane layer as the ratio of diffusivity to the membrane thickness. They have also deduced an equation which gives the maximum thickness of the membrane for a given fraction of the dispersed hydrocarbon phase, Goswami and co-workers [5] have devoted considerable attention to the determination of this film thickness. They have found the variation of membrane thickness with dispersed phased holdup, qO, through experiments. Results show that at lower values of internal phase droplet holdup, the membrane thickness increases. This finding supports the views of Casamatta et al. [4] that in an emulsion the excess water which drains out from between the droplets under gravity spreads around these drops in a more or less uniform manner to form an outer layer of constant thickness. This thickness increases as more water drains out with decreasing hydrocarbon phase in the emulsion. Goswami and co-workers compared their results with the equation given by Kataoka et al. [6] and found wide deviations at higher values of qb. However, they did not suggest any correlation from which membrane thickness can be determined without going into experiments. Chakraborty and Datta [7] have checked the validity of the assumptions made by Casamatta et al. [4] by performing experiments for the permeation of hydrocarbons through emulsion liquid membranes. Based on their experimental results they have proposed an equation for the accurate prediction of membrane thickness. But this equation also does not correlate the variation of membrane thickness with microdrop holdup because it does not accommodate any holdup terms, Kataoka et al. [6] arrived at the following expression for the inter-microdrop distance in an emulsion: { A,.rr ~
1/3
where fi is the membrane thickness (m), R~, the radius of the rnicrodrop in the emulsion (m) and qb the volume fraction of dispersed phase in the emulsion. They used this distance as the thickness of the membrane. Though, until now, this is the only equation which can correlate thickness with internal phase droplet holdup; unfortunately, it is found to be not so satisfactory in the higher regions of internal phase droplet holdup. The failure, as pointed out by Goswami and co-workers [5] is due to the occurrence of size distribution of droplets at higher values of holdup while Kataoka et al.'s equation assumes a uniform droplet size. Thus, there is a clear need for developing an equation which can predict accurately the variation in membrane thickness with internal phase droplet holdup particularly for hydrocarbon separations where the liquid membrane offers the major resistance to mass transfer. Accordingly, the present study proposes an equation based on the experimental mass transfer data of Goswami and co-workers [5] and can predict the accurate value of membrane thickness in the case of non-facilitated transport through liquid surfactant membrane. The experimental work of Goswami and co-workers is based on a system consisting of an inner hydrocarbon mixture of benzenen-heptane (50:50 w / w ) and 0.2 wt% Hyoxyd X-200 surfactant in aqueous layer with kerosene as the receiving phase.
2. Discussion It is a fact of solid geometry that an assembly of spheres of equal radius can be placed in a position of densest packing when the spheres are found to occupy 74.02% of the total assembly volume, the remaining 25.98% being empty space [4,8]. Hence in an O / W emulsion, the maximum volume fraction of hydrocarbon that can be taken to form a stable emulsion is 0.74. The water layer of uniform thickness would exist in the periphery of the emulsion drop only when the volume fraction of the dispersed hydrocarbon phase, q~, is less than 0.74, so that excess water drains out of the emulsion and forms a uniform ring around it. Thus, theoretically, the thick-
R. Chakraborty, S. Datta / Journal of Mernbrane Science 115 (1996) 129-132
131
ness of the peripheral water layer can be taken to be zero or minimum when 4' is maximum, The above observation is true only in the case of monosized spherical particles. But this is not valid in case of liquid membrane systems where deformation of emulsion drop increases the stable hydrocarbon volume fraction significantly beyond this theoretical ~max" So even at maximum volume fraction of hydrocarbon some amount of water is always squeezed out due to deformation to form a ring of uniform thickness. In the case of liquid membrane systems, we can consider it to be the minimum membrane thickness (Smi,). Further decrease in • and a corresponding increase in the aqueous phase volume resuits in an increase in the thickness of the membrane, The experimental data of Goswami and co-workers [5] obtained while studying the permeation of benzene through a liquid surfactant membrane is in
and co-workers [5] and from the above concept of deformation of drop we propose an equation for the prediction of liquid membrane thickness for any value of an internal phase droplet holdup. The equation is:
close conformity with the explanations given above. But this concept of deformation of emulsion drops in the case of liquid membrane systems has not been taken into account by Kataoka et al. [6] for the calculation of the liquid membrane thickness, Based on the experimental results of Goswami
~min =
(2)
= C1 e - c J a + ~min
where 8 is the actual thickness of the membrane (m), C 1 is a constant in Eq. (2), C 2 is another constant in Eq. (2), • the volume fraction of the internal phase droplet holdup and 8mi. the minimum membrane thickness (m). The above equation was fitted through all the 8 vs. • data of Goswami and co-workers [5] by a least squares method and the following values were obtained by curve fitting: CI = 9.895 × 10 -4 , C 2 = 17.6 and 12.6 × 10 - 6 m
Fig. 1 shows the variation of membrane thickness, 8, with internal phase droplet holdup, qb, for the experimental data of Goswami et al. [5] and the theoretical predictions of both Kataoka et al. [6] and
! 30
-~
. . . . Theoretical ( Kataoka et at. ) J 0 0 Experimental (Goswami et 0.1,~ i
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I
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0.50
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internal droplet holdup,~b Fig. 1. Variation of membrane thickness with internal phase droplet hold up.
132
R. Chakraborty, S. Datta/Journal of Membrane Science 115 (1996) 129-132
the equation proposed in the present study. It is evident from Fig. 1 that Kataoka et al.'s equation fails to predict the actual membrane thickness particularly in the region of high internal droplet holdup. On the other hand, the equation proposed in this study is found to be in excellent agreement with the experimental results of Goswami and co-workers [5] in all regions of internal phase droplet holdup, It should also to be noted that the minimum membrane thickness, 6m~., in Eq. (2) can be evaluated independently. If an emulsion is prepared with ~m~x = 0.74 then the water content of an emulsion drop of radius R is given by Vm = 4 / 3 7 r R 3 ( 1 - ~bmax). (3) When the same emulsion is stirred in the external phase, deformation of the drops take place and q0 in the inner core becomes greater than ~bm~x. So some water drains out of the emulsion to form an outer membrane of minimum thickness, 6mi n. If we denote this ~b after deformation by ~bde f then the initial volume of water is distributed between the inner core and the outer aqueous layer so that Vm = (1 - ~def)4/37r( R -
~min)3
[ ) ] + 4/37r_ R 3 - ( R -- 6min 3. Eqs. (3) and (4) give ~min ] 3 (~rnax = 1 ff)def R )
(4)
(5)
where (~def is the volume fraction of hydrocarbon inside the emulsion drop when deformation has taken place, ~bmax the maximum volume fraction of hydrocarbon in the emulsion corresponding to the closest packing of the non-deformable spheres and R the radius of an emulsion drop (m). In this case the minimum value of membrane thickness (12.6 × 10 - 6 ) is obtained from the above
equation when the value of ~bd~f is equal to 0.84 which is obviously greater than ~bmax.
3, Conclusions An attempt has been made in the present study to develop an equation which would correlate membrane thickness, 6, with the volume fraction of dispersed hydrocarbon phase in the emulsion, ~b. Kataoka et al.'s equation fails to predict the correct membrane thickness in all regions of internal droplet holdup and Goswami and co-workers confined their work only within experimental limits. The proposed equation can predict satisfactorily the membrane thickness in all regions of internal phase droplet holdup and is found to be in excellent agreement with the experimental data of Goswami and coworkers.
References l I] N.N. Li, Separating Hydrocarbonswith liquid membranes, US Pat., 3,410,794 (1968). [2] R.P. Cahn and N.N. Li, Separation of organic compounds by liquid membrane process, J. Membrane Sci., 12 (1976) 129. [3] E.S. Matulivicius and N.N. Li, Facilitated transport through liquid membranes, Sep. Purif. Methods, 4(1) (1975) 73. [4] G. Casamatta, C. Chavarie and H. Angelino, Hydrocarbon separation through a liquid water membrane: modelling of permeation in an emulsion drop, AIChE J., 24 (1978) 945. [5] T.C.S.M. Gupta, A.N. Goswami and B.S. Rawat, Mass transfer studies in liquid membrane hydrocarbon separations, J. Membrane Sci., 54(1990)119. [6] T. Kataoka, T. Nishiki and S. Kimura, Phenol permeation through liquid surfactant membrane-permeation model and effective diffusivity, J. Membrane Sci., 41 (1989) 197. [7] R. Chakraborty and S. Datta, Prediction of membrane thickness in hydrocarbon permeation through liquid surfactant membrane, Sep. Sci. Technol., 29 (1994) 1967. [8] P. Becher, Emulsions, Theory and Practice, 2nd edn., Reinhold, New York, 1965, p. 101.