Effect of surfactant type on microbubble formation behavior using Shirasu porous glass (SPG) membranes

Colloids and Surfaces A: Physicochem. Eng. Aspects 326 (2008) 129–137

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Effect of surfactant type on microbubble formation behavior using Shirasu porous glass (SPG) membranes Masato Kukizaki a,∗ , Yoshinari Baba b a b

Miyazaki Prefecture Industrial Technology Center, 16500-2 Higashi-kaminaka, Sadowara, Miyazaki, 880-0303, Japan Faculty of Engineering, Department of Applied Chemistry, University of Miyazaki, 1-1, Gakuen Kibanadai Nishi, Miyazaki, 889-2192, Japan

a r t i c l e

i n f o

Article history: Received 11 December 2007 Received in revised form 16 May 2008 Accepted 18 May 2008 Available online 24 May 2008 Keywords: Monodispersed microbubbles Shirasu porous glass membrane Surfactant Gaseous-phase flux

a b s t r a c t We have recently proposed a new method for generating monodispersed microbubbles from Shirasu porous glass (SPG) membranes with a narrow pore size distribution. In this study, to investigate the effects of surfactant type on microbubble formation behavior from SPG membranes, the microbubble formation experiments were performed using differently charged surfactants. Sodium n-dodecylbenzenesulfonate (SDBS), polyoxyethylene (20) sorbitan monolaurate (Tween 20) and cetyltrimethylammonium bromide (CTMA) were used as anionic, nonionic and cationic surfactants, respectively. Air was pressurized into a surfactant solution of 2.0 mol m−3 through an SPG membrane with a mean pore diameter of 5.1 ␮m at a transmembrane/bubble-point pressure ratio of 1.1. In systems containing SDBS and Tween 20, monodispersed microbubbles with mean bubble diameters of 35.6 and 43.0 ␮m were generated, respectively, from the membrane. The CTMA-containing system resulted in polydispersed bubble formation, due to the adsorption of CTMA molecules (cations) onto the negatively charged membrane surface, which lowered the hydrophilicity of the membrane surface. The microbubbles generated were smaller for SDBS than for Tween 20. This is probably because for the case of SDBS, the microbubbles detached from the pores as soon as they were formed, due to a strong electrostatic repulsion between the negatively charged bubble surface and the negatively charged membrane surface, which assists in microbubble detachment from the pore openings. The gaseous-phase flux was about 11–15 times larger for Tween 20 than for SDBS, but much smaller for CTMA, which is a consequence of the fact that the proportion of active pores is significantly lower for SDBS than for both Tween 20 and CTMA. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Microbubbles have many potential applications in such areas as the pharmaceutical, food, chemical, and cosmetic industries. In the field of medicine, microbubbles are expected to be applicable to areas such as the development of ultrasound contrast agents and targeted drug delivery [1–6], while in the food industry, the density and texture of, for example, gel and cream-based foods would be controlled by the uniform and fine dispersal of bubbles into these materials [7]. Furthermore, in the chemical industry, microbubbles are expected to be applicable to the development of porous materials such as microcellular plastic foam [8]. The size control of the microbubbles produced is critical in all these applications. In addition, surfactants must be added to the water phase in these applications to facilitate microbubble formation and to stabilize the formed microbubbles. Surfactants have two main roles to play

∗ Corresponding author. Tel.: +81 985 74 4311; fax: +81 985 74 4488. E-mail address: [email protected] (M. Kukizaki). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.05.025

in bubble formation [9]: first, surfactant molecules adsorb to the newly formed gas-water interface to reduce the gas-water interfacial tension and consequently to facilitate microbubble formation, second, surfactants stabilize the formed microbubbles against coalescence and/or aggregation. Therefore, the choice of surfactant is very important for these applications. With regards monodispersed microbubble formation, several papers have been published to date [7,10–14]. For example, Ganan-Calvo and Gordillo [7] first described the formation of monodispersed microbubbles in capillaries by the flow-focusing method. Garstecki et al. [10,11] reported a microfluidic method for the direct on-chip generation of monodispersed microbubbles. Yasuno et al. [12] showed that monodispersed microbubbles were generated using a microfabricated silicon microchannel. Moreover, Xu et al. [13] described the formation of monodispersed microbubbles using the cross-flowing rupture technique in a microfluidic device. We have recently proposed a new method for generating monodispersed microbubbles [14,15] using Shirasu porous glass (SPG) membranes having a narrow pore size distribution [16–18]. This technique allows monodispersed microbubble formation by

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Nomenclature A Db Dm E Jg k Mw pm PBP Pr P q Q Rm tf u Vb Vp x

effective membrane area (m2 ) mean bubble diameter (m) mean pore diameter (m) streaming potential (V) gaseous-phase flux (m3 m−2 s−1 ) proportion of active pores molecular weight (g mol−1 ) membrane porosity bubble point pressure (Pa) ratio of transmembrane pressure to bubble point pressure transmembrane pressure (Pa) volumetric air flow rate through a single pore (m3 s−1 ) volumetric air flow rate through a membrane (m3 s−1 ) hydrodynamic resistance of the membrane (m−1 ) bubble formation time (s) gaseous-phase velocity through a single pore (m s−1 ) volume of a bubble (m3 ) pore volume per unit membrane mass (m3 kg−1 ) membrane thickness (m)

Greek letters ε0 permittivity of free space (C2 J−1 m−1 ) εr relative permittivity of water phase g viscosity of gaseous phase (Pa s) viscosity of water phase (Pa s) w w conductivity of water phase (−1 m−1 )  contact angle between the membrane surface and water phase (◦ ) true density of membrane (kg m−3 ) m pore tortuosity

zeta potential of membrane (V) Subscripts b bubble g gaseous phase m membrane w water phase

forcing a gaseous phase into a water phase containing a surfactant through an SPG membrane under suitable conditions. The size and size distribution of the microbubbles generated from SPG membranes are affected by various operating and process parameters: membrane pore size [14,19], pore uniformity [14,19], membrane wettability [20], transmembrane pressure [14,19], cross-flow velocity of the water phase [19], water phase viscosity [15], and gas-water interfacial tension (surface tension) [19]. With this method, the addition of surfactants to the water phase is essential for monodispersed microbubble formation, and thus the surfactants would have a profound effect on the microbubble formation behavior. In our previous study, we reported on the effect of surfactant concentration on bubble formation from SPG membranes in an airwater dispersion system containing sodium dodecyl sulfate (SDS) as an anionic surfactant [19]. The experimental results showed that the resulting bubble size was barely affected by the surfactant concentration between air and the SDS solution of 0.05–0.5 wt.%, corresponding to the surface tension of 58.0–36.5 mN m−1 . By contrast, larger polydispersed bubbles were generated from the

membrane at very low SDS concentrations (less than 0.05 wt.%, corresponding to less than the surface tension of 58.0 mN m−1 ). This is most likely because the probability of bubble coalescence at the membrane surface increases due to the unsaturated adsorption of SDS molecules (ions) at the newly formed air-water interface during bubble formation [19]. However, the influence of surfactant type on bubble formation has not been investigated to date. The objective of the present study is therefore to investigate the effect of surfactant type on microbubble formation from SPG membranes. Using three different types of surfactants (cationic, anionic and nonionic surfactants), the effects of the surfactant type on the degree of the monodispersity of microbubbles formed, bubble/pore diameter ratio, and gaseous-phase flux were examined. The interaction between the membrane surface and the hydrophilic groups of the surfactant during microbubble formation are also discussed. 2. Experimental 2.1. Materials The gas-liquid dispersion system was composed of air and aqueous solution of 10 mol m−3 KCl containing a surfactant. Sodium n-dodecylbenzenesulfonate (SDBS; molecular weight, Mw = 349 g mol−1 ), polyoxyethylene (20) sorbitan monolaurate (Tween 20, Mw = 1228 g mol−1 ) and cetyltrimethylammonium bromide (CTMA, Mw = 364 g mol−1 ), were, respectively, used as anionic, nonionic and cationic surfactants. To determine the critical micelle concentration (cmc) of these surfactants, the relationship between the air-water surface tension and surfactant concentration of the water phase was measured by the Wilhelmy-plate method using a surface tensiometer (CBVP-A3, Kyowa Interface Science Co., Ltd., Saitama, Japan) at 298 K. As shown in Fig. 1, the cmc values of SDBS, Tween 20 and CTMA were determined as 0.50, 0.14 and 0.11 mol m−3 , respectively. Thus, each surfactant concentration was set at 2.0 mol m−3 higher than its cmc [19]. The pH values of all the water phases measured with a Digital-pH-meter (HM-20J, DKKTOWA Co., Ltd., Tokyo, Japan) were in the range from 6.8 to 7.0. SDBS (reagent grade) was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). KCl, Tween 20 and CTMA (all reagent grade) were also purchased from Wako Pure Chemical Industries Co., Ltd.

Fig. 1. Relationship between air-water surface tension and surfactant concentration. () SDBS, () Tween 20, and () CTMA.

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Table 1 The measured values of mean pore diameter and porosity of SPG membranes used in this study Mean pore diameter, Dm (␮m)

Membrane porosity, pm (–)

1.0 3.1 5.0 10.0

0.58 0.55 0.57 0.58

(Tokyo, Japan). Air cylinders (synthetic air, purity > 99.999%) were obtained from Japan Fine Products Co., Ltd. (Tochigi, Japan). 2.2. SPG membranes Flat SPG membrane disks (10 mm × 40 mm, and 0.5 mm in thickness) with four different mean pore diameters of 1.0, 3.1, 5.0 and 10.0 ␮m were prepared by phase separation of the mother glass in the Na2 O–CaO–MgO–Al2 O3 –B2 O3 –SiO2 system and subsequent acid leaching. The preparation procedures of the membranes have been described previously [18]. In this case, the SPG membranes have uniform-sized pores that form a three-dimensional network, reflecting the phase-separated structure of the mother glass [17,18]. The mean pore diameters and porosities of all the membranes determined with a mercury porosimeter (Poresizer 9320, Micromeritics Co., Ltd., USA) are listed in Table 1. The mean pore diameter was expressed as the diameter corresponding to 50 vol.% on a relative cumulative pore diameter distribution curve. The porosity, pm was calculated using the following equation: pm =

Vp Vp + (1/m )

(1)

where Vp is the membrane pore volume per unit membrane mass, which was determined with the above mercury porosimeter in this study; and pm is the true density of the membrane, which was determined with a pycnometer (Quantachrome-1000, YUASA-IONICS, Co., Ltd., Osaka, Japan). The zeta potentials of the SPG membranes were determined by the streaming potential method [21,22], in which the streaming potential, E was created by a pressure drop over the membrane (transmembrane pressure, P), and the zeta potential, was then calculated using the Helmholtz-Smoluchowski equation [23,24]:

=

4w w E ε0 εr P

(2)

where w and w are the viscosity and conductivity of the water phase, respectively, ε0 is the permittivity of free space, and εr is the relative permittivity of the water phase. KCl was used as a supporting electrolyte. A pair of platinum black electrodes was located on both sides of the membrane. The membrane module was initially filled with the water phase. The transmembrane pressure was then applied by the following three steps [21]: (1) pressurizing from 0 to 50 kPa, (2) maintaining pressure, and (3) depressurizing to 0 kPa. The viscosity of the water phase was measured using a rotational viscometer (DVL-B, TOKIMEC Co., Ltd., Tokyo, Japan). The conductivity of the water phase was measured with a conductivity meter (ES-12, Horiba Co., Ltd., Kyoto, Japan). The relative water-phase permittivity was approximated to that of water. All measurements were carried out at 298 K. Zeta potentials were calculated from measured values of E/P using Eq. (2). The contact angles of the SPG membranes were evaluated from the following [20]: as the temperature is raised above 873 K, nonporous and smooth glass plates can be prepared from flat SPG membranes [17]. By this treatment, the silanol groups on the glass surface condense to form siloxane groups and water is evolved, as shown in Fig. 2(a). Because the siloxane groups are essentially

Fig. 2. (a) Dehydration of the silanol groups and rehydration of the siloxane groups on an SPG membrane or the resultant glass plate and (b) dissociation of the silanol group on the surface of the SPG membrane surface.

hydrophobic [25], the hydrophilicity of the calcined glass plate would be lower than the SPG membrane. However, when the glass plate is immersed into a hydrochloric acid solution, the siloxane bonds on the surface react with water to regenerate silanol groups [26]. Therefore, if the SPG membrane is calcinated above 873 K and then the resultant glass plate is immersed into a hydrochloric acid solution, the density of the silanol groups on the SPG membrane surface would be the same as that of the silanol groups on the surface of the glass plate. Consequently, the surface wettability of the glass plate would be identical with that of the SPG membrane. In this study, non-porous glass plates were prepared by heating SPG membranes at 1023 K for 3 h and then were immersed into a hydrochloric acid solution of 2 mol dm−3 . The contact angles of the water-phase droplets on the surface of the glass plates were then measured by the sessile drop method using a contact angle meter (DropMaster 500, Kyowa Interface Science Co., Ltd., Japan) at 298 K. 2.3. Formation of microbubbles and measurements of the bubble size distribution The bubble formation experiments were performed in a fused silica optical cell (10 mm × 40 mm × 50 mm, and 2 mm in thickness), which was placed in a particle size distribution analyzer (SALD2100, Shimadzu Co., Ltd., Kyoto, Japan) employed for measuring the bubble diameter distribution (Fig. 3). An SPG membrane disk was attached to the bottom of an optical cell, using a silicone rubber seal. The cell, with an inner volume of 10.8 cm3 , was initially filled with a water phase. Air (gaseous phase) was introduced to the undersurface of the membrane and gradually forced into the flowing water phase through the membrane, while the cell was simultaneously irradiated with laser light of wavelength 690 nm at 298 K. The transmembrane pressure was calculated as the difference between the air pressure and mean pressure of the water phase. The flow rate of the water phase was kept constant at 20 cm3 h−1 . When microbubbles began form from the SPG membrane, a light diffraction/scattering peak was detected using the laser diffraction particle size analyzer. Thus, the bubble point pressure was determined by measuring the transmembrane pressure at which the light diffraction/scattering peak began to be detected. The observed bubble point pressures in this study are listed in Table 2. At transmembrane pressures larger than the bubble point pressure, the diameter distributions of the microbubbles formed from the membrane were measured using the above particle

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M. Kukizaki, Y. Baba / Colloids and Surfaces A: Physicochem. Eng. Aspects 326 (2008) 129–137 Table 2 The observed values of bubble point pressures for surfactant solutions Mean pore diameter, Dm (␮m)

Surfactant

Bubble point pressure, PBP (kPa)

1.0

SDBS Tween 20 CTMA

125 148 89

3.1

SDBS Tween 20 CTMA

34 48 20

5.0

Freea SDBS Tween 20 CTMA

51 19 22 13

10.0

SDBS Tween 20 CTMA

9 13 4

a

Fig. 3. Schematic diagrams illustrating the bubble formation from a flat SPG membrane disk, and the measurement of the bubble size distribution by the laser diffraction method.

size distribution analyzer [14,15]. The transmembrane pressures were applied in the range from 9 to 148 kPa, corresponding to the transmembrane/bubble-point pressure ratio of 1.00–1.55. The refractive index of air (1.0) was used. This analyzer allowed the detection of bubbles in the range of 0.05–1000 ␮m. In all of the experiments, no light diffraction/scattering peak of the water phase

10 mol m−3 KCl aqueous solution.

before bubble formation was detected. The mean bubble diameter expressed as the bubble diameter corresponding to 50 vol.% on a relative cumulative bubble diameter distribution curve. The flux of the gaseous phase (air), Jg was calculated using the following [19]: Jg =

Q A

(3)

where Q is the volumetric flow rate of the air measured using a flow meter and expressed as atmospheric pressure (101.3 kPa); and A is the effective membrane area (2.16 cm2 in this study). For the cases of SDBS and Tween 20, the microbubbles generated from the 5.0 ␮m-membrane were observed using an optical microscope (BHS-323, Olympus Co., Ltd., Japan).

Fig. 4. Diameter distributions of bubbles formed from an SPG membrane with a mean pore diameter of 5.0 ␮m using (a) SDBS, (b) Tween 20, (c) CTMA. (d) Diameter distribution of the generated bubbles when using a water phase without surfactant. Transmembrane/bubble-point pressure ratio was set at 1.1. All surfactant concentrations were 2.0 mol m−3 .

M. Kukizaki, Y. Baba / Colloids and Surfaces A: Physicochem. Eng. Aspects 326 (2008) 129–137 Table 3 The measured values of zeta potential and contact angle of an SPG membrane with a mean pore diameter of 5.0 ␮m, and air-water surface tension Surfactant

Zeta potential,

(mV)

Contact angle,  (◦ )

Surface tension,

(mN m−1 )

Freea SDBS Tween 20 CTMA

−31.3 −25.3 −20.3 −1.8

22 8 13 55

73.1 29.6 37.2 26.6

a

10 mol m−3 KCl aqueous solution.

3. Results and discussion 3.1. Zeta potential and contact angle of an SPG membrane As listed in Table 3, the measured values of the zeta potential and contact angle of an SPG membrane with a mean pore diameter of 5.0 ␮m were respectively - 31.3 mV and 22◦ in a 10 mol m−3 KCl aqueous solution. These results indicate that the membrane is negatively charged and hydrophilic in this condition due to the presence of hydroxyl groups such as silanol groups on their surface [26–28]. The dissociation of the silanol groups on the membrane surface occurs, as shown in Fig. 2(b) [26]. 3.2. Effect of surfactant type on the size and size distribution of microbubbles The effect of surfactant type on the bubble size and size distribution using a 5.0-␮m membrane was investigated. Fig. 4 shows the diameter distributions of bubbles generated from the SPG membrane in the system without surfactant (in a 10 mol m−3 KCl solution), and in the systems containing SDBS, Tween 20 and CTMA at a transmembrane/bubble-point pressure ratio of 1.1. For the case without surfactant, polydispersed large bubbles with a mean bubble diameter of 729 ␮m were formed, as shown in Fig. 4(d). This is probably because the formed microbubbles immediately coalesced at the pore openings. A similar phenomenon was observed for microbubble formation from a microfabricated silicon microchannel in a system consisting of air and a water phase without

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surfactant [12]. Yasuno et al. [12] used a silicon microchannel plate to observe the in situ formation of individual microbubbles using an optical microscope equipped with a video recording facility. They observed that in the system without surfactant, monodispersed microbubbles formed at the outlets of the microchannel and immediately coalesced, while in systems containing sodium dodecylsulfate (SDS) and Tween 20, monodispersed microbubble formation occurred from the microchannel. For the cases of SDBS and Tween 20, monodispersed microbubbles with a mean bubble diameter of 35.6 and 43.0 ␮m were formed, as shown in Fig. 4(a) and (b). Fig. 5 shows the optical micrographs of the microbubbles generated from the 5.0 ␮m-membrane using both surfactants. By contrast, the CTMA-containing system resulted in the formation of polydispersed bubbles with a mean bubble diameter of 63.2 ␮m (Fig. 4(c)). 3.3. Analysis of bubble formation behavior for anionic, nonionic and cationic surfactants From these experimental results, the effect of the surfactant type on the bubble formation behavior using SPG membranes is discussed. Maintaining the hydrophilicity of the SPG membrane surface is necessary for achieving monodispersed microbubble formation from the membrane [20]. The interaction between the surfactant and membrane surface is a key factor that affects the hydrophilicity of the membrane surface. The zeta potential of the membrane is also an important parameter, and is indicative of the interaction between surfactants and the membrane surface. Moreover, the contact angle is an important parameter in understanding the wettability of the membrane surface in the water phase. Table 3 shows the measured zeta potentials of the 5.0-␮m membrane, and the contact angles formed between the membrane surface and the water phase for the experimental systems. For the case of SDBS, an electrostatic repulsive interaction exists between the anionic polar groups of the SDBS molecules (ions) and the negatively charged membrane surface. For Tween 20, although no strong repulsion exists between the hydrophilic groups of the Tween-20 molecules and the membrane surface, a hydrated layer still covers the hydrophilic groups of the membrane. Therefore, the membrane

Fig. 5. Optical micrographs of the microbubbles generated from an SPG membrane with a mean pore diameter of 5.0 ␮m using (a) SDBS and (b) Tween 20 at a transmembrane/bubble-point pressure ratio of 1.1. Both surfactant concentrations were 2.0 mol m−3 .

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surface can be kept hydrophilic during bubble formation. For SDBS and Tween 20, the original membrane had low contact angles of 8◦ and 13◦ , respectively, which support the idea that the membrane surface remains hydrophilic during microbubble formation. We believe that the monodispersed microbubble formation for SDBS and Tween 20 can be explained by the above elucidations. The measured surface tension of 26.6 mN m−1 for the CTMA solution was lower than that for the SDBS and Tween-20 solutions, as listed in Table 3. This result indicates that CTMA has an adequate surface activity, as compared with SDBS and Tween 20. However, the addition of CTMA to the water phase brought about an increase in the measured value of the contact angle from 22◦ to 55◦ . The cationic polar groups of the CTMA molecules (ions) are attracted to the negatively charged membrane surface. This electrostatic attractive interaction between the surfactant and the membrane surface causes the adsorption of the surfactants to the membrane surface, which leads to a decrease in the absolute zeta potential value of the membrane from 31.3 to 1.8 mV, as listed in Table 3. As a result, the hydrophilicity of the membrane surface becomes lower, and thus, the contact angle between the membrane surface and water phase increases. In our previous study [20], we reported that monodispersed microbubbles were generated from SPG membranes with a contact angle smaller than 45◦ , while polydispersed larger bubbles were generated from membranes with a contact angle larger than 45◦ . This means that the hydrophilicity of the SPG membrane surface appears essential to the monodispersed microbubble formation from the membrane. In the contact-angle range of 0◦ <  < 45◦ , the formation of bubbles at the pore openings occurs at a fixed diameter of the three-phase line [20,29], as illustrated in Fig. 6(a). When the bubble volume reaches a certain value, the bubble detaches by necking and the mean bubble diameter is almost independent of the contact angle [20]. By contrast, at a contact angle larger than 45◦ , the lowering of the membrane hydrophilicity would facilitate the three-phase line expansion [20,29]. After a bubble exits from the pore opening, the three-phase line expands and consequently the bubble-membrane contact area spreads over several pore openings, as illustrated in Fig. 6(b). As a result, a growing bubble can be fed by several pores simultaneously. The larger bubble finally detaches from the membrane surface due to the shear force caused by the water phase flow [13,19]. We can conclude that the above explanations resulted in the formation of larger polydispersed bubbles in the systems where the functional groups of the surfactant have a charge opposite to that of the membrane surface. 3.4. Effect of surfactant type on mean bubble/pore diameter ratio The effect of surfactant type on bubble/pore diameter ratio was investigated using SDBS, Tween 20 or CTMA. Fig. 7 shows the relationship between the mean bubble diameter and mean pore diameter of the membrane at a transmembrane pressure 1.1 times higher than each bubble point pressure. For the cases of SDBS and Tween 20, the mean bubble diameter increased linearly with increasing mean pore diameter. The mean bubble/pore diameter ratio, Db /Dm was 7.6 for SDBS, but 9.2 for Tween 20. In general, the sign of the microbubble charge is determined by the polar groups of the surfactant molecules adsorbed on its surface [30,31]. For example, the zeta potential of the nanobubbles generated by ultrasonication with SDS as an anionic surfactant was found to be ca. −50 mV in a KCl solution of 10 mol m−3 at pH 7, while that of the nanobubbles generated with Tween 20 as a nonionic surfactant was ca. −7 mV under the same conditions [30]. For the case of SDBS, the microbubbles generated would be negatively charged because SDBS ions are adsorbed on the bubble surface. Due to strong electrostatic repulsions between the negatively charged microbubbles and

Fig. 6. Schematic representation of bubble formation from the pore openings of a porous membrane with (a) a small contact angle (0◦ <  < 45◦ ) and (b) a larger contact angle ( > 45◦ ).

the negatively charged membrane surface, microbubbles became detached from the pore openings as soon as they were formed. By contrast, for Tween 20 the microbubbles remained attached to the membrane surface, until they were pushed away by the next bubble formed at the same pore opening. This was a consequence of the negligible surface charge of the microbubbles generated with Tween 20 in comparison with the microbubbles generated with SDBS. For the case of CTMA, the mean bubble diameter increased with increasing mean pore diameter. However, it was difficult to control the size of the microbubbles generated from the SPG membranes by varying the membrane pore size. This is because the hydrophilicity of the membrane surface becomes lower, and thus, the contact angle between the membrane surface and water phase increases, as described in the Section 3.3. 3.5. Effect of surfactant type on bubble formation time Due to the existence of a strong electrostatic repulsive interaction between the microbubbles and membrane surface, it is expected that the bubble formation time, tf , which is defined as

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Table 4 The calculated values of bubble formation time for SPG membranes in the systems containing SDBS, Tween 20 and CTMA

Fig. 7. Relationship between the mean bubble diameter and mean pore diameter of the membrane for the cases of () SDBS, () Tween 20 and () CTMA. Transmembrane/bubble-point pressure ratio was set at 1.1. The concentrations of the surfactants were 2.0 mol m−3 .

the time required to generate a microbubble from a pore, will be shorter for SDBS than for both Tween 20 and CTMA. To confirm this prediction, the bubble formation times were calculated for all cases. In the bubble formation process from a single pore, the bubble formation time can be expressed from the ratio of the volume of a bubble, Vb and the volumetric flow rate through a single pore, q [15]: tf =

3 (/6)Db3 Vb 2 Db 1 = = 2 u 2 u q 3 Dm (/4)Dm

(4)

where u is the gaseous-phase velocity through a single pore, which can be expressed from the following equation [15]: u=

Jg pm k

(5)

where is the pore tortuosity of the membrane. For SPG membranes, the pore tortuosity is found to be 1.28, independent of the membrane pore diameter [28], k is the proportion of active pores, which is defined as the proportion of pores taking part in droplet formation to all pores [15,32]. In the bubble formation process, the gaseous-phase (gas) flux through an SPG membrane, Jg can be expressed according to the Hagen-Poiseuille law [15,19]: Jg =

2 ( P − P ) 2 P (P − 1) kpm Dm k(P − PBP ) kpm Dm BP BP r = = g Rm 32g x x 32g 2

(6)

where P is the applied transmembrane pressure, PBP is the bubble point pressure, g is the viscosity of the gaseous phase (g = 1.82 × 10−5 Pa s for air at 298 K), Rm is the hydrodynamic resistance of the membrane. For SPG membranes, the hydrodynamic resistance, Rm is given by [28]: Rm =

32 x 2 pm Dm

(7)

where x is the membrane thickness, and Pr is the transmembrane/bubble-point pressure ratio (Pr = P/PBP ). By substituting Eq. (6) into Eq. (5) and the resultant Eq. (5) into Eq. (4), the bubble formation time is given by: tf =

3 64 Db g x 4 3 Dm PBP (Pr − 1)

(8)

Mean pore diameter, Dm (␮m)

Surfactant type

1.0

SDBS Tween 20 CTMA

Mean bubble diameter, Db (␮m) 7.4 9.2 24.2

Bubble formation time, tf (ms) 8.2 13.0 396

3.1

SDBS Tween 20 CTMA

21.9 28.9

5.0

SDBS Tween 20 CTMA

35.6 43.0

9.7 15.0

63.2

80.3

10.0

SDBS Tween 20 CTMA

75.7 92.1

12.2 14.9

52.1

103

8.3 13.6 190

67.8

By substituting g = 1.82 × 10−5 Pa s for air, = 1.28 for SPG membranes [28], and the measured values of Db, Dm (from Fig. 7 or Table 4) and PBP (from Table 2) at a transmembrane/bubble-point pressure ratio of Pr = 1.1, one obtains the bubble formation times for each membrane in the systems containing SDBS, Tween 20 and CTMA, as listed in Table 4. As expected, the bubble formation time was shorter for SDBS than for both Tween 20 and CTMA under the same conditions. Similar results were observed with droplet formation from SPG membranes for the cases of anionic and nonionic surfactants (SDS and Tween 80) [33]. 3.6. Effect of surfactant type on gaseous-phase flux Monodispersed microbubbles were found to be generated from SPG membranes in the transmembrane/bubble-point pressure ratio range of 1 ≤ Pr ≤ 2 [19]. In this study, the gaseous-phase flux through a 5.0-␮m membrane was measured in the range of 1.03 ≤ Pr ≤ 1.55 for the cases of SDBS, Tween 20 and CTMA. Fig. 8 shows the effect of the transmembrane/bubble-point pressure ratio on the gaseous-phase flux. As expected from Eq. (6), for all cases the gaseous-phase flux through the membrane increased with increasing applied transmembrane pressure in the transmembrane/bubble-point pressure ratio range investigated. The gaseous-phase flux was about 11–15 times larger for Tween 20 than for SDBS, but much smaller for CTMA. Fig. 9 shows the calculated proportion of active pores in the membrane as a function of the transmembrane/bubble-point pressure ratio for the given conditions in Fig. 8. The proportion of active pores, k was calculated from the following equation, which is rewritten from Eq. (6), using the measured values of the gaseous-phase flux, Jg at a given transmembrane/bubble-point pressure ratio, Pr [15,18]: k=

32g 2

x 2 P (P − 1) pm Dm BP r

(9)

Only 0.028–0.036%, 0.29–0.56% and 0.88–3.2% of the pores were active for the cases of SDBS, Tween 20 and CTMA, respectively. One reason for the very low proportions of active pores in this work was probably due to a low transmembrane/bubble-point pressure ratio. As shown in Figs. 8 and 9, for the case of SDBS, a linear relationship between the gaseous-phase flux and transmembrane pressure was obtained, and the proportions of active pores was independent of the transmembrane pressure under these conditions. By contrast, for both Tween 20 and CTMA, an increase in gaseous-phase flux

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was observed at a higher transmembrane pressure. This is probably due to an increase in the number of active pores, as shown in Fig. 9. Under the same conditions, the higher flux for both Tween 20 and CTMA compared to that for SDBS is a consequence of the fact that the proportion of active pores is significantly higher for both Tween 20 and CTMA than for SDBS. 4. Conclusions

Fig. 8. Effect of transmembrane/bubble-point pressure ratio on the gaseous-phase flux through an SPG membrane with a mean pore diameter of 5.0 ␮m using () SDBS, () Tween 20 and () CTMA. The concentrations of the surfactants were 2.0 mol m−3 .

The effect of surfactant type on microbubble formation behavior from SPG membranes was investigated using a gas-liquid dispersion system consisting of air and a surfactant solution. Monodispersed microbubbles are formed from SPG membranes using SDBS and Tween 20 as anionic and nonionic surfactants, respectively. The repulsive surfactant/membrane-surface interaction and low contact angles helped to keep the membrane surface hydrophilic, which is a prerequisite for monodispersed microbubble formation. By contrast, the attractive surfactant/membrane-surface interaction in the system containing CTMA as a cationic surfactant resulted in polydispersed large bubble formation, probably because the cationic surfactant adsorbs to the membrane surface, which leads to a lowering of the hydrophilicity of the membrane surface. Under the same conditions, the microbubbles generated with SDBS were smaller than the microbubbles generated with both Tween 20 and CTMA. For SDBS, the microbubbles became detached from the pores as soon as they were formed due to a strong electrostatic repulsion between the microbubbles and the membrane surface, which assists in microbubble detachment from the pore openings. For both Tween 20 and CTMA, the microbubbles remained attached to the membrane surface after formation, before being pushed away by the next bubble formed at the same pore opening. The gaseousphase flux was about 11–15 times larger for Tween 20 than for SDBS, but much smaller for CTMA because the proportion of active pores is significantly lower for SDBS than for both Tween 20 and CTMA. Acknowledgements This work was supported by Practical Application Research for the Japan Science and Technology Agency. We would like to thank Ms. Junko Takeshita of JST Satellite Miyazaki in Japan for the measurement of the surface tension. References

Fig. 9. Effect of transmembrane/bubble-point pressure ratio on the proportion of active pores in an SPG membrane with a mean pore diameter of 5.0 ␮m using () SDBS, () Tween 20 and () CTMA. The concentrations of the surfactants were 2.0 mol m−3 .

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