pubs.acs.org/Langmuir © 2010 American Chemical Society
Drop Production and Tip-Streaming Phenomenon in a Microfluidic Flow-Focusing Device via an Interfacial Chemical Reaction Thomas Ward,*,† Magalie Faivre,‡ and Howard A. Stone*,§ †
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910, ‡Laboratoire Microfluidique, MEMS et Nanostructures CNRS UMR7083, ESPCI Paris-Tech, 10 rue Vauquelin, F-75005 Paris, France, and §Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 Received January 4, 2010. Revised Manuscript Received March 8, 2010 Microfluidic flow-focusing technology is used to investigate the effect on drop formation due to the production of a surfactant via an interfacial chemical reaction. The reactants are an aqueous solution of sodium hydroxide (NaOH) and a mixture of oleic acid (C17H33-COOH) and mineral oil, for the dispersed and continuous phase fluids, respectively, at concentration e 5 mM. In the absence of a chemical reaction, the drop shapes remain constant from just after breakup into droplets down at the flow-focusing nozzle until the drops exit the channel. In the presence of the chemical reaction, there is modification of the shape depending on the concentration of reactants. The drop speeds, O(10) mm/s, lengths, O(1-100) μm, and relative displacements, O(100-1000) μm, are measured for a variety of flow conditions with observable trends that correlate with the reaction rate, which we rationalize by using the Damk€ohler number to characterize drop production and transport in these types of flows.
1. Introduction 1.1. Motivation. One difficulty in producing useful emulsions suitable for long-term storage and handling is the stabilization of the dispersed phase fluid. Stabilization is needed because of two main features of emulsions, and multiphase fluids in general, which are settling and coalescence of the dispersed phase fluid. In a typical oil and water emulsion, a surfactant is often used for stabilization. Carboxylic acids, which can be converted into surfactants by chemical reaction with a base, naturally occur in many common oils, such as vegetable and animal oils, that are used in cooking and also as diesel fuels. Therefore, another possible route to produce a stable emulsion is to chemically react a long chain carboxylic acid that may already be present or added to the continuous phase fluid (for example an oleic or linoleic acid) through a carboxylic acid-base chemical reaction. To perform this reaction requires no more than mixing the oil/carboxylic acid mixture with aqueous sodium hydroxide to produce the carboxylic acid salt, which is the surfactant. Our goal is to study the emulsification of water in oil where there is, simultaneous with the drop formation, an interfacial chemical reaction as the liquids come into contact. In particular, we study the production of micrometer-sized droplets using microfluidic flow-focusing technology to determine qualitative and quantitative features of the reaction of oleic acid, dissolved in mineral oil as the continuous phase, with aqueous sodium hydroxide as the dispersed phase fluid. Recently it has been shown that reducing the surface tension through the presence of surfactant in at least one of the bulk phases can lead to additional features of droplet breakup in microfluidic devices such as tip streaming1 and can also impact bulk flows along drop surfaces in the presence of surfactants.2,3 Tip-streaming, and any process that produces extremely small *To whom correspondence should be addressed. E-mail: hastone@ princeton.edu. (1) Anna, S. L.; Mayer, H. C. Phys. Fluids 2006, 18, 121512. (2) Eggleton, C. D.; Tsai, T. M.; Stebe, K. J. Phys. Rev. Lett. 2001, 87, 048302. (3) Johnson, R. A.; Borhan, A. Phys. Fluids 2000, 12, 773–784.
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droplets, would be beneficial for emulsion production, since small droplets have very slow sedimentation velocities (the settling velocity is proportional to the square of the diameter) and tend to coalesce on a much longer time scale. In this paper, we study drop formation in a microfluidic flowfocusing geometry in the presence of an interfacial chemical reaction that produces a surfactant. The flows are at low Reynolds and variable capillary numbers. The Damk€ohler number, which is the ratio of reaction rate to the convective transport rate, will be used as the operating parameter and its approximate value determined based on previous results for drop speeds under similar conditions.4 In particular, we expect that the results will document distinct differences in the droplet formation and transport processes due to the presence of surfactant that is produced by the chemical reaction. Although we have not yet succeeded in rationalizing all of these differences, it is clear that the influence of the reduction in surface tension is the major contributor to the differences we have identified between similar systems with varying concentrations of the chemical reactants. 1.2. Operating Parameters. Microfluidic approaches to the manipulation of multiphase systems allow the production of micrometer-sized dispersions using flow-focusing technology. Of general importance is the ability to control the size and even shape of these dispersions. We focus our attention on the microfluidic production of droplets. Given that it has been shown that all of the laboratory bench processes, that is, mixing, sensing, reactions, and so on, may be performed at the microscale, then it seems possible to determine quantitative aspects for a variety of chemical reactions through microfluidic technology.5-7 Very little though is understood as to how these chemical reactions may affect (4) Ward, T.; Faivre, M.; Abkarian, M.; Stone, H. A. Electrophoresis 2005, 3716–3724. (5) Stone, H. A.; Stroock, A. D.; Ajdari, A. Annu. Rev. Fluid Mech. 2004, 36, 381–411. (6) Stroock, A. D.; Dertinger, S. K. W.; Ajdari, A.; Mezic, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647–651. (7) Thorsen, T.; Maerkl, S. J.; Quake, S. R. Science 2002, 298, 580–584.
Published on Web 03/24/2010
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Figure 1. Illustration of experimental setup for the study of chemical reactions in a microfluidic flow-focusing geometry. An aqueous solution of NaOH is dispersed as droplets into a continuous phase of mineral oil containing oleic acid.
the production of droplets. Our interest is in using microfluidic flow focusing to study a chemical reaction to determine what effects, if any, the chemical reaction may have on drop production. In experiments involving drop formation at the end of a capillary tube, it has already been shown that these chemical reactions can lead to tip-streaming where extremely small droplets are ejected from the tip of a fluid thread.8-10 There are several regimes for controlling the size of the dispersed phase fluid depending on a few common operating parameters. These parameters are based on measurements that are typically the droplet velocity U, the droplet length l, which is some measure of the drop volume, and the relative distance between consecutive drops d, which is a measure of the dispersed phased concentration where a small value indicates a high concentration of the dispersed phase fluid and vice versa (see Figure 1 for description of these measurements). With these measured quantities, combined with physical properties such as density Fi and absolute viscosity μi, where the subscripts denote either dispersed (w) or continuous (o) phase fluid properties, it is possible to determine common dimensionless operating parameters. Typically, these parameters are the Reynolds Re = FoU/νo and capillary Ca = μoU/γ numbers, where νo = μo/Fo is the kinematic viscosity of the continuous phase and γ is the surface tension between the two fluids. For droplet production, the capillary number represents a measure of the relative importance of viscous forces to surface tension forces. For chemical reactions along an interface, a convenient dimensionless parameter is the Damk€ohler number Da,8 which is a measure of the chemical reaction rate k (with units of s-1, for a first order chemical reaction) to some physical transport rate. Since our interest is in understanding an interfacial chemical reaction in a flow-focusing geometry, then the physical transport rate may be based on how long the two reactants are in contact prior to drop production or Da ¼
kd U
ð1Þ
The velocity is analogous to the production frequency, ω = U/d; 4 therefore, the definition of the Damk€ohler number is a ratio of the reaction rate and production frequency. Continuing with this line of reasoning, we can qualitatively understand the transport of the surfactant, with surface concentration Γ, using the interfacial (8) Fernandez, J.; Homsy, G. M. J. Fluid Mech. 2003, 480, 267–281. (9) Fernandez, J. M.; Homsy, G. M. Phys. Fluids 2004, 16, 2548–2555. (10) Krechetnikov, R.; Homsy, G. M. Phys. Fluids 2004, 16, 2556–2566. (11) Stone, H. A. Phys. Fluids A 1990, 2, 111–112.
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convection-diffusion equation,11 Γt þ rs 3 (vΓ) = Dsrs2Γ þ kΓ, where we have inserted a model for a first-order chemical reaction r = kΓ, v is the fluid velocity at the interface, and Ds is the surface diffusivity. The subscript denotes a partial derivative with respect to time and rs is the surface gradient operator. We can nondimensionalize the equation by using the chemical reaction rate, 1/k, as the time scale and d as the length scale, so the equation becomes Γt þ rs 3 ðvΓÞ ¼
1 r2 Γ/ þ Γ/ Pes Da s
ð2Þ
where the dimensionless variables are r*s = drs, v* = v/kd, t* = kt, and Γ* = ΓΓ0, with Γ0 being a representative upper limit for surfactant concentration such as the maximum surface density. The dimensionless velocity is inversely proportional to the Damk€ohler number (Da = kd/U) with our choice of scaling, and given the fact that the velocity is proportional to the drop speed, where a large value indicates a slow moving droplet relative to the chemical reaction rate and vice versa. The Peclet number, Pes = Ud/Ds, is the ratio of convective to diffusive transport and is typically much greater than unity for drops based on typical values for the diffusivity. In our problem, we assume surface diffusivity values that are typically Ds < 10-9 m2/s (we have assumed that the bulk and surface diffusivity are similar), drop velocities of U = 1-10 mm/s, and relative displacements of d = 100 μm. So we assume a range of Pes = O(102-103) for the following discussion. There are a number of relevant time scales that are necessary to justify assumptions used to describe the interfacial transport equation with chemical reaction. The main assumption is the partial absorption of the oleic acid onto the aqueous fluid interface, which must be the first step in the chemical reaction. This step is assumed to be rapid so that it is not the rate determining step. The oleic acid is insoluble in the aqueous phase fluid, but it is considered an insoluble surfactant that can reduce the surface tension. The oleic acid reacts with the NaOH to produce sodium oleate (the carboxylic acid salt) and water. The chemical reaction is essentially irreversible, and the sodium oleate is insoluble in the oil (since it is an ionic species) and only partially soluble in water due to its long carbon chain. Therefore, we have assumed that the chemical reaction is interfacial, and the organic product, sodium oleate, is trapped on the interface; that is, it does not diffuse into either bulk phase. Our interest in presenting the surfactant transport equation is not to find solutions but to determine qualitative features of the surfactant transport based on extreme values of the dimensionless groups. Specifically, we want to determine for what range of parameters can we expect to observe gradients in surfactant Langmuir 2010, 26(12), 9233–9239
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concentration that are developed through chemical reaction. These gradients will lead to Marangoni stresses that may alter droplet speed and morphology. For large Da, indicating a slow moving drop relative to the chemical reaction, and subsequently where DaPes . 1, the diffusive term is negligible and the concentration dynamics are governed by a balance between convection and reaction. This translates into a situation where the convection of drops downstream has some non-negligible effects on the surfactant transport and chemical reaction. The drop motion may aid or hinder the chemical reaction, but it clearly has some influence on the transport. One possibility is the unsteady transport of surfactant to the rear of the drop, by convection, leads to gradients in the concentration. The transport may be considered unsteady because the chemical reaction produces some surfactant near the front, but convection drives it to the rear (assuming that diffusion is negligible). This feature has been observed, and proposed as a transport mechanism, in some systems where surfactant transport occurs without chemical reaction.12,13 For Da ≈ 1, where PesDa is finite, the diffusive term may be non-negligible and all of the terms, convection, diffusion, and reaction, are significant. It is difficult to determine transport dynamics in this situation, since small changes in Da may result in rather large changes in system behavior. For Da , 1, indicating a fast moving drop relative to the chemical reaction, where subsequently PesDa , 1, then the diffusion term dominates the surfactant transport. In this situation, gradients in surfactant are not favorable but there still may be some modification in drop shape and speed due to the presence of surfactant, which reduces the surface tension. This range is not observed in the experiments presented in this paper but is noted in this section for completeness. In the following section, we describe the experimental setup for the formation of water/NaOH drops in oil/oleic acid streams. We then report in section 3 on differences in the droplet formation as a function of the ratio of applied pressures Pw/Po. In order to characterize the drop formation process, we report the droplet speed U, distance between two consecutive drops d, and the drop length l. In the last section, we discuss effects of in situ reduction in surface tension on droplet formation.
2. Experimental Section 2.1. Materials and Procedure. The microfluidic experiments use relief molds that are produced using common softlithography techniques.14 The experiments are performed using a flow-focusing geometry15,16 with a single input channel for both fluids. An illustration of the setup is shown in Figure 1. The channel height is 75 μm, as measured by using a profilometer, the inlet channel width is 100 μm, and the outlet channel width is 100 μm with a 50 μm contraction. The channels are made of poly(dimethylsiloxane) (PDMS) and bonded to a thin sheet of PDMS by surface plasma treatment in air. The region following the flow-focusing contraction is a straight channel of width 100 μm. The combination of geometry following the contraction, and uniform surface properties (PDMS for each wall), may be essential in producing the experimental results that are reported. The continuous phase fluid is a mixture of mineral oil (kinematic viscosity νo ≈ 40 cSt and density Fo = 880 kg/m3 at room temperature) mixed with oleic acid (viscosity ν ≈ 32 cSt and density F = 863 kg/m3 at room temperature) provided by (12) Stebe, K. J.; Maldarelli, C. J. Colloid Interface Sci. 1994, 163, 177–189. (13) Chen, J.; Stebe, K. J. J. Colloid Interface Sci. 1996, 178, 144–155. (14) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974–4984. (15) Anna, S. L.; Bontoux, N; Stone, H. A. Appl. Phys. Lett. 2003, 82, 364–366. (16) Ga~nan-Calvo, A. M. Phys. Rev. Lett. 1998, 80, 285–288.
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Unilever. The concentration of oleic acid is fixed in each experiment at 0.5 mM. The dispersed phase fluid is a mixture of deionized water with sodium hydroxide (NaOH) at concentrations of 0.5, 1.0, and 5.0 mM. The interfacial tension of the mineral oil and water in the absence of surfactant (used for reference) is estimated to be γ = O(10) mN/m from published data for surfactant-free mineral oil and water systems. We assume that all of the fluid properties (density and viscosity) remain constant at their established values, for either phase, since the concentration of reactants is small. Then the only property that varies is the surface tension, which is reduced by the interfacial chemical reaction. Also, the surfactant is assumed to remain on the interface once it is formed there. The fluids are driven by static pressure. This method is distinct from flow-rate-driven pumping (e.g., a syringe pump), since the use of specified pressures sets up corresponding flow rates. Although in a single-phase flow these two types of pumping methods would be equivalent, the same is not true in a multiphase flow since the shape of the fluid-fluid interface, which is determined by the flow itself, complicates the relationship between the pressure drop and the flow rate.4 In the static-pressure pumping approach, the fluids are placed in syringe tubes and the pressure in the air above the fluid is regulated. The pressure is controlled by precision regulators (Bellofram Type 10) with a sensitivity of 5 10-3 psig. The pressure is measured using a test gauge (Wika brand) with a resolution of 0.150 psig. All pressures are reported relative to atmosphere or psig. It is possible to estimate a range of values for the Damk€ ohler number in the presence of a chemical reaction with varying concentrations of reactants; we use previous quantitative measurements of drop length, relative displacement, and speed in pressure-driven microfluidic flow-focusing without chemical reaction,4 and an estimate for the reaction rate in a similar chemical reaction8 where it was shown that the reaction rate depends on the initial concentration of the reactants. The values for speed and displacement, which are taken from earlier measurements,4 may vary slightly in this experiment because the length and channel height are not matched, and these have a non-negligible effect on pressure-driven droplet production. Note that there is a distinction between the chemical reaction rate, k, and the rate of chemical reactants being consumed, or produced, per unit area of interface, r = kΓ.17 We have assumed that the chemical reaction is first order so that the chemical reaction rate, k, has units of s-1, which is used in determining the Damk€ ohler number. However, the chemical reaction rate has been observed to depend on the initial concentration of reactants,8 and we are using this information in determining a range of values for the Damk€ ohler number. Given reaction rate values of approximately 0.1 Hz for a concentration ratio of 10:1 (NaOH-acid) and also values for velocity, 110 mm/s, and relative displacement, 100 μm, we estimate that the range of Damk€ ohler numbers for the experiments with chemical reaction are Da = O(1) for the experiments with the highest concentration. Also, Da . 1 as the concentration decreases. Given these two bounds for surfactant production, it is now possible to comment on the various trends seen in the experiments using this dimensionless parameter. 2.2. Quantitative Measurement Methods. The images are obtained using high-speed video at frame rates (2-4 kHz) as needed depending on the experiment. The sequence of images obtained using a fast camera provides the information necessary to determine droplet length, relative distance, and speed. The drop length is a measure of the volume of the drops that are being produced. The relative displacement is a measurement of the likelihood of droplet interactions where closer drops are more likely to interact (possibly coalesce) than drops with a larger relative distance. The drop velocity measurement is proportional to the speed of the surrounding fluid, so its value is also a measure (17) Holland, C. D.; Anthony, R. G. Fundamentals of Chemical Reaction Engineering, 2nd ed.; McGraw-Hill, Inc.: New York, 1989.
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Figure 2. Images of a microthread that breaks up into small droplets for the largest concentration of NaOH = 5.0 mM at pressure ratios as listed in the image. All of the pressure ratios are small, indicating very little flow of the dispersed phase fluid. The thread forms at the tip of the aqueous NaOH stream in a thread that appears to break up downstream. The scale bar is shown at the bottom. of the continuous phase fluid speed. Nevertheless, the presence of surfactant can alter this measurement as the speed will be influenced by the drop chemistry in the form of Marangoni stresses.3,11,18,19,13 A single algorithm, written in MATLAB programming language, is used to determine all three measurements. All lengths reported in the results below, unless otherwise noted, are scaled by the orifice diameter which is 50 μm. Since the algorithm relies on image contrast, there will be some unavoidable errors in the measurements. This effect will be clear when comparing results for different concentrations, since all of the experiments for a given concentration were typically performed at a given time. So, when comparing experiments for a given concentration, the results will be more robust. Nevertheless, the errors associated with the contrast are minimal for most of the results shown.
3. Experimental Results 3.1. Qualitative Observation. 3.1.1. Tip-Streaming Phenomenon. We begin the discussion of the experimental results with observations of droplet production for Da = O(1), where we observe the appearance of a thin thread that forms at the lowest pressure ratios for penetration of the dispersed phase fluid,4 and at the highest reactant concentrations used of 5 mM NaoH with 0.5 mM oleic acid. Images of thin threads that form are shown in Figure 2 with the pressure ratio listed to the right of each image. These images are results of experiments when droplets are first produced; that is, at water pressures less than these values, there are no observations of droplets produced in these experiments at these concentrations. In Figure 2a, with a pressure ratio of Pw/ Po = 4.75/7.5, a narrow thread is formed and then it breaks up at a distance of about two channel widths (∼200 μm) downstream. In the (18) Rednikov, A. Y.; Ryazantsev, Y. S.; Velarde, M. G. Phys. Fluids 1994, 6, 451–468. (19) Ratulowski, J.; Chang, H.-C. J. Fluid Mech. 1990, 210, 303–328.
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Figure 3. Representative images of droplets being produced for fixed pressures of (a-d) Pw = 6.0 psig and Po = 12.5 psig at various concentrations of (a) no oleic acid or NaOH, (b) 0.5 mM oleic acid and 0.5 mM NaOH, (c) 0.5 mM oleic acid and 1 mM NaOH, and (d) 0.5 mM oleic acid and 5.0 mM NaOH. (e-h) Pw = 9.0 psig and Po = 12.5 psig at various concentrations of (e) no oleic acid or NaOH, (f) 0.5 mM oleic acid and 0.5 mM NaOH, (g) 0.5 mM oleic acid and 1.0 mM NaOH, and (h) 0.5 mM oleic acid and 5.0 mM NaOH. Note that at the highest concentration shown the droplet shape is not constant. The scale bar is shown at the bottom.
next image, Figure 2b with Pw/Po = 4.75/10.0, the thread appears to be slightly thinner and the breakup into small droplets occurs further upstream (closer to the flow-focusing contraction) than in the previous image. The trend continues with Figure 2c with Pw/Po = 5.5/12.5 where the thread that forms is too thin to determine precisely where breakup occurs. This experiment is an example of tip-streaming, since the thread cannot remain stable for longer distances and must break up by capillary instability mechanism.20 Tip-streaming is also observed in flow-focusing geometries in the presence of surfactants,1 so we do not believe that this phenomenon is caused solely by the chemical reaction, but rather by a combination of surfactant that is produced by the chemical reaction and transport to the tip where it lowers the surface tension to a level that is sufficient to support cusp formation. In Figure 2d, with Pw/Po = 6.5/15, the thread that forms is barely visible with our camera resolution at our magnification. While the size of the thread and subsequent droplets that form cannot be measured, it is observed that they are on the order of a single pixel for the image, which is approximately 1 μm. 3.1.2. Drop Size and Relative Displacement. At pressure ratios higher than those used in the previous results, drops are produced with sizes comparable to the orifice. Figure 3a-d shows images from experiments performed using each of the four different concentration pairs at pressures of Po = 12.5 psig and Pw = 6.0 psig. The first image, Figure 3a, shows the results for drops with no chemical reaction, while Figure 3d is an experimental image with the maximum aqueous dispersed phase concentration of 5 mM NaOH, and 0.5 mM oleic acid in the continuous phase. The most noticeable trend is the decrease in the size of the drops as the concentration of the aqueous phase NaOH is increased. Another feature is the relative displacement of the drops after formation. There appears to be little difference in the relative displacement in the first two images, Figure 3a and b. (20) de Bruijn, R. A. Chem. Eng. Sci. 1993, 48, 277–284.
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There is a noticeable increase in distance between drops in Figure 3b and c, though this trend though does not hold when comparing Figure 3c and d where the distance between the drops decreases significantly. For comparison, we consider another set of images with a continuous phase pressure that is similar to the previous example. In this set of images, shown in Figure 3e-h, the continuous phase pressure is Po = 12.5 psig and the dispersed phase fluid pressure is Pw = 9.0 psig. Again, the first image, Figure 3e, is the result for drops with no chemical reaction, while Figure 3h is an experimental image with the maximum aqueous dispersed phase concentration of 5 mM NaOH and 0.5 mM oleic acid in the continuous phase. The size of the drops after formation does not appear to have the same clear trend of a decrease in size as the concentration is increased, although there is a noticeable decrease in size from Figure 3e to g. The other observable feature related to the relative displacement of the droplets is similar to the experiments shown in Figure 3a-d. Another distinctive feature of the surfactant production is shown in Figure 3h. In this experiment, the concentrations of reactants are the largest at 5 mM NaoH with 0.5 mM oleic acid. In the image, it is evident that as the drops are formed and travel downstream, there is a change in length of the drops. This phenomenon is illustrated by considering the front-to-rear distance between consecutive drops, shown in Figure 3h, where this distance decreases as the drops travel downstream. A similar trend is observed in Figure 3g, although the change in length is not as evident as in Figure 3h. These observations suggest that the drop lengths are not constant, so that for a drop of constant volume the implications are an increase in the region separating the drops from the walls of the microfluidic channel.19 This dynamical effect should change some of the dynamics of droplet motion that are discussed in the quantitative analysis section. 3.2. Quantitative Measurements. We next report the quantitative results for the experiments. In sections 3.2.1-3, we report trends with changes in chemical reactant concentrations when discrete drops are formed. In each of the figures, each color represents the relative concentration of the NaOH to oleic acid with green = no oleic acid or NaOH, red = 0.5 mM oleic acid and 0.5 mM NaOH, blue = 0.5 mM oleic acid and 1 mM NaOH, and black = 0.5 mM oleic acid and 5 mM NaOH. Each symbol represents a given continuous phase fluid pressure with O = 7.5 psig, ) = 10 psig, 4 = 12.5 psig, and = 15.0 psig. Each symbol represents an average value. The standard deviation bars for each averaged value are typically smaller than the size of the symbol, indicating either a large number (>10), or a robust set, of measurements. 3.2.1. Relative Distance. We report, in Figure 4a, the trends for the relative distance between drops (normalized by the width of the orifice a) after they are formed and travel downstream. There are trends in the data for a given concentration. The general trend appears as a decrease in the distance between consecutive drops and then an increase. The minimum is at approximately d/a = 2-3 depending on the concentrations used. Also, the trends when comparing one concentration to another are a decrease in the distance between drops as the concentration increases, with the experiments with no chemical reaction (green) having the largest distances and the experiments with the largest concentration (black) having the smallest. In fact, it appears that the experiments with the largest concentration have what looks like a nearly constant distance between drops of approximately d/a = 2. This result is not reported in any of the other experiments shown in the plot. Data for several of the largest pressure ratios, and at the highest concentration, are not measured because the Langmuir 2010, 26(12), 9233–9239
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drops merge downstream. Note that the error in measuring the drop length (due to deformation of the drop as it travels downstream) does not appear in this set of data, since the relative distance is a measurement of the center-to-center distance between drops which appears to remain constant for a given experiment. 3.2.2. Drop Velocity. The next set of data, Figure 4(b), shows results of the velocity of the drops (in mm/s) which is a measurement of the dynamics of the drop motion as they are produced and travel downstream. These values are also a measurement of the droplet production frequency, ω, according to our previous results with the velocity U = ωd. Here, the data are shown for a single continuous phase fluid pressure of Po = 12.5 psig (4) while varying the dispersed phase fluid pressure. The velocities appear to be in the range of 6-18 mm/s depending on the concentrations used. The trends appear to be dependent on the specific experiment. The experiments with zero concentration have the largest speed and also the largest error bars, but the fractional errors are small. This result is consistent with previous studies.4 Note that the large deviation is probably due to the images that are blurry at these higher speeds, so the position with respect to time has some variations. This error could potentially have been reduced by increasing the frame rate, but sufficient lighting then became an issue. The next highest concentrations, red and blue, show a strong decrease in the drop speed which appears to be approximately linear. The red experiments with a concentration of 0.5 mM oleic acid and 0.5 mM NaOH show an increase in speed only at the very highest pressure ratio, while the blue experiments with a concentration of 0.5 mM oleic acid and 1.0 mM NaOH do not. Surprisingly, though, the black experiments do not show the same decrease as the other experiments with chemical reaction and instead, similar to the experiment without the chemical reaction, have a nearly constant velocity ranging 12-14 mm/s. 3.2.3. Drop Length. The experimental results for the drop sizes are shown in Figure 5. The most noticeable trend is the similarity in the curves based on their concentrations. These trends are analogous to those first reported by Ward et al.,4 where similar experiments were performed. The trends comparing the data for one concentration to another are not large, suggesting the results are nearly independent of concentration except at the lowest pressures and highest concentration where the drops produced are smaller than the orifice (see Figure 2). This feature is highlighted in Figure 5 by an absence of data for the largest concentration experiments at the lowest pressure ratios. Otherwise, it appears that the 0.5 mM oleic acid and 0.5 mM NaOH concentration (red) produces the largest droplets in Figure 5, while the 0.5 mM oleic acid and 1 mM NaOH concentration (blue) produces the smallest drop sizes, with no discernible trend for the highest concentration results (black). The overall trend of an increase in drop size with increasing pressure ratio in each experiment is shown.
4. Discussion and Conclusion 4.1. Drop Size and Displacement. We begin this section with some additional discussion on the effects of in situ surfactant production on the drop length, which is a measure of the volume, and relative displacement in a microfluidic flow-focusing geometry. Microthread formation and tip-streaming occur around Da ≈ 1 based on our results. For tip-streaming, the carboxylic acid must first adsorb more quickly to the surface than the rate of interfacial convection, which is approximately U/d. Without this, there would be no surfactant on the surface. The reaction rate, k, must DOI: 10.1021/la100029q
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Figure 4. (a) Measurement of the distance between consecutive drops produced in a microfluidic flow-focusing geometry combined with the production of a surfactant along the interface. The symbols represent the oil pressure: O = 7.5 psig, ) = 10.0 psig, 4 = 12.5 psig, and = 15.0 psig. (b) Graph showing the quantitative measurement of the average velocity, in mm/s, for a drop produced in a microfluidic flowfocusing geometry combined with the production of a surfactant along the interface with a constant oil pressure of 4 = 12.5 psig while the water/NaOH pressure is varied. The colors represent the relative concentration of the NaOH to oleic acid with green = no oleic acid or NaOH, red = 0.5 mM oleic acid and 0.5 mM NaOH, blue = 0.5 mM oleic acid and 1.0 mM NaOH, and black = 0.5 mM oleic acid and 5.0 mM NaOH.
Figure 5. Measurement of the length of drops produced in a microfluidic flow-focusing geometry combined with the production of a surfactant along the interface. The symbols represent the oil pressure: O = 7.5 psig, ) = 10.0 psig, 4 = 12.5 psig, and = 15.0 psig. The colors represent the relative concentration of the NaOH to oleic acid with green = no oleic acid or NaOH, red = 0.5 mM oleic acid and 0.5 mM NaOH, blue = 0.5 mM oleic acid and 1.0 mM NaOH, and black = 0.5 mM oleic acid and 5.0 mM NaOH.
also be at least as fast as the convection rate (Da ≈ 1) so that a sufficient amount of the adsorbed carboxylic acid species can be converted into the surfactant sodium oleate, which is insoluble in oil and partially soluble in water. With enough conversion of the acid, the sodium oleate collects at the dispersed phase fluid tip, causing a dramatic reduction in surface tension at the tip, which creates streaming. So the mechanism for tip-streaming is a unique one, as we rely on one soluble surfactant (oleic acid) to adsorb 9238 DOI: 10.1021/la100029q
rapidly on the surface. In addition, we rely on a reaction to generate an insoluble surfactant at a sufficient rate to allow for a large enough concentration at the tip. The key is the insolubility of the carboxylate anion; it does not desorb off of the surface, which ensures accumulation and streaming. Soluble surfactants can cause tip-streaming, but they must be properly selected so that the desorption rate of the soluble surfactant at the tip is slow relative to the interfacial convection rate. An interfacial reaction ensures that this is true. Another feature of the experiments with chemical reaction is the change in the relative distance between drops at the various reactant concentrations shown in Figure 4a. Here the trends are a flattening of the curve for the relative displacement versus pressure ratio until it approaches a nearly constant value. Another trend is the increase in the maximum pressure ratio for higher Da relative to the Da ≈ 1 result. The implications here are based on the fact that the distance between drops not only provides some measure of the concentration of the dispersed phase fluid but also provides a measure of when to expect thread formation (thread formation occurs when l = d). So the flattening of the curve suggests that the system will form a thread at a much lower pressure ratio than that in a similar experiment without a surfactant producing interfacial chemical reaction. We do not believe this trend has been previously reported in the literature. 4.2. Chemical Reaction Driven Dynamics. Information on the droplet speed will be used in this section to discuss the dynamic morphology of a drop after it forms and travels downstream. The speed of a drop is, in general, significantly influenced by the shape of the drop. At low dispersed phase fluid pressures, or equivalently low pressure ratios, the drops are nearly spherical in shape. At higher pressure ratios, the droplets fill the downstream channels and their shapes can therefore be influenced by the channel walls. Previous experiments for pure fluids4 determined that the continuous phase fluid pressure (or equivalently the continuous phase fluid flow rates) was not seen to influence the Langmuir 2010, 26(12), 9233–9239
Ward et al.
shape of the drops as they traveled downstream. This observation was based, in part, on the fact that the shapes of the drops were constant post formation and the lengths of the drops were all similar for a given pressure ratio, at least for the range of parameters studied, where the capillary numbers were small (Ca < 10-2, based on continuous phase fluid viscosity). For the experiments discussed in this paper, the same fact is not true. The drop shapes are clearly modified at higher continuous phase fluid pressures, and therefore external fluid speeds, as the concentration of chemical reactants increases; an example is shown in Figure 3h. This effect will modify the droplet speeds, especially at higher dispersed phase fluid pressures, or equivalently higher pressure ratios, since the modification in shape may lead to deformation of the drop resulting in retraction of the drop length or elongation of the drop, relative to a surfactant free drop. An elongated drop will move faster, since the fluid film between the drop and the wall will be thicker; that is, more fluid will be able to pass between the drop and wall so that the drop can move with a speed that is closer to that of the fluid speed in the center of the channel. A retracted drop would move slower, since there is a thinner film and hence less leakage past the drop. Another possible explanation for changes in droplet velocity with changes in chemical reactants is Marangoni stresses. The presence of surfactants along a fluid interface are known to produce additional drag as part of the interface becomes immobile. Deformation can occur when the dominance of forward translational drop motion due to the external fluid pressure overcomes the additional drag created by the presence of the surfactant.19,18,13,12 Distinguishing between these two effects, high capillary number or Marangoni stresses, is not possible with our experiments, so we comment on the features based on the data presented. The main result in our experiments is the decrease in the velocity versus pressure ratio plots, shown in Figure 4b, for the experiments with concentrations of 0.5 mM oleic acid and 0.5 mM NaOH (red) and 0.5 mM oleic acid and 1.0 mM NaOH (blue). In these plots, the velocity shows a nearly linear decrease as the pressure ratio increases. For these experiments, the chemical reactions occur faster than the drops are produced, which suggests that once the drops are formed, no new surfactant is produced. Since there is no new surfactant being produced, then all of the surfactant is convected to the rear of the drop.21 This effect should be expected to produce Marangoni stresses. The experiments with the highest reactant concentration, and hence the largest concentration of surfactant, with 0.5 mM oleic acid and 5.0 mM NaOH (black), do not show the same monotonic decrease in drop velocity as the other two experiments with chemical reaction. In these experiments, the Damk€ohler number is O(1), suggesting that the chemical reaction is still proceeding as the drop travels downstream. This feature is probably the main cause for the lack of monotonic behavior as the pressure ratio is (21) Borhan, A.; Pallinti, J. Phys. Fluids 1999, 11, 2846–2855.
Langmuir 2010, 26(12), 9233–9239
Article
increased, since the surfactant decreases the interfacial tension over a larger portion of the drop interface. This increase in surfactant concentration, and production, also results in the ability to deform the interface over a larger domain so that the front of the drops experiences significant deformation. Indeed, this feature is shown in Figure 3h where the distance between consecutive drops increases with time. Since the length increases while the volume remains constant, then it is possible to drag more liquid past the drop; that is, the distance between the drop interface and the wall increases, resulting in a drop that moves more with the speed of the central portion of the channel which is always faster. 4.3. Conclusion. In this paper, the production of droplets in a microfluidic flow-focusing geometry is studied in the presence of an interfacial chemical reaction. The reactants are an aqueous sodium hydroxide (NaOH) solution as the dispersed (drop) phase and a mixture of mineral oil and oleic acid as the continuous phase. Since the drops are being produced in the presence of an interfacial chemical reaction, it is useful to introduce the Damk€ohler number (Da) as the dimensionless operating parameter, which represents a measure of the chemical reaction rate to the frequency of drop production. The flow conditions are parametrized using the ratio of dispersed phase fluid pressure to continuous phase fluid pressure, Pw/Po. Based on our flow conditions, it is proposed that our Damk€ohler number is approximately unity at our highest concentration and much higher in the other experiments performed. The chemical reaction produces a surfactant that lowers the interfacial tension, which modifies the droplet production process, at low pressure ratios, and also the measured droplet velocities, depending on the value of Da. At low values of Da and also low pressure ratios, a tip-streaming phenomenon is observed. The main results for drop length, relative distance between drops, and drop speed suggest that interfacial chemistry can play a significant role and change the dynamics of droplet motion and breakup. This information may be useful in similar systems where a surfactant is introduced into the bulk phase to aid droplet breakup and also stabilize the system, such as in the formation of emulsions. For the emulsion systems, it may be more efficient to introduce chemical reactants that produce a surfactant in order to generate the dispersed phase, since it may lead to the tip-streaming type phenomenon observed in this work. In the future, it may be beneficial to observe behavior for low Da where the chemical reaction mainly occurs upstream of the flow-focusing geometry. Acknowledgment. Experiments were performed at Harvard University in the Stone fluids lab. We thank a referee for providing useful feedback on a previous version of the manuscript. We thank Unilever Research and the Harvard MRSEC (DMR-082048) for support of this research.
DOI: 10.1021/la100029q
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