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Dynamics of Bubble Formation in Highly Viscous Liquids Ketan Pancholi, Eleanor Stride,* and Mohan Edirisinghe Department of Mechanical Engineering, UniVersity College London, Torrington Place, London WC1E 7JE, United Kingdom ReceiVed December 10, 2007. In Final Form: January 14, 2008 There has recently been considerable interest in the development of devices for the preparation of monodisperse microbubble suspensions for use as ultrasound contrast agents and drug delivery vehicles. These applications require not only a high degree of bubble uniformity but also a maximum bubble size of 8 µm, and this provides a strong motivation for developing an improved understanding of the process of bubble formation in a given device. The aim of this work was to investigate bubble formation in a T-junction device and determine the influence of the different processing parameters upon bubble size, in particular, liquid viscosity. Images of air bubble formation in a specially designed T-junction were recorded using a high-speed camera for different ratios of liquid to gas flow rate (Ql/Qg) and different liquid viscosities (µl). It was found that theoretical predictions of the flow profile in the focal region based on analysis of axisymmetric Stokes flow were accurate to within 6% when compared with the experimental data, indicating that this provided a suitable means of describing the bubble formation process. Both the theoretical and experimental results showed that Ql/Qg and µl had a significant influence upon bubble formation and eventual size, with higher flow rates and higher viscosities producing smaller bubbles. There were, however, found to be limiting values of Ql/Qg and µl beyond which no further reduction in bubble size was achieved.
Introduction The use of gas microbubbles stabilized by a surfactant or polymer coating as contrast agents for ultrasound imaging is well established, and there has been increasing interest in their use as vehicles for ultrasound-mediated targeted drug delivery and gene therapy.1-3 This latter application requires a high degree of control over the size and uniformity of microbubbles in order to ensure accurate dosing of a given drug and maximize delivery efficiency. T-junction devices provide a means of achieving this control, enabling monodisperse microbubble suspensions to be prepared by the impingement of a gas stream into a liquid flow at a narrow orifice.3 A further requirement for microbubbles which are to be administered intravenously, however, is that they are smaller than 8 µm in diameter in order to minimize the risk of embolism. There is consequently a significant need for improved understanding of bubble formation in terms of the key parameters controlling the process. The dynamics of bubble formation have been studied widely, both theoretically and experimentally, and it has been shown that bubbles are formed via a “pinch-off” process due to instability of the gas/liquid interface.4-6 The wavelength of this instability determines the size of the bubble formed,7 with more rapid pinching-off producing smaller bubbles. This, in turn, depends * To whom correspondence should be addressed. Phone: +44(0)2076793938. Fax: +44(0)2073880180. E-mail:
[email protected].
Figure 1. Schematic of the T-junction device: (a) system apparatus and (b) junction geometry.
(1) Talu, E.; Lozano, M. M.; Powell, R. L.; Dayton, P. A.; Longo, M. L. Long-term stability by lipid coating monodisperse microbubbles formed by a flow-focusing device. Langmuir 2006, 22 (23), 9487-9490. (2) Unger, E. C.; Porter, T.; Culp, W.; Labell, R.; Matsunaga, T.; Zutshi, R. Therapeutic applications of lipid-coated microbubbles. AdV. Drug DeliVery ReV. 2004, 56 (9), 1291-1314. (3) Pancholi, K.P.; Farook, U.; Moaleji, R.; Stride, E.; Edirisinghe, M. Novel methods for preparing phospholipid coated microbubbles. Eur. Biophys. J. 2008, in press; DOI 10.1007/s00249-007-0211-x. (4) Ganan-Calvo, A. M.; Gordillo, J. M. Perfectly monodisperse microbubbling by capillary flow focusing. Phys. ReV. Lett. 2001, 87 (27), 274501-274504. (5) Gordillo, J. M.; Cheng, Z. D.; Ganan-Calvo, A. M.; Marquez, M.; Weitz, D. A. A new device for the generation of microbubbles. Phys. Fluids 2004, 16 (8), 2828-2834. (6) Jensen, M. J.; Stone, H. A.; Bruus, H. A numerical study of two-phase Stokes flow in an axisymmetric flow-focusing device. Phys. Fluids 2006, 18 (7), 077103-077113.
upon the liquid:gas flow rate ratio, which must be increased in order to reduce bubble size. For a fixed gas pressure, however, there will be a maximum liquid flow rate above which the gas flow will become choked and no bubbles can be formed.4 Similarly, the gas pressure cannot be increased indefinitely without resulting in atomization of the liquid. Moreover, the maximum liquid flow rate will also be limited by the diameter of the channel through which it is flowing. The aim of this study, therefore, was (7) Garstecki, P.; Fuerstman, M. J.; Whitesides, G. M. Oscillations with uniquely long periods in a microfluidic bubble generator. Nat. Phys. 2005, 1 (3), 168-171.
10.1021/la703849x CCC: $40.75 © 2008 American Chemical Society Published on Web 03/11/2008
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Figure 2. Time evolution of a bubble: (a) Air meets liquid at the T-junction, and two-phase flow is established. The cross-sectional area available for the liquid flow is reduced, and since liquid flow rate is kept constant by the syringe pump the liquid pressure increases sharply, causing the bubble to “pinch-off” as shown in the sequence b, c, d, e. At the appropriate flow rate ratio, bubble generation is continuous, as illustrated in (f).
Figure 3. Relationship between pinch-off time and minimum neck radius during bubble formation for different flow rate ratios and liquid viscosities: (a) 48.5, (b) 485.5, (c) 4.85, and (d) 192.4 mPa s.
to investigate the mechanism of bubble formation in detail and determine the influence of other variables, in particular, liquid viscosity, to determine the extent to which bubble size could be controlled.
Materials and Methods 1. Apparatus. A specially designed T-junction device has been developed which is capable of operating at high pressures (∼1 MPa) without undergoing elastic deformation.6 Two Teflon FEP (fluori-
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Pancholi et al. Table 1. Comparison of Theoretical Prediction of the Gas Flow Profile with Experimental High-Speed Camera Images for Different Flow Rate Ratios and Liquid Viscosities air column radius (r)
Figure 4. Relationship between power law coefficient (eq 5) and liquid viscous stress. nated ethylene polypropylene) capillaries with internal diameter D ) 150 µm are coaxially aligned and embedded in a rigid acrylic perspex block (100 × 100 × 10 mm) with their ends separated by a distance h ) 70 µm. A third capillary is inserted into the block with its axis perpendicular to that of the others in order to form the T-junction (see Figure 1). Each capillary is secured mechanically to the block via a standard HPLC (high-performance liquid chromatography) connector to prevent any slippage at the junction during operation at high pressure. The capillary forming the upper arm of the T-junction (Figure 1) is connected to a gas cylinder supplying air at constant pressure Pg as measured by a digital manometer. The capillary forming the perpendicular lower arm is connected to a reciprocating plunger HPLC pump, which provides nonpulsating liquid flow at a constant flow rate Ql, maintained by the flow meter in the digital pump. Microbubbles are collected from the outlet of the third capillary. Hereafter Q, U, F, µ, σ, P, and G will be used to denote flow rate, velocity, density, viscosity, interfacial tension, pressure, and strain rate, respectively, whereas subscripts g and l will indicate gas or liquid. The coordinate system used to describe the process is shown in Figure 1b in terms of axial position (z) and radial position (R) measured from the intersection of the perpendicular capillary axes. To the best of the authors’ knowledge, the only previous studies of bubble formation in viscous liquids were carried out using a planar geometry with a maximum liquid viscosity of 100 mPa s.7,8 In this study, microbubble generation in a three-dimensional geometry was investigated, with silicone oils having viscosities from 4.85 to 485.5 mPa s used as the continuous liquid phase (Univar, Cheadle, Chesire, U.K.). Air was used as the disperse phase. The densities and surface tension values for the oils were approximately equal.9 Real-time video images of bubble formation were taken with a Phantom V5 high-speed camera (Vision Research Ltd. Bedford, U.K.) using the manufacturer-supplied software (version 605.2). The bubble formation process was captured with 5× magnification, and screen resolution was kept constant at 512 × 512 during image capture so that the image resolution was 1.5 µm per pixel. Exposure time was varied between 15 and 43 µs, and the interval between two images was between 4 and 14 µs. A typical sequence is shown in Figure 2. 2. Experimental Procedure and Analysis. For each oil of given viscosity, the effect of varying the gas pressure (Pg) from 0.64 to (8) Garstecki, P.; Fuerstman, M. J.; Stone, H. A.; Whitesides, G. M. Formation of droplets and bubbles in a microfluidic T-junction - scaling and mechanism of break-up. Lab on A Chip 2006, 6 (3), 437-446. (9) Jayasinghe, S. N.; Edirisinghe, M. J. Electrically forced jets and microthreads of high viscosity dielectric liquids. J. Aerosol Sci. 2004, 35 (2), 233-243.
liquid viscosity (mPa s)
flow rate ratio
theoretical (m)
experimental (m)
difference (%)
48.5 48.5 48.5 4.85 48.5 48.5 48.5 192.4 192.4 192.4 485.5 485.5 485.5
0.11 0.19 0.09 0.50 0.07 0.91 0.63 0.03 0.08 0.09 0.02 0.03 2.04
0.096 0.068 0.09 0.112 0.121 0.072 0.096 0.076 0.055 0.062 0.087 0.075 0.035
0.095 0.069 0.089 0.110 0.117 0.076 0.100 0.08 0.058 0.060 0.088 0.077 0.037
1.3 -2.1 0.8 2.0 3.1 -5.0 3.5 4.7 1.1 4.5 3.2 -2.3 -6.0
17 kPa was determined for different liquid flow rates (Ql) from 1.66 × 10-10 to 8.33 × 10-8 m3/s. For each flow rate ratio (Ql/Qg) 15 sets of video data were taken, with a 10 min settling time allowed between changes to any of the flow parameters. In order to ensure that the system was in dynamic equilibrium, the liquid pressure Po was observed on the pump pressure gauge each time a microbubble formed to confirm that any fluctuations in gas and liquid pressure at the T-junction were confined to a small range ((5%). Between experiments the junction was flushed with ethanol for 60s at 0.083 mL/s and with air at 0.5 MPa pressure. All experiments were carried out at 22 °C ambient temperature. For each set of conditions (µl, Pg, and Ql) measurements were made from the video images of the following: (i) the air jet diameter (Rg(z,t)) along the capillary at each time interval; (ii) the time (tc) taken for bubble pinch-off to occur, taken as the time from when a neck first begins to form in the air column to that of the last frame before it ruptures (due to the finite frame rate of the camera this measurement had an associated error of (5 µs); (iii) the length of the resulting microbubble (slug); and (iv) its velocity. Average values were then calculated for further analysis. The liquid velocity (Ul) was found by dividing the volume flow rate by the cross-sectional area occupied by liquid at a given point (z) along the capillary Ul )
Ql π(Rc - Rg2) 2
(1)
where Rc is the inner radius of the capillary (D/2) and Rg is the radius of the air column measured from the video images (Figure 2). The Reynolds numbers for the liquid and gas were calculated, respectively, as Q lF l µ lD
(2)
Q gF g µg2Rg
(3)
Rel ) and Reg )
The capillary number for the liquid was found as Cal )
U l µl σ
(4)
Results and Discussion 1. Relationship between Minimum Neck Radius and PinchOff Time. The liquid velocity (Ul) ranged from 2.6 × 10-2 to 10.6 ms-1 and the corresponding Reynolds numbers (Rel) from 0.0078 e Rel e 3.15 (for the gas, 0.160 e Reg e 255). Similarly,
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Figure 5. Comparison of theoretical prediction of the gas flow profile with experimental high-speed camera images for flow rate ratio 0.194 and liquid viscosity 48.5 mPa s. Z is normalized with respect to capillary radius (Rc).
the calculated liquid capillary numbers were in the range 14.05 e Cal e 0.634, indicating that bubble formation was more strongly influenced by viscous forces than by either inertial or surface tension effects. As may be seen in the consecutive images in Figure 2, the air column enters the liquid at the T-junction and, after a short distance, a neck begins to form. The neck becomes increasingly narrow, and eventually a bubble (or “slug”) detaches from the main air column. The relationship between the minimum radius (Rm) of the neck and the time taken for bubble pinch-off to occur was investigated by plotting Rm against time before separation10 (τ ) tc - t) for different flow rate ratios and liquid viscosities (Figure 3). It was found that the data could be described by a power law
Rm ) Rτx
(5)
where the parameters R and x depend upon both viscosity and flow rate ratio, i.e., bubble formation depends upon the rate of evolution of viscous stress. In a quiescent liquid, a linear relationship would be expected, i.e., x ) 1, but in this study x was found to be
