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Membrane Emulsification with Oscillating and Stationary Membranes Richard G. Holdich,*,† Marijana M. Dragosavac,† Goran T. Vladisavljevic´,† and Serguei R. Kosvintsev‡ Department of Chemical Engineering, Loughborough UniVersity, Leicestershire, LE11 3TU, United Kingdom, and Micropore Technologies, Ltd., Epinal Way, Loughborough, Leics., LE11 3EH, United Kingdom
Membrane emulsification of sunflower oil in aqueous solutions of 2% (v/v) Tween 20 was performed using a stationary disk membrane with a rotating paddle stirrer and, for comparison, a tubular membrane oscillating normal to the direction of oil flow in an otherwise stationary continuous phase. The oscillation frequency ranged from 10 to 90 Hz. The oil was injected through a sieve-type membrane with a 10 µm pore size and 180 µm between pore spacing at low flux rates to minimize any droplet interference. Using the same membrane material under identical peak shear conditions in both systems, smaller and more uniform drops (30-50 µm median sizes) were produced in the oscillating system. In oscillation, the drop size was modeled by a force balance, including a correction for neck formation at the pore surface, but in the rotating paddle system, neck formation did not appear to be relevant. Drop size was not found to be frequency of oscillation dependent, apart from its influence on the shear stress at the membrane surface. Introduction Membrane emulsification is a membrane-assisted dispersion process to produce an emulsion of one liquid phase (such as oil) in a second immiscible liquid phase (such as water). A number of studies have described,1-3 and reviewed,4-6 the production of fine drops using crossflow of the continuous phase in order to provide the shear at the membrane surface to remove the emerging discontinuous phase drops. However, when aiming to produce larger drops, that may be applied in industries such as ion exchange resins, food and flavor encapsulation, controlled release depots under the skin, electronic ink capsules, medical diagnostic particles, high value fillers, and other species with a particle, or drop, size greater than approximately 20 µm, a crossflow system is not appropriate, due to the need to recycle the dispersion over the membrane surface, leading to damage to the previously formed large drops within the pump and fittings of the crossflow system. For the controlled production of larger drops, laboratory test systems have been described, based on microchannels,7 rotating the membrane in an otherwise stationary continuous phase,8 and rotating a stirrer above a stationary membrane.9,10 In the latter case, a previous work demonstrated how it was possible to model the drop formation process based on a force balance model, taking into account the formation of a “neck” between the emerging drop and the membrane pore. Further analysis led to the understanding of what is termed the “push-off” force,10,11 due to the interaction of drops forming at adjacent pores on the membrane surface. If the drop size is equal, or larger, than the spacing between the pores, the drops will touch each other, causing deformation from a spherical shape, and an additional force encouraging drop detachment from the membrane surface. In the following work, the injection rate has been kept low (less than 35 L per square meter of membrane area per hour) to avoid any influence due to the push-off effect. Hence, the work compares shear based detachment of drops in the stirred and oscillating membrane systems. A previously published piezo activated experimental study reported very mixed results for * To whom correspondence should be addressed. Tel.: +44 1509 222519. Fax: +44 1509 223923. E-mail:
[email protected]. † Loughborough University. ‡ Micropore Technologies, Ltd.
vibration assisted emulsification, using high frequency membrane vibration.12 Furthermore, the role of inertia in droplet detachment is uncertain, and it has not been considered here in the modeling. A numerical study of inertia during high frequency (500 to 20 000 Hz) vibrating membrane generation13 has been published previously, and it was shown to have only a limited effect. In fact, using the conditions used in the study reported here (maximum frequency of 90 Hz), during the generation of 100 µm drops, the inertial force on the drop is 3 orders of magnitude less than the shear drag force, and for 200 µm drops it is 2 orders of magnitude lower. Likewise, it has been shown that buoyancy is also very small for drop sizes below 1000 µm and sunflower oil in water emulsions.14 Hence, this study considered only shear drag as the major detachment force and capillary force as the main attraction force to the membrane. The two described laboratory techniques, rotating membrane8 and rotating paddle stirrer above a stationary membrane,10 are useful for assessing the possibility of membrane emulsification for the larger drops, but neither technique can easily be scaled to productivity appropriate for industrial use for the industrial products mentioned previously. This paper describes the application of an alternative method to generate the shear at the membrane surface, that can minimize the risk of breakup of the drops previously formed; the technique is based on the low frequency oscillation of the membrane surface in a direction normal to the flow of the injected phase through the membrane. High frequency oscillation of the membrane, normal to the injected phase flow, has been described before,12,13 but this work compares the results obtained with the planar stationary membrane using a stirrer, the Dispersion Cell,9,10 with exactly the same membrane material used in oscillation using low frequencies between 10 and 90 Hz. The comparison is of the drop size formed in the two different devices, under conditions of the same shear stress at the membrane surface. Previous work on vibrating membranes has concentrated on oscillating the membrane rapidly,12 to generate fine drops, or has criticized this method of shear application on an energy analysis that demonstrates that there is no advantage to using an oscillating membrane compared to a simple crossflow system for the production of fine drops.13 In the study presented here, the intention is not to generate fine drops but to be able to generate
10.1021/ie900531n 2010 American Chemical Society Published on Web 03/23/2010
Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010
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Figure 1. Schematic illustration of (a) Dispersion Cell containing a paddle stirrer above a disk membrane and (b) the oscillating tubular membrane. Both systems use the same illustrated membrane material.
drops larger than 30 µm in a highly controllable method that can scale to provide a method of industrial significancesby simply increasing the area of the membrane oscillating. In the previous study,9 employing the simple paddle stirrer positioned over the stationary membrane, it was argued that, at a certain point on the membrane surface, there is a transitional point between the forced and free vortex around the paddle blade stirrer. At this point, the shear stress is greatest, leading to a region where the pressure on the surface of the membrane would be lowest; hence a region which will be more productive in terms of droplets formed through the membrane, as the pressure difference across the membrane will be the greatest at this radius. Hence, monosized droplets can be generated from the system because they are predominantly generated from a narrow radial annular region on the disk membrane. Hence, the analysis of drop size may be based on the shear conditions obtained at the position of maximum shear in the simple stirred system. The alternative approach would be to consider the average shear over the entire surface of the membrane. A similar problem, whether to use peak shear or average shear, exists for modeling the low frequency oscillating membrane system. In the case of a membrane oscillating normal to the flow of the dispersing phase, the velocity of the membrane will be changing very rapidly at the same time that the dispersed phase drops emerge from the membrane. This highly fluctuating shear field could be argued to promote a wide drop size distribution. However, the emerging drop will preferentially detach when it experiences maximum shear stress between the membrane and
the surrounding liquid. Hence, in order to produce a monosized drop distribution, it is only necessary to keep a constant peak shear and to have at least one peak shear event during the drop formation process; i.e., the peak shear frequency should be equal to, or greater than, the drop formation frequency. In other words, the drop formation time should be greater than the time between peak shear. Dispersed Drop Size Modeling The equations used in this study were introduced in the previous work.10 The initial, and simplest, approach is where the droplet diameter is calculated from a force balance of the capillary force and the drag force acting on a strongly deformed droplet at a single membrane pore:
x)
√18τ r
2 2 p
+ 2√81τ4r4p + 4r2pτ2γ2 3τ
(1)
where rp is the pore radius, τ is the shear stress, γ is the interfacial tension, and x is the formed drop diameter. For the simple stirred cell, illustrated in Figure 1a, the shear stress at the base of a paddle stirred vessel must be determined. In eq 1, it can be argued that the appropriate shear stress to use is either the average, or maximum, value. The maximum value determined from a stirred system, such as the Dispersion Cell, is given from a knowledge of the location of the transitional radius (rtrans) along the paddle blade radius:
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τmax ) 0.825µωrtrans
1 δ
(2)
The transitional radius is the point at which the rotation changes from a forced vortex to a free vortex rtrans )
D D b 1.23 0.57 + 0.35 2 T T
(
0.036 0.116 nb
)( )
Re 1000 + 1.43Re (3)
where b is the blade height, T is the tank width, D is the stirrer width, and nb is the number of blades. The Reynolds number is defined by Re ) (FωD2)/(2πµ), where F is the continuous phase density, ω is the angular velocity, and µ is the continuous phase coefficient of dynamic viscosity. For the experimental equipment used, H ) 16 cm, D ) 3.2 cm, nb ) 2, and T ) 4 cm. The boundary layer thickness, δ, is defined by the Landau-Lifshitz15 equation: δ)
Fwµ
(4)
The approach based on eqs 1 to 4 is called model A. The alternative approach is to use the average shear in eq 1, for the stirred cell, where the average shear is given by16
∫
rtrans
0
τav )
1 0.825µωr (2πr) dr + δ rtrans Dm/2 0.825µωrtrans rtrans r 2 πDm /4
( )
∫
{
[( )
3 1.6 rtrans Dm 6.6 1 rtrans + ) 2 µω 1.4 2 Dm δ 3
1.4
0.6
-
Fstat
FCa - Fstat ) FD
)
(11)
The existence of drop diameter in so many of the constituent equations led to the need for a mathematical software package to solve eqs 8 to 11. This modeling approach will be called model C. When considering an oscillating membrane, illustrated in Figure 1b, the equation for the shear rate (γ˙ ) with respect to time is18
( )
γ˙ ) Vo
ωfF 2µ
1/2
[sin(ωft) - cos(ωft)]
(12)
]}
ωfµF 2
1/2
[sin(ωft) - cos(ωft)]
(13)
In eqs 12 and 13, the term ωf is the angular frequency, and it is determined during oscillation from the following equation
1.4 rtrans
ωf ) 2πf
(5)
(7)
dp x
(10)
Hence, it is possible to write a force balance using all of the above equations:
τ ) Vo
It is possible to modify the capillary force in order to consider the neck:
(
( 2δx ))
(
V ) ωrtrans 1 - exp -
(8)
When the droplets are in a region close to the pore diameter, the expression considering the neck underestimates the net capillary force, and the correction for this neck static pressure is no longer applicable. In such cases, it is preferable to use the uncorrected expression, eq 7. The expression for the drag force
(14)
where f is the frequency of the oscillation. The peak velocity, Vo, is related to both the angular frequency and the amplitude (a) of oscillation by the equation Vo ) ωfa
(15)
and the droplet formation time (td), useful for comparison of the number of times an emerging droplet is subject to maximum shear, is obtained from a material balance:17,19 td )
(6)
FCa ) πdpγ
(9)
where V is the relative velocity between the drop and the continuous phase
( )
1 (2πr) dr δ
where the neck diameter is approximated to the membrane pore diameter (dp). The force due to interfacial tension (capillary force) is
FCa - Fstat ) πdpγ 1 -
FD ) 3πkwlµVx
and the equation for shear stress will be
where Dm is the active diameter of the membrane, i.e., the diameter exposed to the continuous phase. For the experimental equipment used, Dm ) 3.2 cm. Use of eqs 1, 3, 4, and 5 will be called model B. However, eq 1 does not take in to account the “neck”, which exists between the forming drop and the membrane pore. This can be included by introducing another force: the so-called static force,11,17 Fstat. As shown previously, there is a static pressure difference due to pressure between the inside and outside of the droplet, which can be expressed as 4γ π 2 d ) x 4 p
is based on Stokes’s drag expression, with a correction factor (kwl) to consider the effect of the nearby walls in the motion of a droplet, for the system reported here kwl is 3.4926.10
3 2εkd(4,3)
3d2pJd
(16)
where k is the fraction of pores taking part in the emulsification, d(4,3) is the mean drop diameter by volume, Jd is the dispersed phase flux, and ε is the porosity of the membrane surface. The objective behind the work reported here is to compare the performance of dispersion generation between a stirred, but stationary membrane, system and one that uses oscillation of the membrane. If the drop size is dependent only on the shear conditions at the membrane surface, then it should be possible to calculate the shear stress in the oscillating system using eq 13 and obtain comparable results with the stirred stationary membrane system, provided that oscillation of the membrane can be used to generate drops of a reasonable degree of uniformity. Experimental Section The dispersed phase for the oil in water emulsions was commercially available food grade sunflower oil. The continuous
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phase was purified water (obtained from a reverse osmosis system) containing 2% vol/vol Tween 20 surfactant (polysorbate 20 or polyoxyethylene sorbitan monolaurate) obtained from Sigma Aldrich. Emulsification using a stationary membrane was performed using a Micropore Technologies Ltd. Dispersion Cell. This device uses a 24 V DC motor to drive a paddle-blade stirrer, which provides the shear at the membrane surface (Figure 1a). Stirrer speed settings ranging from 2 to 10 V were used, which are expressed in the Results section as their (maximum) shear stress equivalent values at the transitional radius using eq 2, or for average shear values using eq 5. Membranes with a 10 µm pore size, and 180 µm spacing between the pores, were supplied by Micropore Technologies Ltd. for the production of all the emulsions. The dispersed phase was injected through the membrane pores using a very low rate of 30 L of dispersed phase injected per square meter of membrane area per hour (L m-2 h-1). A low injection rate was employed to minimize any push-off effect.10 The continuous phase volume was 150 cm3, and 10 cm3 of the dispersed phase was injected for each experiment. The oscillating membrane system used is also illustrated in Figure 1 and was supplied by Micropore Technologies Ltd. For the oscillation, the membrane was in the form of a candle, with an external diameter of 15 mm and a working length of 57 mm. At the bottom end of the membrane, a stainless steel cap sealed off the membrane tube, and the cap had a pointed end to reduce turbulence during oscillation. At the top of the membrane candle, there was a 1/8 in. BSP fitting to enable the candle to be attached to the injection manifold, to which an accelerometer was fixed. The injection manifold had internal drillings to allow the passage of the oil phase to be injected, which was provided by a syringe pump (Harvard Apparatus 11 Plus). The accelerometer (PCB Piezotronics model M352C65) was connected to a National Instruments Analogue to Digital Converter (NI eDAQ-9172) which was interfaced to a LabView executable program running on a PC. The information provided by the program from the accelerometer was the frequency and amplitude of the oscillation, the frequency being determined by the direction of travel, and the amplitude was deduced from the acceleration measurement. The oscillation signal was provided by an audio generator (Rapid Electronics), which fed a power amplifier driving the electro-mechanical oscillator on which the inlet manifold was mounted. See Figure 1b for a schematic illustration of the equipment. Before each experiment, it was important to ensure that no air gaps or bubbles were trapped within the oil phase. For that reason, the membrane was immersed into the continuous phase, and the continuous phase was sucked into the membrane and injection manifold using a syringe. When air was completely removed, the injection tube was attached to the pump, and the oil phase was introduced very slowly to the membrane. Oscillation did not start until the oil phase emerged on the membrane surface in order to prevent premixing within the membrane. Interfacial tension measurements were made using the Du Nouy ring method, with a White Elec. Inst Co Ltd. model DB2KS. The number distributions for the o/w emulsions were obtained using a Malvern Mastersizer (model S). The uniformity of the number distributions is expressed in terms of the span of the distribution: span )
d(n, 0.9) - d(n, 0.1) d(n, 0.5)
(17)
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Figure 2. Comparison of experimental drop diameters produced in Dispersion Cell and predicted values calculated using different models: the values of d(n,0.5) were obtained at 30 L m-2 h-1. Model C uses eqs 1-4, model B is based on eq 5, in which τ ) τav, and model A uses eq 5, in which τ ) τmax.
where the numbers in the parentheses represent the drop size corresponding to the position when 0.1, 0.5, and 0.9 of the cumulative number distribution occur. A span of significantly less than unity represents a monosized material.2 The median value of the number distribution was taken from the statistics provided by the instruments and is used for comparison with the mathematical models. A number of experiments were repeated several times, to investigate the reproducibility of the results. These are discussed in greater detail within the Results section. Results and Discussion Figure 2 compares the results from the Dispersion Cell, i.e., the stationary membrane with rotating paddle stirrer to create the shear (Figure 1a) system, with the three models: A, which uses peak shear in the force balance equation; B, which uses average shear in the force balance, and C, which employs peak shear and takes into account the neck formation of the drop at the pore opening. It is clear that the experimental data are closest to the models not based on neck formation at the pore opening. During these experiments, the oil flux rate was very low, at 30 L m-2 h-1, so that any effect due to droplet “push-off” was minimized, and drop growth before detachment was also low. It is well-known that drop size is influenced by the injection rate of the phase being dispersed:10 increasing injection rate giving increasing drop size. Hence, for these tests, the injection rate was kept very low to minimize these effects, so that the influence of shear on the drop detachment could be investigated for the paddle stirred system. A similar comparison is illustrated in Figure 3, for the oscillating membrane system. In this figure, the curves for models A and C are retained, so that a comparison between the results obtained in the stirred and oscillating systems is possibleson the basis of conditions of peak shear within either system. When stirring with a paddle stirrer, the control of the shear is from the rotation speed of the stirrer, but for the oscillating system, varying shear can be obtained by varying the frequency, or the amplitude of oscillation. The data in Figure 3 record the frequency used to achieve the given peak shear stress, and the corresponding amplitude can be estimated from eqs 13, 14, and 15. Under identical conditions of shear stress, a higher frequency is compensated by using a lower amplitude of oscillation, where amplitude is half of the peak-to-peak displacement of the membrane motion. There does not appear
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Figure 3. Comparison of experimental drop diameters produced in oscillating membrane emulsification and predicted values using models A and C: the values of d(n,0.5) were obtained at 30 L m-2 h-1.
to be any significance in the combination of the frequency and amplitude used: the resulting drop size is apparently a function of the peak shear stress only and not the frequency used to achieve it. Also, there is a significant difference between the most applicable model for the paddle stirred system, where neck formation is seemingly not relevant, and the results from the oscillating system where it is. Almost all the results of drop size from the oscillating membrane system are placed between the peak shear model with correction for neck formation (model C) and peak shear without neck formation correction (model A), with a better fit to the data from model C. However, at intermediate values of shear, smaller drops are generated in the oscillating membrane system than model C predicts, indicating the possible existence of an additional drop detachment mechanism to shear at the membrane surface. The transmembrane flux was kept at a value of only 30 L m-2 h-1 in the oscillating membrane tests, so that the effects of “push-off” and drop growth are again avoided. On increasing peak shear, the droplet size decreases sharply and for most frequencies reaches a constant value after a peak shear of 4 Pa. It appears that the non-neck formation models work better in the paddle stirred system, where the droplets are detached by shear only in one direction (i.e., that of the direction of rotation of the paddle), and that in the oscillating system, where the drops are displaced in two directions, upward and downward, the model which applies maximal shear stress with neck formation gives a better prediction of the drop size. As an indication of the reproducibility of the results, and the drop size span, Figure 4 illustrates the data obtained from triplicate experiments for an oscillator frequency of 15 Hz and over the range where the drop size is a significant function of peak shear stress. At each shear condition, the results from three experiments are reported as a circular marker. Where only a single marker is visible, it is because the markers all fall onto the same place. The results show that the experiments were reproducible and that there is a set of operating conditions that provide the narrowest drop size distribution. For this frequency, and injection rate, the most narrow drop size distribution was obtained at a peak shear stress of 3.6 Pa, giving a median drop size on a number distribution of just below 50 µm and a drop size span in the range of 0.37-0.45. The narrowest size distribution span in the Dispersion Cell tests was 0.53 and was obtained at a peak shear stress of about 6 Pa. Therefore, the oscillating membrane system can afford better uniformity of the produced drops than the Dispersion Cell, which can be attributed to the fact that in the oscillating system the shear
Figure 4. Three experiments performed for each peak shear stress, to estimate the reproducibility of results. The frequency was kept constant 15 Hz and transmembrane flux was 30 L m -2 h-1.
Figure 5. Photographs of emulsions produced by applying different peak shear stresses on the membrane surface: (a) 1.3 Pa, (b) 2.5 Pa, (c) 3.6 Pa, and (d) 5.5 Pa. Frequency was kept constant at 15 Hz, and transmembrane flux was 30 L m -2 h-1.
conditions can be more finely adjusted by varying two parameters, the frequency and amplitude of membrane oscillation. On the other hand, in Dispersion Cell, the shear can be controlled only by varying the rotation speed of the stirrer. The influence of the shear condition on the degree of uniformity of the produced drops is also illustrated in Figures 5 and 6, which supports the information contained in Figure 4. Optical microscope images are shown in Figure 5, at four values of peak shear stress: 1.3, 2.5, 3.6, and 5.5 Pa. It can be seen that the most uniform drops are provided at a shear stress of 3.6 Pa, and in Figure 6, it is noticeable that the cumulative distribution curve at this peak shear is also the steepestsindicating the narrowest drop size distribution. Hence, it appears that the narrowest drop size distribution, i.e., lowest span value, is not simply determined by conditions of the highest shear, or lowest shear giving the smallest, or largest, drops. It is likely that the most uniform drop distribution is provided by a complex function of all the parameters influencing the process, including disperse phase injection rate, peak shear, membrane properties, and the physical properties of the two immiscible liquids. There has been previous work showing that very monosized distributions can be obtained when the push-off force is applicable.10 This occurs when the drop production rate is large and drops from adjoining pores may touch each other, leading to a distortion of the drop shape from spherical and an additional force to assist in droplet detachment. This touching between
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Figure 6. Cumulative distribution curves of produced emulsions presented in Figure 5, with a constant frequency of 15 Hz and transmembrane flux of 30 L m -2 h-1 (where amplitude ) peak-to-peak/2).
Figure 7. Variation of number-based median diameter and span of a droplet size distribution with dispersed phase flux at 10 Hz frequency and peak to peak displacement of 1.2 mm. Maximum peak shear stress in all experiments was 0.3 Pa.
the drops may also help the drops grow to the same volume. In the previous work, it was noticeable that, under constant conditions, apart from dispersed phase injection rate, the drop size increased with injection rate until a certain value was achieved at which the drop size reduced again, and the uniformity of the distribution became excellent. That work was performed with a membrane having spacing between the pores of 80 µm. In the work reported here, the pore spacing was 180 µm, to ensure that the investigation was limited to that of surface shear and not pushoff. Nevertheless, an investigation of increasing injection rate was performed, to investigate if pushoff could be induced with the oscillating system. It is worth noting that in the oscillating system the drops will be distorting from one direction to the other, rather than simply distorting within a consistent shear field such as that obtained in a stirred system. Clearly, pushoff will be more likely when generating larger drops; hence the test was performed for conditions of the lowest shear: a frequency of 10 Hz and a peak to peak displacement of 1.2 mm. The results are presented in Figure 7. The dispersed phase flux was varied from 30 to 13 900 L m-2 h-1 and median droplet diameter increased from 180 to 340 µm, falling back to just over 300 µm at the fastest injection rate. The span value (measure of uniformity of the distribution) went from 0.75 at the lowest injection rate to 0.5 at an intermediate rate and then up to 0.8, corresponding to the largest drop size, before rising to 0.9 at the fastest injection rate. It is likely that the lower median drop size and poorer span value at
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Figure 8. Influence of frequency on median droplet diameter under conditions of constant shear stress: varying amplitude and frequency.
Figure 9. Shear rate with time where the maximal peak shear for both frequencies was 1.3 Pa. The dashed/dot line represents the average shear rate of 828 s-1.
the highest injection rate is due to either some degree of jetting or the break up of the larger drops in the local shear field within the oscillating membrane system. Given that the pore spacing was 180 µm, it should be possible that the drops, which were all greater than this size, could experience some form of pushoff. However, the evidence for this is not strong: the span does reach a minimum at an injection rate of between 1000 and 2000 L m-2 h-1, but the drop size continues to increase with injection rate until the fastest injection rate is achieved. From Figure 3, it is evident that another drop detachment force supplements the peak shear detachment. As previously discussed, the inertial force is low: 2 orders of magnitude below the shear force for a 200 µm drop, and this is consistent with a numerical study provided for high frequency membrane oscillation.13 However, the study presented here used much lower frequencies, 10 to 90 Hz, and an investigation into the influence of frequency of oscillation was performed. Figure 8 shows the median drop diameter as a function of frequency for a constant peak shear stress at the membrane surface. Shear stress is a function of frequency and amplitude, so an increasing frequency can be compensated by a decreasing amplitude, in accordance with eqs 15 and 13, to maintain the same overall shear stress. It can be seen that the drop size is substantially independent of the frequency of oscillation used but depends on the shear stress at the membrane surface, as anticipated by models A to C described earlier. Figure 9 illustrates how the shear rate varies at the membrane surface at two frequencies: 10 and 50 Hz. The amplitudes are 2.61 and 0.2335 mm, respectively, providing the same peak
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Table 1. Droplet Formation Time from Continuity and Its Dependence on Amount of Active Pores percentage of active pores d(n,0.5) (µm)
d(4,3) (µm)
1%
32 56 99 149 198
34 60 112 194 265
0.9 4.9 31 160 420
5%
10%
15%
50%
droplet formation time, td (ms) 4.4 24 160 820 2100
8.8 48 310 1600 4200
13 73 470 2500 6200
44 240 1600 8200 21000
shear stress of 1.3 Pa. Also marked in Figure 9 is the average shear rate, as a dotted line, and this can be seen to be the same for the two different conditions of frequency and amplitude. From eqs 13, 14 and 15, the peak shear stress is given by τmax ) ω3/2a(µF)-1/2 ) (2π)3/2(µF)-1/2af 3/2
(18)
Therefore, in order to keep a constant peak shear for the two different conditions of amplitude and frequency 1 and 2, it is necessary to satisfy the following condition: a1/a2 ) (ω2/ω1)3/2 ) (f2/f1)3/2. This equation is satisfied for the sets of experimental conditions shown in Figure 9. A peak-shear event will take place twice for every cycle: once during upward movement and again during downward movement. Hence, for the slowest frequency used, 10 Hz, the number of peak-shear events is 20 per second, or a peak shear every 50 ms. It is possible to compare this with the drop formation time; it is desirable to have a drop formation time in excess of a peak shear event time. The drop formation time depends on the number of active pores, which is known to be significantly lower than 100%.19 However, the number of active pores was not measured. Hence, the drop formation time has been estimated for a range of amounts of active pores, varying from 1% to 50%, and is reported in Table 1. Equation 16, based on continuity, was used to estimate the drop formation time for the range of drop sizes illustrated in Figure 3. Table 1 reports both the median by number and the mean by volume of the drops. The latter spherical diameter is important in the calculation of the drop formation time based on a continuity balance. Drop formation times lower than 50 ms are highlighted in the table in bold italic values. In these cases, the formation time is less than the peak-shear time (based on 10 Hz oscillation frequency). Hence, this is not an appropriate frequency to use for the generation of the smallest drops: a median size of 32 µm. This low frequency was not used to generate drops with this median size. However, it was used to generate drops with a size slightly greater than 56 µm. At this size, the drop formation time is between 4.9 and 48 ms, depending on the fraction of active pores used by the membrane (from 1 to 10%, respectively). Hence, it is likely that the drop formation time is shorter than the peak-shear time under these conditions. This may explain why the median droplet diameter at 10 Hz and a peak shear stress of 3.6 Pa, illustrated in Figure 8, was slightly higher when compared to the other frequencies; i.e. the peak-shear-event time is too long and drops can form and detach at shear conditions other than the peak value, which gives rise to larger drops being formed. Conclusions The median drop sizes obtained in stirred and oscillating membrane emulsification systems have been compared with
the predicted values calculated using different force balance models. The drop sizes produced in the Dispersion Cell were very close to a model that does not include the neck formation at the pore opening. Most of the drops formed by the oscillating system had median diameters between the simple peak shear model (model A) and the peak shear model that takes into account the neck formation (model C). However, both models overestimated the drop size at intermediate shear values, suggesting the existence of another drop detachment force to supplement the shear-induced drag force during oscillation. Under constant peak shear stress at the membrane surface, the drop size was essentially independent of the frequency of oscillation, in the tests where the effect of an increasing frequency was compensated by a decreasing amplitude to maintain the same shear stress at the membrane surface. On increasing peak shear, the droplet size decreased sharply and for most frequencies reached a constant value at a peak shear stress of about 4 Pa. The most narrow drop size distribution with a span of 0.37 to 0.45 and a median drop size of just below 50 µm was obtained at a peak shear stress of 3.6 Pa. For the generation of the drops with a size lower than 56 µm, the slowest frequency of 10 Hz was not appropriate, because the drop formation time for the amount of active pores of 10%, or less, was shorter than the peakshear-event time. On increasing the dispersed phase flux from 30 to 13 900 L m-2 h-1, no significant improvement of the uniformity of distribution, due to droplet push-off effect, was observed with the membrane using 180 µm spacing between the pores. The formation of uniform drops using low frequency membrane oscillation has been described. The technique is applicable to the generation of larger drops than cannot be reliably achieved by a crossflow membrane emulsification process, where drop breakage after formation occurs. The oscillating membrane technique can be scaled by providing a larger membrane area in the oscillating membrane assembly, whereas the stationary membrane with a rotating paddle stirrer is a technique that cannot be scaled to larger membrane areas so readily. Literature Cited (1) Lambrich, U.; Schubert, H. Emulsification using microporous systems. J. Membr. Sci. 2005, 257, 76. (2) Williams, R. A.; Peng, S. J.; Wheeler, D. A.; Morley, N. C.; Taylor, D.; Whalley, M.; Houldsworth, D. W. Controlled production of emulsions using a crossflow membrane Part II: industrial scale manufacture. Trans. IChemE. 1998, 76, 902. (3) Nakashima, T.; Shimizu, M.; Kukizaki, M. Particle control of emulsion by membrane emulsification and its applications. AdV. Drug DeliVery ReV. 2000, 45, 47. (4) Abrahamse, A. J. G.; van der Padt, A.; Boom, R. M. Status of crossflow membrane emulsification and outlook for industrial application. J. Membr. Sci. 2004, 230, 149. (5) Joscelyne, S. M.; Tragardh, G. Membrane emulsification - a literature review. J. Membr. Sci. 2000, 169, 107. (6) Vladisavljevic´, G. T.; Williams, R. A. Recent developments in manufacturing emulsions and particlulate products using membranes. AdV. Colloid Interface Sci. 2005, 113, 1. (7) Sugiura, S.; Nakajima, M.; Seki, M. Preparation of monodispersed polymeric microspheres over 50 µm employing microchannel emulsification. Ind. Eng. Chem. Res. 2002, 41, 4043. (8) Vladisavljevic, G. T.; Williams, R. A. Manufacture of large uniform droplets using rotating membrane emulsification. J. Colloid Interface Sci. 2006, 299, 396. (9) Stillwell, M. T.; Holdich, R. G.; Kosvintsev, S. R.; Gasparini, G.; Cumming, I. W. Stirred cell membrane emulsification and factors influencing dispersion drop size and uniformity. Ind. Eng. Chem. Res. 2007, 46, 965. (10) Egidi, E.; Gasparini, G.; Holdich, R. G.; Vladisavljevic, G.; Kosvintsev, S. R. Membrane emulsification using membranes of regular
Ind. Eng. Chem. Res., Vol. 49, No. 8, 2010 pore spacing: Droplet size and uniformity in the presence of surface shear. J. Membr. Sci. 2008, 323, 414. (11) Xu, J. H.; Luo, G. S.; Chen, G. G.; Wang, J. D. Experimental and theoretical approaches on droplet formation from a micrometer screen hole. J. Membr. Sci. 2005, 266, 121. (12) Zhu, J.; Barrow, D. Analysis of droplet size during cross-flow membrane emulsification using stationary and vibrating micromachined silicon nitride membranes. J. Membr. Sci. 2005, 261, 136. (13) Kelder, J. D. H.; Janssen, J. J. M.; Boom, R. M. Membrane emulsification with vibrating membranes: a numerical study. J. Membr. Sci. 2007, 304, 50. (14) Kosvintsev, S. R.; Holdich, R. G.; Gasparini, G. Membrane emulsification: Droplet size and uniformity in the absence of surface shear. J. Membr. Sci. 2008, 313, 182. (15) Landau, L. D. Lifshitz, E. M. Fluid Mechanics; Pergamon Press: Oxford, U. K., 1959. (16) Dragosavac, M. M.; Sovilj, M. N.; Kosvintsev, S. R.; Holdich, R. G.; Vladisavljevic´, G. T. Controlled production of oil-in-water emulsions
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containing unrefined pumpkin seed oil using stirred cell membrane emulsification. J. Membr. Sci. 2008, 322, 178. (17) Schro¨der, V.; Behrend, O.; Schubert, H. Effect of dynamic interfacial tension on the emulsification process using microporous, ceramic membranes. J. Colloid Interface Sci. 1998, 202, 334. (18) Jaffrin, M. Y. Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems. J. Membr. Sci. 2008, 324, 7. (19) Vladisavljevic´, G. T.; Schubert, H. Preparation and analysis of oilin-water emulsions with a narrow droplet size distribution using Shirasuporous-glass (SPG) membranes. Desalination 2002, 144, 167.
ReceiVed for reView April 7, 2009 ReVised manuscript receiVed February 10, 2010 Accepted February 17, 2010 IE900531N
