(de-ionized water, viscosity η=0.9 mPa.s at 25oC) and immiscible (perfluorohexane, η=1.1 mPa.s at 25oC) lubricants were used in this work. The interfacial ...
MICROFLUIDIC LUBRICATED EXTENSIONAL FLOW OF VISCOELASTIC FLUIDS J. Wang*, D.F. James and A. Günther Dept. of Mechanical & Industrial Engineering, University of Toronto, CANADA ABSTRACT Fluids that are routinely used in microfluidic devices have complex micro and nanostructures that can lead to viscoelastic flow behavior. In this paper an experimental technique is developed to estimate the extensional flow resistance of dilute polymer solutions using flow in a lubricated, converging microfluidic channel. The two-dimensional channel has a hyperbolic profile, and the viscous or viscoelastic core fluid is lubricated by a less viscous Newtonian fluid that is introduced through side channels upstream. Information on the velocity field is obtained from flow rate measurements, microscopy, the loci of the fluid/fluid interface and particle image velocimetry and tracking. The extensional behavior is characterized from pressure drop measurements along with a balance of stresses at the fluid interface. KEYWORDS: Viscoelasticity, Polymer Solution, Lubrication, Instability INTRODUCTION The shear properties of these complex fluids can be characterized by conventional techniques, but not their extensional properties, especially at strain rates relevant to some microfluidic applications. Microfluidic systems provide an opportunity to establish structure-property relationships for complex fluids [1, 2]. Attempts have been made to develop a microfluidic extensional rheometer, including that of Rodd et al. [3] who used a sudden contraction geometry and that of Arratia et al. [4] who estimated viscosity from filament thinning and breakup in a cross flow channel. These techniques, however, involve either significant secondary flow [3] or restricted flow conditions [4], and they cannot be used as general techniques to characterize fluid extensional behavior. We report a technique for estimating the extensional flow resistance of dilute polymer solutions using a lubricated converging-channel flow. The technique promises to yield measurements of extensional viscosity, the most elusive of fluid properties, as a function of strain as well as strain rate, under general flow conditions. The method may also be applied to complex biological fluids such as Matrigel and Collagen Type I using fluid volumes as little as 10-7 m3. EXPERIMENTAL Our single-layer microfluidic device consists of a network of channels, as shown in Figure 1. The planar convergent channel has an upstream channel width, wu, of 500 μm, a convergent-channel exit width, wc, of 26 μm, a convergent channel length, lc, of 422 μm and a uniform channel depth, h, of 46 μm. Lubricants are introduced through 50 μm-wide side channels immediately upstream of the convergent channel. Channels are fabricated in PDMS using standard softlithography techniques and SU-8 photolithography. The PDMS channels are bonded to PDMS-covered glass slides in order to achieve uniform surface properties on all four walls of the channels. To obtain an accurate channel geometry, a layer of glycerol is applied between the photomask and photoresist during UV exposure. The glycerol works as an indexmatching material which minimizes diffraction of UV light [5] and yields sharp features at the convergent channel exit and near-vertical channel walls along the entire length of the channel. Pressure taps were installed 4mm upstream and 3mm downstream of the contraction plane, to measure the differential pressure drop, ΔP12, as a function of flow rate for each of the polymer solutions and for the Newtonian fluid. The volumetric flow rates of both the core fluid and the lubricant are controlled via precision syringe pumps (Harvard Apparatus PHD2000), in order to achieve a range of flow rates between 0.01 ml/h and 4 ml/h. These correspond to characteristic shear rates between 110 s-1and 4.4x104 s-1 at the convergent channel exit. For flow visualization, the aqueous fluids are seeded with 1.1μm diameter fluorescent particles (excitation/emission=520/580 nm) at a concentration of 0.05 wt.%. Both streak images and transient behavior (e.g. instability) are acquired on a 3MP CCD camera. Four aqueous solutions containing 0, 50 ppm, 200 ppm, and 500 ppm polyethylene oxide (Mw=4x106 g/mol) were used in this work. The Newtonian solvent is a 30 wt.% aqueous solution of polyethylene glycol (Mw=8,000). The steady shear viscosities of the solutions were determined using a controlled-stress rheometer; values at 25oC were between 50 mPa.s and 60 mPa.s depending on polyethylene oxide concentration but almost independent of shear rate. Both miscible (de-ionized water, viscosity η=0.9 mPa.s at 25oC) and immiscible (perfluorohexane, η=1.1 mPa.s at 25oC) lubricants were used in this work. The interfacial tension between the miscible lubricant and the viscous or viscoelastic core fluid is considered negligible while the interfacial tension between the immiscible lubricant and the core fluid varies between 5mN/m and 45 mN/m, as measured on a surface tensiometer, depending on the concentration of surfactant (perfluorooctanoic acid) in the core fluids.
978-0-9798064-3-8/µTAS 2010/$20©2010 CBMS
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14th International Conference on Miniaturized Systems for Chemistry and Life Sciences 3 - 7 October 2010, Groningen, The Netherlands
Figure 1: Schematics of the lubricated hyperbolically convergent channel; Inset: a viscous Newtonian fluid lubricated by water
Figure 2: Schematics and photos of flow patterns: (a) a viscous Newtonian core fluid lubricated by water (miscible); (b) the same viscous Newtonian core fluid lubricated by perfluorohexane (immiscible, no surfactant); In both cases Q core = Q lub = 0.1 ml/hr
RESULTS AND DISCUSSION A Newtonian fluid (η=50 mPas), lubricated by de-ionized water, was tested first in the convergent channel. The water completely encapsulated the core fluid beyond a certain position in the convergent channel, as shown by the highlighted region in Figure 2(a) and illustrated by the red dotted lines in the schematic. Because of encapsulation, a significant lubricating effect is produced, as shown by the large decrease in the pressure drop, in Figure 3(a). The flow pattern was very different, however, when an immiscible lubricant was used. As shown in Figure 2(b) and illustrated by the blue dotted lines in the schematics, two distinct sets of contact lines can be observed under a microscope on the upper and lower channel walls. The two fluids essentially flow side by side when a zero or low concentration (less than 0.2 wt.%) of surfactant is added to the core fluid, corresponding to an interfacial tension of at least 10mN/m, and much less lubricating effect (i.e., decrease of pressure drop) is produced compared to miscible lubricated flow, as shown in Figure 3(b). For a Newtonian core fluid, the flow is steady regardless of the lubricant used.
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(a) (b) Figure 3: Pressure drops over the hyperbolically-convergent channel: (a) a viscous Newtonian core fluid lubricated by water (miscible) compared with the pressure drops created by the core fluid or the lubricant alone; (b)The same experiment but with an immiscible lubricant; 0.3 wt.% surfactant is added to the core fluid to reduce interfacial tension When a small amount (50 ppm, 200 ppm, or 500 ppm) of polyethylene oxide (Mw ≈ 4,000,000) was dissolved in the core fluid, the viscosity barely increased, but the core flow separated from the sidewalls upstream, as illustrated by the photos in Figure 4. This change in the interface profile resulted from extensional stresses caused by the dissolved polymer. These stresses also caused the interface to wobble sideways, as seen by the multiple interfaces in Figure 4(d), (e), and (f). Streak images show that the lubricant is first drawn into upstream channel on exiting the side channel, likely because of a negative pressure gradient, and then reverses in flow direction to join the core fluid. The separation of core flow from the sidewalls as well as the magnitude and frequency of interface wobbling become more significant as the flow rate (deformation rate) and polymer concentration is increased. Pressure drops were measured for these unstable miscible lubricated flows. Compared to lubricated flows of the solvent at the same flow rates, the miscible lubricated flow of dilute polymer solutions show a significant excess pressure drop (i.e., pressure drop in excess of that of the solvent at 1059
the same flow rate), which increases with polymer concentration and flow rate. The pressure sensor showed more fluctuations because of the instability at the interface. The interfacial instability was eliminated by using an immiscible lubricating fluid. The flow pattern in this case is similar to that of immiscible lubricated flow of the viscous solvent (Figure 2(b)), with distinct contact lines observable on the upper and lower channel walls. The interface, however, separates from the sidewalls upstream at a distance similar to that of miscible lubricated flow of the same polymer solution at the same flow rate. Because the core fluid is much more viscous than the lubricant, both calculation and PIV measurement show that core fluid velocity can be considered uniform across the convergent-channel width. The average extensional rate was then evaluated over the mid-plane (at half channel thickness) of the channel from the flow rate and the position of the interface using the following equation:
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d § 3Qcore · ¸ ¨ dx ¨© 2h w( x) ¸¹
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where vmax,core is the velocity at half channel thickness and w(x) is the width of the core fluid stream which varies in the direction of flow. As shown in Figure 5 for several flow conditions, the average extensional rate increases sharply towards the channel exit. An estimation of the extensional viscosity of the dilute polymer solution, which varies as a function of strain and strain rate, is then possible by considering the excess pressure drop generated in addition to the pressure drop of viscous solvent under similar flow rates or by considering the balance of stress at the fluid interface. 140
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Figure 4: Streak images from fluorescent micrograph and bright-field images of miscible flow of 50ppm 4M PEO solution: (a) and (d) at 0.1ml/hr; (b) and (e) at 0.2ml/hr; (c) and (f) at 0.5ml/hr; Flow rate of the lubricant is the same as that of the core fluid
Figure 5: Estimated average extensional rates for immiscible lubricated flow at different flow rate ratios
CONCLUSION A technique is developed to investigate the extensional flow resistance of a dilute polymer solution using a planar hyperbolically-convergent microfluidic channel. Stable lubricated flows can be achieved for a viscous core fluid and a miscible or immiscible lubricant, although the flow patterns differ significantly because of interfacial tension. A medium to high interfacial is needed to stabilize lubricated flow of dilute polymer solutions, and estimation of extensional rate and extensional viscosity is possible from measurements of flow rate, pressure drop, the loci of fluid interface, and velocity distribution. ACKNOWLEDGEMENTS We acknowledge financial support from the Natural Science and Engineering Research Council of Canada. REFERENCES [1] T.M. Squires and S.R. Quake, Microfluidics: fluid physics at the nanoliter scale, Review of Modern Physics 77, 977 (2005). [2] J. Tang, D.W. Trahan and P.S. Doyle, Coil-stretch transition of DNA molecules in slitlike confinement, Macromolecules 43, 3081 (2010). [3] L.E. Rodd, J.J. Cooper-White, D.V. Boger and G.H. McKinsey, Role of the elasticity number in the entry flow of dilute polymer solutions in microfabricated contraction geometries, Journal of Non-Newtonian Fluid Mechanics 143, 170 (2007). [4] P.E. Arratia, J.P. Gollub and D.J. Durian, Polymeric filament thinning and breakup in microchannels, Physical Review E 77, 036309 (2008). [5] S. Natarajan, D.A. Chang-Yen and B.K. Gale, Large-area, high-aspect-ratio SU-8 molds for the fabrication of PDMS microfluidic devices, Journal of Micromechanics and Microengineering 18, 045021 (2008). 1060
