pubs.acs.org/Langmuir © 2010 American Chemical Society
Hysteresis in Multiphase Microfluidics at a T-Junction Michele Zagnoni,* Jamie Anderson, and Jonathan M. Cooper* Department of Electronics and Electrical Engineering, University of Glasgow, G12 8LT, United Kingdom Received January 28, 2010. Revised Manuscript Received April 27, 2010 Multiphase microfluidics offer a wide range of functionalities in the fields of fluid dynamics, biology, particle synthesis, and, more recently, also in logical computation. In this article, we describe the hysteresis of immiscible, multiphase flow obtained in hydrophilic, microfluidic systems at a T-junction. Stable and unstable state behaviors, in the form of segmented and parallel flow patterns of oil and water, were reliably produced, depending upon the history of the flow rates applied to the phases. The transition mechanisms between the two states were analyzed both experimentally and using numerical simulations, describing how the physical and fluid dynamic parameters influenced the hysteretic behavior of the flow. The characteristics of these multiphase systems render them suitable to be used as pressure comparators and also for the implementation of microfluidic logic operations.
Introduction A system is said to have hysteresis, or to present a memory effect, when its current output state cannot be predicted without knowing the initial state of the system and the history of the inputs. These properties, typical of magnetic and elastic materials, are considered of great importance in technology. For instance, the ability to define system states provides means to perform threshold recognition and to store information in electronic devices.1 Microfluidic systems have been previously used to mimic the hysteretic behavior of bistable electronic components, either by exploiting the non-Newtonian properties of the fluids2 or by using multiphase droplet-based systems.3-5 Emulsion systems in microfluidics, which make use of immiscible fluids (i.e., oil and water) to form compartmentalized and stable microdroplets, are increasingly gaining the attention of the scientific community, spanning a variety of technological applications in the fields of analytical/ combinatorial chemistry and biochemistry,6-8 cell analysis,9-11 and particle synthesis.12-14 Two fundamental types of emulsions *Corresponding author. Michele Zagnoni, Bioelectronics Research Centre, Department of Electronics and Electrical Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, G128LT, Glasgow, United Kingdom. E-mail addresses:
[email protected];
[email protected]. (1) Bertotti, G.; Mayergoyz, I. D. The Science of Hysteresis; Academic Press: London, 2006. (2) Groisman, A.; Enzelberger, M.; Quake, S. R. Science 2003, 300, 955–958. (3) Toepke, M. W.; Abhyankar, V. V.; Beebe, D. J. Lab Chip 2007, 7, 1449–1453. (4) Cheow, L. F.; Yobas, L.; Kwong, D. L. Appl. Phys. Lett. 2007, 90, 054107. (5) Cybulski O.; Garstecki P. Lab Chip 2010, DOI: 10.1039/b912988j. (6) Chen, D.; Du, W.; Liu, Y.; Liu, W.; Kuznetsov, A.; Mendez, F. E.; Philipson, L. H.; Ismagilov, R. F. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 16843–16848. (7) Edgar, J. S.; Milne, G.; Zhao, Y.; Pabbati, C. P.; Lim, D. S. W.; Chiu, D. T. Angew. Chem., Int. Ed. 2009, 48, 2719–2722. (8) Frenz, L.; El Harrak, A.; Pauly, M.; Begin-Colin, S.; Griffiths, A. D.; Baret, J. C. Angew. Chem., Int. Ed. 2008, 47, 6817–6820. (9) Brouzes, E.; Medkova, M.; Savenelli, N.; Marran, D.; Twardowski, M.; Hutchison, J. B.; Rothberg, J. M.; Link, D. R.; Perrimon, N.; Samuels, M. L. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 14195–14200. (10) Koster, S.; Angile, F. E.; Duan, H.; Agresti, J. J.; Wintner, A.; Schmitz, C.; Rowat, A. C.; Merten, C. A.; Pisignano, D.; Griffiths, A. D.; Weitz, D. A. Lab Chip 2008, 8, 1110–1115. (11) Liu, W.; Kim, H. J.; Lucchetta, E. M.; Du, W.; Ismagilov, R. F. Lab Chip 2009, 9, 2153–2162. (12) Dendukuri, D.; Tsoi, K.; Hatton, A.; Doyle, P. S. Langmuir 2005, 21, 2113–2116. (13) Shah, R. K.; Kim, J. W.; Agresti, J. J.; Weitz, D. A.; Chu, L. Y. Soft Matter 2008, 4, 2303–2309. (14) Nisisako, T.; Torii, T.; Higuchi, T. Chem. Eng. J. 2004, 101, 23–29.
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are often used: either water droplets in oil (W/O), which are naturally suitable for biological and biochemistry applications, or oil droplets in water (O/W), which are primarily employed for particle synthesis. In addition, the two emulsion templates can also be combined together to form complex, flow-encapsulated structures from multiple emulsions.15 Recently, it has been suggested that segmented flow systems could also be used to encrypt and decrypt signals coded in a network of W/O droplets16 or bubbles,17 exploiting the property of reversibility of laminar flows and the pressure-driven flow characteristics of emulsions in microchannels. The behavior of multiphase flow in microfluidics has been characterized and reviewed both for W/O18,19 and for O/W droplet systems.12,20-23 However, the memory effect of these types of flow has not yet been described. The aim of this paper is to characterize the hysteresis of immiscible viscous fluids at a microfluidic, hydrophilic T-junction, providing a description of the flow mechanisms by means of experiments and numerical simulations. In our work, a bistable behavior of the phases (output) was reproducibly obtained depending upon the history of the applied phase flow rates (inputs), which produced a memory effect between two states, in the form of segmented flow (O/W) and co-flowing phases (oil and water phases flowed parallel inside the microchannel). We also explore how the property of bistability, being similar to that of solid-state electronic logic gates, could offer an alternative to already existing droplet-based, computational, and logic operations.4,5,22
Materials and Methods Materials. The water phase consisted of either Milli-Q water or Milli-Q water with surfactant Tween80 at 2 wt %, while the oil phase consisted of either calibration oil (Sheen Instr. Ltd., (15) Abate, A. R.; Weitz, D. A. Small 2009, 5, 2030–2032. (16) Fuesterman, M. J.; Garstecki, P.; Whitesides, G. M. Science 2007, 315, 828–832. (17) Prakash, M.; Gershenfeld, N. Science 2007, 315, 832–835. (18) Christopher, G. F.; Anna, S. L. J. Phys. D: Appl. Phys. 2007, 40, R319– R336. (19) Teh, S. Y.; Lin, R.; Hung, L. H.; Lee, A. P. Lab Chip 2008, 8, 198–220. (20) Dreyfus, R.; Tabeling, P.; Willaime, H. Phys. Rev. Lett. 2003, 90, 144505. (21) Shui, L.; van der Berg, A.; Eijkel, J. C. T. Lab Chip 2009, 9, 795–801. (22) Nie, Z.; Seo, M.; Xu, S.; Lewis, P. C.; Mok, M.; Kumacheva, E.; Whitesides, G. M.; Garstecki, P.; Stone, H. A. Microfluid. Nanofluid. 2008, 5, 585–594. (23) Seo, M.; Paquet, C.; Nie, Z.; Xu, S.; Kumacheva, E. Soft Matter 2007, 3, 986–992.
Published on Web 05/13/2010
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η = 7.2 mPa s at 25 °C) or mineral oil (Sigma-Aldrich, η = 35-40 mPa s at 25 °C), where both oils were used with and without surfactants Span80 (Sigma-Aldrich) at 2 wt %. A 5 mM solution of 2-[methoxy (polyethyleneoxy)propyl]trimethoxysilane (Gelest) in toluene (99.9%, Sigma-Aldrich) was prepared and stored at 4 °C for up to a week. Fabrication. The devices were fabricated using poly(dimethylsiloxane), PDMS, (Sylgard 184 Silicone Elastomer, Dow Corning) and standard photolithography (details in Supporting Information). The structure consisted of microfluidic channels with a T-junction (Figure 1a), fabricated in PDMS, and bonded to a flat PDMS slab using oxygen plasma. In order to obtain the required hydrophilic surface properties for the channels, within 20 min of bonding, the silane solution was flushed through the microfluidic channels for 1 min and the devices were then placed on a hotplate for 5 min at 100 °C. This changed the natural hydrophobic property of PDMS, producing a stable condition characterized by a contact angle of TDC. By choosing the amplitude of the water pressure fluctuation ΔPW(x) as a reference variable, a hysteresis loop can be plotted as a function of Ca, as shown in Figure 8, where the variation ΔCa in the simulation is the same order of magnitude of the one experimentally obtained in Figure 6b (γ = 4.5 mN/m). In a second set of simulations, the transition mechanism that takes place between co-flowing phase state and segmented flow state was analyzed numerically. As shown in Figure 9a starting from a co-flowing phase condition, when QW is increased stepwise (at t = 0), a fast increment of pressure in the region of the junction produces a stress upon the oil-water interface. As a response, the oil thread is pushed momentarily against the junction by the water (arrows in Figure 9a), resulting in a thinner oil thread at the corner of the junction and in a thicker oil thread in the channel downstream (due to the conservation of volume). Overall, this initial transient behavior of the oil-water interface propagates downstream, creating a traveling wave of the oil-water interface that disrupts the pre-existing equilibrium between viscous and interfacial stresses. Three different outcomes could be simulated depending upon the value of ΔQW and γ. In the first case, the co-flow condition was maintained: this is illustrated in Figure 9b and Figure 5d-f, where the pressure in the oil phase balanced the effects on the oil-water interface produced by the traveling wave. The wave amplitude was damped in time and a new equilibrium condition was achieved, progressively thinning the oil thread in the channel as QW increased. In the second case, segmented flow could be reestablished from co-flowing phases to a jetting regime, with the traveling wave at the interface generating an imbalance of pressure at the oil-water interface. As marked by arrows in Figure 9c and Figure 5g, a critical thinning of the oil thread produced surface tension stresses that induced the oil thread to break up, due to surface minimization. Finally, in the third case, if ΔQW was excessively large, a drastic increase of pressure could squeeze the oil thread directly at the junction, resetting the oil phase to the initial condition achieved for decreasing QW. These simulation results are in agreement with the experimental findings that the transition thresholds depend on the magnitude of the applied step ΔQW. In addition, as shown in Figure 6, higher values of TCD are necessary to re-establish a segmented flow when lower values of interfacial tensions are present between the phases. The formation of a traveling wave at the interface obtained from the simulation, due to a stepwise increase of QW, gives a matching
Figure 9. Numerical simulation results showing the hydrodynamic pressure distribution of the phases following an incremental step of QW. (a) Time sequence of initial behavior of the phases: QO = 1 μL/min and QW is raised from 1 to 7 μL/min. As a consequence, the oil phase is pushed against the junction corner, creating a traveling wave that propagates along the oil-water interface. (b) Time sequence of the phase behavior in which a new equilibrium of coflow has been reached (QW raised from 1 to 4 μL/min). The traveling wave amplitude at the oil-water interface is damped over time. (c) Time sequence of the phase behavior in which a segmented flow has been obtained from co-flow (QW raised from 1 to 7 μL/min). Arrows indicate the point at which interfacial stresses cause oil breakup in a process similar to Rayleigh instability. Langmuir 2010, 26(12), 9416–9422
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interpretation of the phenomenon, as lower values of interfacial tension allow for more “flexible” oil-water interfaces. Discussion. By analogy with previous surface tension and pressure-driven flow examples, the memory effect of the flow described in this paper could be exploited to implement microfluidic equivalents of electronic logic gates. Interpreting the segmented and parallel flow states as binary outcomes, the hysteresis cycle parameters could be tuned by choosing the appropriate characteristics of the fluids. In one example, the monostable condition of co-flow, obtained in the cases of QW e QO, behaves as an event counter: every time a perturbation occurs in one of the phases, the co-flow condition is disrupted and subsequently restored (movie 5 in Supporting Information), with a time response that is proportional to the viscosity of the fluids and the magnitude of the flow rates. In a second example, the bistable condition, triggered by the ratio of the flow rates, that produced either droplets or coflow, mimics a flip-flop mechanism: assigning the binary value ”1” to coflow state and the binary value ”0” to droplet state for storing information. In addition, the oil and water phase flow rates could be used as ”set” and ”reset” inputs to control the output states. It has been proposed that miniaturized fluidic devices could provide operational advantages in harsh environments.4,5,20-22 Nonetheless, no applications that make use of this technology have yet been demonstrated. Two fundamental properties of electronic logic operations render microfluidics a nonoptimal platform for the task, such as the need to cascade a signal without loss of information and a speed comparable to that of electronic data transfer. However, alternatively to computational operations, the multiphase flow behavior described in this work could potentially (33) van Steijn, V.; Kleijn, C. R.; Kreutzer, M. T. Phys. Rev. Lett. 2009, 103, 214501. (34) Vanapalli, S. A.; Banpurkar, A. G.; van den Ende, D.; Duits, M. H. G.; Mugele, F. Lab Chip 2009, 9, 982–990.
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find applications as a sensor platform to determine pressure variations in dynamic systems and as hydrodynamic pressure comparators when using immiscible fluids.34
Conclusions In this work, we showed that multiphase flow in a hydrophilic, microfluidic T-junction has hysteresis. Different flow patterns, in the form of segmented flow and co-flowing phases, can be obtained depending on the capillary number, the volumetric ratio of the phases and, most importantly, on the history of the applied phase flow rates. The characteristic of bistability of the system were described varying the fluid dynamic and physical parameters of the phases, through experimental results and numerical simulations, giving an interpretation of the transition mechanisms and of the hysteresis cycle properties. These results show that multiphase systems have the potential to be used either as sensors, exploiting the characteristics of passive-driven flow or, for computational means, taking advantage of the memory effect characteristics of the flow. Acknowledgment. This work was supported by BBSRC (BB/ F005024/1). Supporting Information Available: Device fabrication details. Contact angle and interfacial tension measurements. Numerical simulation details. Figures S1 and S2: flow pattern results using calibration and mineral oil, respectively. Figure S3: Drop formation regimes in W/O systems. Figures S4 and S5: phase plot of the system as a function of Reynolds number and Weber number, respectively. Experimental condition of Movie1.mov, Movie2.mov, Movie3.mov, Movie4.mov, and Movie5.mov. This material is available free of charge via the Internet at http://pubs.acs.org..
Langmuir 2010, 26(12), 9416–9422
