Ultrafiltration Rate of Sugar Solutions

Transcription

1 Ultrafiltration Rate of Sugar Solutions Shiro Kishihara, Satoshi Fujii and Masahiko Komoto Faculty of Agriculture, Kobe University, Nada-ku, Kobe 657 In application of ultrafiltration, it is very important to predict the permeate flux. For macromolecular solution, many investigations have been presented in the literatures, whereas only a little for micromolecular solutions. For various sugar solutions, ultrafiltration experiments were carried out in a stirred batch cell through different membranes. The effects of feed concentration, temperature, stirring speed and operating pressure on flux were investigated. It was found that the flux could be expressed as a function of viscosity. At the same constant stirring speed and operating pressure, the logarithm of flux inversely related to the logarithm of viscosity. In consideration of Reynolds number, the flux was inversely proportional to viscosity and directly proportional to operating pressure. (Received July 28, 1979) 1. Introduction In recent years membrane ultrafiltration has gained increasing attention as a simple and convenient technique for concentrating, purifying and fractionating the solutions of low-to-high molecular-weight solutes. Both laboratory and industrial applications of ultrafiltration are becoming a reality. In the practical applications, it is very important to predict the ultrafiltration rate. At present, many ultrafiltration applications involve the concentration and/or purification of high-molecularweight (macromolecular) solutes, accompanied by the elimination of water and/or low-molecular-weight (micromolecular) impurities through membrane. A number of theory have been developed for ultrafiltration of such solutions. Michaelsl) has suggested a concentration polarization and gel layer model to develop a basic analysis. De Filippi et al.2) and Blatt et al.3) have discussed the effects of fluid flow situation and solute concentration on flux under the conditions of concentration polarization and gel formation, based on Michaels' expression. Kozinski et al.4), Joseph et al.5) and Probstein et al.8) have presented a boundary layer model, taking into account the viscosity and diffusivity. for the separation and purification of micromolecular solutes. Baker et al.7) have introduced a pore flow model into the permeation mechanism of micromolecular solutions through membrane to develop a equation for ultrafiltration rate which is based on Hagen-Poiseille equation and compensates for the osmotic pressure difference across membrane. Although the estimated fluxes were considerable different from their experimental ones for ultrafiltration of sucrose and raffinose solutions through PM-10 and UM-10 membranes, they concluded that the ultrafiltration can generally be described by a pore flow model. Hashimoto8a) has &scribed that, for the ultrafiltration of 20% glucose solution at 20 `40 Ž, the product of flux and viscosity was a constant value. We have a great interest in estimating the flux on ultrafiltration of a solution containing much micromolecular solutes and little macromolecular solutes such as that of sugar solutions in sugar factory for the purpose of purification or that of caramel color solution for the purpose of quality improvement9-12). This paper examines parameters which determine ultrafiltration rate on various sugar solutions, and develops a equation applied to ultrafiltration of such solutions. On the other hand, ultrafiltration has some promise

2 52 Kishihara, Fujii, Komoto: Ultrafiltration Rate of Sugar Solutions Table 1 Characteristics of membranes (30 Ž, 4kg/cm2) * for 10% sucrose solution 2. Experimental Apparatus and Procedure The ultrafiltration experiments were carried out in a MC-2 type batch cell with an effective area of 10.7 cm2 manufactured by Bio-Engineering Co. Ltd. The membranes used were Amicon PM-10 membrane and Bio-Engineering G-05T and G-05H membranes. The characteristics of membranes are given in Table 1. Samples of feed were 5-70% sucrose, 5-50% glucose, 10-50% washed-sugar and % caramel color solutions. Fifty milliliters of the solution in the cell was ultrafiltrated and the flux was calculated from the flow rate of first 5ml of permeate. The cell was always kept in a constant temperature bath in which the temperature was varied between 20 and 70 Ž. The stirring speed was controlled between 250 and 1500 r.p.m. by varying the speed of magnetic stirrer on which the cell was rested. The stirrer speed was measured by a phototachorneter. The operating pressure was adjusted between 1 and 4 kg/cm2 by nitrogen gas. The values of densities, viscosities and diffusivities of sucrose or glucose solution were available in literature 13-15). In the case of washed-sugar solution, its densities and viscosities were substituted by those of sucrose solution. Densities and viscosities of caramel solution were measured with a picnometer andan Ostwald Fig. 1 Effect of operating pressure on flux ternperature=30 Ž; stirring speed=1,500 r.p.m. of 30 Ž and a stirring speed of 1500 r.p.m. is shown in Fig. 1. In all cases, the flux increased fairly linealy with the operating pressure. This result is similar to one obtained by Baker et al71. A limiting flux which has been observed for a macromolecular solution such as protein4,5,16), dextran17), polyethyleneglycol17 j or surfactant18) solution was not observed in this case. The effect of temperature on flux for PM-10 and G-05T with 10% sucrose solution, G-05H with 5% sucrose solution and PM-10 with 3.5% caramel solution at a pressure of 4kg/cm2 and a stirring speed of 1500 r.p.m. is shown in Fig. 2. The flux increased with the temperature. Similar observations have been also presented for protein solutions3,19-21). In any case, the solution must be kept at higher temperature as long as the feed and the membrane do not suffer from any damage, in order to increase the flux. viscometer, respectively. 3. Results and Discussion In Fig. 3, the fluxes for PM-10, G-05T and G-05H with sucrose solution and PM-10 with caramel solution at a temperature of 30 Ž and a stirring speed of Effects of feed concentration and operating conditions on flux The effect of operating pressure on flux for PM-10, G-05T and G-05H with 10% sucrose solution and PM-10 with 3.5% caramel solution at a temperature r.p.m. are plotted against the logarithms of feed concentrations. As presented in the previous paper"), the curve for PM-10 with caramel solution was approximately linear, whereas the curve for other systems were nonlinear.

3 Fig. 2 Effect of temperature on flux Fig. 3 Effect of feed concentration on flux stirring speed=1, 500 r.p.m.; operating pressure,=4kg/cm2 temperature=30 Ž. stirring speed=1, 500 r.p.m.; The stirring speed had also influence on the fluxes. operating pressure-=4kg/cm2 Reynolds number can be applied to examine the effect of stir ring speed on flux at a constant feed concentration, temperature and operating pressure. The fluxes on 10% sugar and 7% caramel solutions at a temperature of 30 Ž and a pressure of 4kg/cm2 are plotted against the Reynolds numbers in Fig. 4. The stirring speed was varied from 250 to 1500 r.p.m. The speed of 1500 r.p.m. corresponds to Reynolds number of and for 10% sucrose and 7% caramel solution, respectively. The linearrelationships between the logarithms of fluxes and the logarithms of Reynolds numbers were observed. The slopes obtained from Fig. 4 were 0.077, 0.077, 0.081, 0.20, and 0.45 for PM-10 with glucose, PM-10 with sucrose, G-05T with sucrose, G-05H with sucrose, PM-10 with washed-sugar and PM-10 with caramel solution, respectively. The slopes were smaller than those ( )8a) generally observed and, especially, those for sucrose solutions were very small. It was found that Reynolds number (stirring speed) had a small,effect on the flux. The rejection of sucrose through PM-10, G-05T and G-05H are small as given in Table 1, and the rejection of compounds in caramel solution through PM-10 is seemed to be also small, since the content of compounds with molecular-weight below 1000 attains to 77.1% on total solidll). Because of the lower rejection, it is clear that the concentration polarization on the membrane surface occurs only to a small extent. We believe that no observation of a limiting flux and small effect of Reynolds number on flax are explained by the insufficient boundary layer. 3.2 Correlation of flux with viscosity Changes in flux with temperature and feed concentration are usually explained in terms of changes in diffusivity and viscosity. The flux for G-05T with sucrose solution at a pressure of 4kg/cm2 and a stirring speed of 1500 r.p.m. is plotted against diffusivity or viscosity in Fig. 5. The linear relationships between the logarithms of fluxes and the logarithms of diffusivities were obtained at the constant temperatures or feed concentration. The flux was largely affected by the diffusivity but could not be described as a function of diffusivity alone. On the other hand, a linear relationship between the logarithms of fluxes and the logarithms of viscosities was obtained over a wide range of feed concentration and temperature. For the other systems at a pressure of 4k g/cm2 and a stirring speed of 1500 r.p.m., the fluxes

4 54 Kishihara, Fujii, Komoto: Ultrafiltration Rate of Sugar Solutions Fig. 4 Relationship between flux and Reynolds number Fig. 5 Correlation of flux with viscosity or diffusivity Table 2 Values of a and 48 in Eq. (1) Table 3 The ratio of viscosity of permeate to feed for G-05H with sucrose solution are plotted against the viscosities in Fig. 6. There existed obvious proportional relationships between the fluxes and viscosities on logarithmic coordinates for all systems. This suggested that the permeation of these solutions through membranes is mainy performed by a pore flow. From the linear relationships between fluxes and viscosities, the flux can be related solely to viscosity by the following equation (1) where the values of ƒ and ƒà are dependent on the characteristics of membrane and solute, and independent of the feed concentration and temperature. Experimentally determined ƒ and ƒà are listed in Table 2. Assuming that the permeation of solution through membrane is a pore flow, the flux must be in inverse proportion to the permeate viscosity. The ratio of viscosity of permeate to that of feed sucrose solution was nearly equal to 1. Even for G-05H, as given in Table 3, the ratio was about 0.94 and, moreover, could be

5 Table4 Modified fluxes (j m) corresponding to viscosity of water at 30 Ž and their ratios (J/m/J/w) to fluxes of water ed-sugar contains also moderate molecular solutes, whose content is much lower than that in caramel color. This is a reason from which ƒà for washed-sugar solution is smaller than one for sucrose solution and larger than one for caramel solution. It may be also considered as another reason for the reduced value of ƒà that macromolecular solute plugs the membrane pore and/or forms the gel layer on the membrane surface to reduce appa Fig. 6 Correlation of flux with viscosity rently the pore size. It is considered that the values of a are dependent on the flux resistances of membrane and gel layer, as the ratios (Table 4) of modified flux to flux of water are also dependent on those resistances. That will be discussed later. 3.3 An equation for ultrafiltration rate Baker et al. have developed a following equation based on a pore flow model 7). regarded as constant, independent of the feed concentration. Therefore, if concentration polarization did not occur, the flux would be inversely proportional to the viscosity, that is, the value of would be-1. The values of 13 for sucrose solutions were observed to decrease with the decrease in the molecular-weight cut-offs of membranes. It seems that concentration polarization increases with the decrease in the pore size and then makes the value of p fall below -1. Caramel color contains the compounds over a wide range of molecularweight") and some of them (moderate molecular solutes) enter into the membrane pores, forming a large concentration polarization. This may explain that /3 for caramel solution is smaller than that for sucrose solution. Wash- (2) Their ratios of experimental fluxes to calculated ones were significantly smaller than 1 and, furthermore, the deviations were strongly dependent on the sugar concentrations. Application of our data to Eq. (2) results in essentially the same profile as theirs. In the development by Baker et al., the fluid flow situation was not considered. Eq. (1) did not also considered the fluid flow situation. Then, the effect of fluid flow situation which is apparently related to the concentration polarization on the flux was examined. Reynolds number is an applicable parameter for the fluid flow situation. There is a corre-

6 56 Kishihara, Fujii, Komoto: Ultrafiltration Rate of Sugar Solutions lation of flux with Reynolds number as illustrated in Fig. 4. In order to modify the effect of Reynolds number on flux, the respective fluxes in Fig. 6 were multiplied by (Re m/re)a Here, Re m is defined as the maximum Reynolds number in the given apparatus and a is the slope of respective lines in Fig. 4. In this paper, the maximum Reynolds number (47000) is got at a temperature of 70 Ž and a stirring speed of 1500 r.p.m. in the use of water. As the result, all the slopes of respective straight lines between the modified flux, J E(Re m/re)a and the viscosity on logarithmic coordinates became-1. That is, the fluxes were inversely affected by the viscosities. From this relationship, the modified fluxes corresponding to the viscosity of water at 30 Ž were obtained, Fig. 7 Correlation of flux with Rea /p and also those fluxes were average values of the product of respective modified fluxes and a/pw. These values and their ratios to the fluxes of water in Table 1 are given in Table 4. The ratio for PM-10A membrane with glucose or sucrose solution was nearly equal to unit and the ratios for PM-10B, G-05T and G-05H membrane with sucrose solution decreased with the increase in rejection of sucrose. It seems that this phenomenon occurred because a larger frictional resistance, namely, crowding effect* for the membrane with the l arger rejection arises near the pore inlet. In the case of PM-10B membrane, the ratios for washed-sugar and caramel solution were smaller than that for sucrose solution. It is apparent that the ratios were reduced by the gel layer formed secondarily of the macromolecular solutes. The caramel color included much more macromolecular solutes than washed-sugar but the ratio for caramel solution was larger than that for washedsugar solution. From this results, we believe that the :formtion of gel layer macromolecular solutes in caramel soluton is not easier than that in washed-sugar solution. In general, it has been seen that the flux is reduced with an increase in osmotic pressure difference between upstream solution and permeate3). Eq. (2) embodies the effect of osmotic pressure difference in a correction. As can be seen from Fig. 1, the response curves of flux to operating pressure are straight lines which go through * This word has be also used by Baker et al.7) the origin. Therefore, the effect of osmotic pressure difference on flux can be negligible. Combining the correlations of flux with Reynolds number, viscosity and operating pressure, the flux can be expressed by Eq. (3). (3) Here, A is the flux of water per unit operating pressure, namely, water permeability coefficient. k is a constant which is dependent on the caracteristics of membrane, feed solution and apparatus, and is equal to the ratio of modified flux to flux of water in Table 4. Finally, the flux could be expressed as a function of Reynolds number, viscosity and operating pressure, and was independent of the feed concentration, temperature and stirring speed. As k, A and Re M are determined when apparatus, membrane and feed solution are fixed, the flux should be proportional to Real g. Then, the fluxes are plotted against Real p on logarithmic coordinates in Fig. 7. The slopes of respective straight lines are 1. It was

7 Fig. 8 Relationship between flux and Reynolds number for CL-500 hollow-fiber module with caramel solution Fig. 9 Ratio of experimental flux to calculated one as a function of viscosity for CL-500 hollow-fiber module with caramel solution found that the ultrafiltration of sugar and caramel solutions with batch cell can be well explained by Eq. (3). Eq. (3) was also applied to the ultrafiltration data in the previous paper 12). The data were obtained for 2 `30% caramel solution at a temperature of 29,..50 Ž, a pressure of 1 kg/cm2 and a flow rate of 0.75, `2.1 /hr in the use of CL-500 hollow fiber module m3 whose specification were molecular-weight cut-off of 13,000, inside diameter of fiber of 0.8mm and effective area of membrane of 0.2m2. When 2% caramel solution (44 ) or 10% caramel solution (35 Ž) was ultrafiltered at a flow rate between 0.75 and 2.1m3/hr, the relationships between flux and Reynolds number were obtained (Fig. 8). The effect of Reynolds number above 2700 on flux differed from that below The slopes of response curves for both 2% and 10% caramel solutions on logarithmic coordinates were 0.32 for Reynolds Ž 4. Conclusions From the ultrafiltration data for various sugar solutions and caramel solution, the following conclusions are made. 1. In agreement with general tendency predicted by theoretical considerations, the permeate flux increased with the decrease in feed concentration and with the increase in temperature, stirring speed and operating pressure. In contrast with protein solutions, the flux on sugar solutions was affected to slight extent by the changes in stirring speed, and a limiting flux was not observed at increased pressure. 2. At the constant operating pressure and stirring speed, the linear relationships between flux and viscosity were obtained on logarithmic coordinates. 3. In consideration of Reynolds number, the flux was expressed by Eq. (3) containing Reynolds number, viscosity and operating pressure. number above 2700 and 0.84 for below Using these slopes as a, 0.68 as k, 0.42m//cm2.min E(kg/cm2) as A and 7000 as Rem, the fluxes were calculated from Eq. (3). The ratios of experimental fluxes to calculated ones are plotted against the viscosities in Fig. 9. The calculated fluxes were in satisfactory agreement with the experimental ones. Thus Eq. (3) would be useful in predicting the ultrafiltration rate of a solution containing much micromolecular solutes and less macromolecular solutes, such as caramel solution or sugar solution in sugar factory. Nomenclature A= water permeability coefficient [ml/cm2. min. (kg/cm2)] J= volume flux of solution [ml/cm2.min] Jw= volume flux of water [ml/cm2.min] Re Reynolds number[-] Rem= maximum Reynolds number [-] a slope of log J vs. log Re k= constant in Eq. (3) P= operating pressure [kg/cm2] ƒî = osmotic pressure difference [kg/cm2] ƒê= viscosity of solution [c.p.]

8 ƒ 58 Kishihara, Fujii, Komoto: Ultrafiltration Rate of Sugar Solutions ƒêw= viscosity of water [c.p.],ƒà=constants in Eq.(1) References 1) A. S. Michaels: Chem. Eng. Prog., 64, 31 (1968) 2) R. p.de Filippi and R. L. Goldsmith: "Membrane Science and Technology" (ed. by J. E. Flinn), p.33, Plenum Press, New York (1970) 3) W. F. Blatt, A. Dravid, A. S. Michaels and L. Nelson: "Membrane Science and Technology" (ed. by J. E. Flinn), p.47, Plenum Press, New York (1970) 4) A. A. Kozinski and E. N. Lightfoot: A. I. Ch. E. J., 18, 1030 (1972) 5) J. S. Joseph and R. F. Probstein: Ind. Eng. Chem., Fundam., 16, 459 (1977) 6) R. F. Probstein, W. F. Leung and Y. Alliance: J. Phys. Chem., 83, 1228 (1979) 7) R. W. Baker, F. R. Eirich and H. Strathmann: J. Phys. Chem., 76, 238 (1972) 8) K. Hashimoto and B. Hagiwara: "Maku niyoru Bunriho", a) p.92, b) p.99, Kodan3ha, Tokyo (1974) 9) M. Komoto, S. Fujii and M. Ozasa: Proc. Rec. Soc. Japan Sugar Refineries' Technologists, 27, 24 (1977) 10) S. Kishihara, S. Fujii and M. Komoto: Kagaku Kogaku Ronbunshu, 2, 445 (1976) 11) S. Fujii, S. Kishihara and M. Komoto: Nippon Shokuhin Kogyo Gakkaishi, 24, 236 (1977) 12) S. Kishihara, M. Komoto and D. Nomura: N ppon Nogeikagaku Kaishi, 53, 305 (1979) 13) W. R. Junk and H. M. Pancoast: "Handbook of Sugars", p.48, p.160, p.161, The AVI Pub. Corn. INC, Westport, Connectcut (1973) 14) D. Schliephake and F. Schneider: Zuker, 18, 138 (1965) 15) Seito Gijutsu Kenkyukai: "Seito Binran", p , Asakura Shoten, Tokyo (1962) 16) R. W. Baker and H. Strathrnann: J. Appl. Polym. Sci., 14, 1197 (1970) 17) R. L. Goldsmith: Ind. Eng. Chem., Fundam., 10, 113 (1971) 18) R. B. Grieves, D. Bhattacharyya, W. G. Schomp and J. L. Bewley: A. I. Ch. E. J., 19, 766 (1973) 19) D. E. Eakin, R. p.singh, G. 0. Kohler and B. Knuckles: J. Food Sci., 43, 544 (1978) 20) D. E. Hensley, J. T. Lawhon, C. M. Cater and K. F. Mattil: J. Food Sci., 42, 812 (1977) 21) J. T. Lawhon, S. H. Lin, C. M. Cater and K. F. Mattil: Cereal Chem., 52, 34 (1975)