Microfluid Nanofluid (2007) 3:101–108 DOI 10.1007/s10404-006-0109-4
RESEARCH PAPER
Efficient mixing of viscoelastic fluids in a microchannel at low Reynolds number Hiong Yap Gan Æ Yee Cheong Lam Æ Nam Trung Nguyen Æ Kam Chiu Tam Æ Chun Yang
Received: 3 May 2006 / Accepted: 8 June 2006 / Published online: 28 July 2006 Springer-Verlag 2006
Abstract In this paper, we examined mixing of various two-fluid flows in a silicon/glass microchannel based on the competition of dominant forces in a flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Experiments were performed over a range of Deborah and Reynolds numbers (0.36 < De < 278, 0.005 < Re < 24.2). Fluorescent dye and microshperes were used to characterize the flow kinematics. Employing abrupt convergent/divergent channel geometry, we achieved efficient mixing of twodissimilar viscoelastic fluids at very low Reynolds number. Enhanced mixing was achieved through elastically induced flow instability at negligible diffusion and inertial effects (i.e. enormous Peclet and Elasticity numbers). This viscoelastic mixing was achieved over a short effective mixing length and relatively fast flow velocities. Keywords Viscoelastic Æ Microchannel Æ Mixing Æ Flow instability
1 Introduction Chaotic and turbulent flow instabilities are recognized to be effective mechanisms for mixing and have been well studied for Newtonian fluids (Landau and Lifshitz 1995; White 1991). Microscale dimensions lead to small
H. Y. Gan Æ Y. C. Lam (&) Æ N. T. Nguyen Æ K. C. Tam Æ C. Yang School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798 e-mail:
[email protected]
Reynolds number and impede turbulent flow instabilities, due to the domination of viscous effects. For a small volume of liquids i.e. liquid flows in a microchannel, interaction between a fluid and the channel wall will be dominant, and the surface to volume ratio increases tremendously compared to that in the macroscopic level. Flows of a Newtonian fluid in microchannels are therefore confined within laminar flow regime and difficult to mix (Madou 2002; Stone 2004). Mixing of multiple streams in microchannels is generally achieved by molecular diffusion mechanism, not by the chaotic/turbulent flow mechanism. Diffusive mixing requires a long channel, while chaotic advection needs external actuators and complex channel structures (Nguyen and Wu 2005). Both concepts lead to complex and expensive fabrication processes. Mixing—or lack thereof—is often a key obstacle to achieve a good performance in microfluidic applications. A different approach that bypasses the low Reynolds number limitation yet provides efficient mixing will be a significant improvement for microfluidic system design (Ottino and Wiggins 2004). It is well known that a solution with a trace amount of deformable polymers, i.e. a viscoelastic fluid, can lead to elastic flow instability (Nguyen and Boger 1979; Pathak et al. 2004; Burghelea et al. 2004a, b; Gan et al. 2006; Rodd et al. 2004). The elastic stress experienced by these fluids will not immediately become zero with the cessation of fluid motion and driving forces, but decay with a characteristic time due to its elasticity. The observations and the understanding of the recirculating vortices in the flow of polymer solutions and melts (i.e. viscoelastic fluids) in macro-channels through an abrupt contraction have been well documented. Recently, elastic fluid’s flow instability and
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enhancement of mixing at microscale were reported (Pathak et al. 2004; Burghelea et al. 2004a, b). However, relatively long mixing path with a large number of turnings at moderate flow rate are the major drawbacks. It appears that hitherto the viscoelastic effects of a fluid have not been exploited effectively. This complex interplay that arises between the elasticity/viscosity of the fluids and the ratio of contraction of the channel is the key for efficient mixing of fluid streams in microchannels. We have recently proven our preliminary concept and reported the results for mixing enhancement, based on a PMMA (polymethyl methacrylate)-based device with a simple convergent/ divergent channel configuration which can trigger viscoelastic flow instability (Gan et al. 2006). However, as the PMMA-based device was laser machined resulting in rough surfaces and poor micro-geometrical profile definition, the proper quantification of the flow field, and in particular mixing, was difficult. Our investigation demonstrated the elastically induced flow instability of viscoelastic fluids in an abrupt convergent/divergent microgeometry. Elastically induced flow instabilities are apparent for the convergent/divergent viscoelastic fluids flow. However a rigorous examination of actual flow dynamic will only be considered at a later stage. In this paper, our aim is to highlight the effects of elasticity on mixing in microchannels. We extended our previous study (Gan et al. 2006) to a high precision micromachined silicon/ glass chip with good surface finish, geometrical definition and optical transmittance. We investigated the dynamics of the various two-fluid flows in abrupt convergent/divergent geometry microchannels, based on the competition of the dominant forces in the flow field, namely viscous/elastic, viscous/viscous and viscous/inertial. Fluorescent dye and microparticles were used with mercury lamp (as illumination source) to characterize the flow.
Microfluid Nanofluid (2007) 3:101–108
_ The flow rate of the two stream flow rate was 0:5Q: _ Thus, the side streams is equal and each has 0:25Q: _ The flow rate ratio total flow rate in the device was Q: was achieved by driving simultaneously three different syringes with the appropriate size ratio by the same pump. The total volumetric flow rates used in our experiments were 1, 10 and 12 ml/h. Deborah number can be defined using the characteristic shear rate, De ¼ k_cchar
! _ _ 2Q 2kQ ¼k ¼ 2 2 wc d wc d
ð1Þ
with the characteristics shear rate expressed as _ _ 2Q cd c_ char ¼ Q=w wc =2 ¼ w2c d ; where k is the relaxation time of the viscoelastic fluid measured in shear, d is the channel depth, and wc is the contraction width. In our experiments, Reynolds number is defined as Re ¼
_ 2qQ go ðwc þ dÞ
ð2Þ
where q and go are the fluid density and the viscosity, respectively. Peclet number is given by Pe ¼
_ char QL Dwc d
ð3Þ
2 Experiment and fluid rheology
where Lchar is the upstream channel width and D is the diffusion coefficient. Generally, a smaller channel has small flow characteristic length and time. Thus, Re is smaller and it is difficult to have viscous/inertia flow instability. Conversely, De becomes larger and is easier to have elastic/ viscous instability. The relative dominance of elastic to inertial effects is typified by the elasticity number (El = De/Re), i.e. the ratio of fluid elasticity to fluid inertia. El is constant for a given fluid and geometry and is dependent only on the fluid properties and the inverse of the characteristic cross-sectional area.
2.1 Dimensionless parameters
2.2 Fluid preparation
For a given geometry, the elastic effects of a viscoelastic fluid flow can be characterized by the Deborah number, De (characteristic relaxation time/flow characteristic time). Generally, smaller dimensions allow a higher characteristic deformation rate for the same flow rate, resulting in higher elastic effects and a higher De. The sample fluids were delivered by a precision syringe pump (Lomir Biomedical Inc.). The main-
The mainstream fluid consists of 1 wt% poly(ethyleneoxide) (PEO) in 55 wt% glycerol water and green fluorescent dye. For brevity, this fluid is denoted as 1% PGW. The fluid of the side streams consists of 0.1 wt% PEO in water, and 3-lm red fluorescent microspheres. For brevity, this fluid is denoted as 0.1% PW. The mainstream fluid (1% PGW) has a higher viscosity and elasticity than the side streams fluid (0.1% PW), see Table 1. The mean molecular weight (Mw) of PEO
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Microfluid Nanofluid (2007) 3:101–108 Table 1 Fluid properties
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Fluid
Zero-shear viscosity go (·10–3 Pa s)
Density q (·103 kg/m3)
Relaxation time k (s)
Water with fluorescence dye 26.1% GW with micro-particle 96.1% GW with fluorescence dye 0.1% PW with micro-particle 1% PGW with fluorescence dye
1.00 1.85 513 1.89 500
1.00 1.06 1.24 0.997 1.13
– – – 1.5 · 10–3 98 · 10–3
(supplied by The Dow Chemical Company) is approximately 2 · 106 g/mol. A fluorescent dye (fluorescein disodium salt C20H10Na2O5) was added to 1% PGW at a weight ratio of 3 · 10–4:1. The solution of dispersed 3-lm red fluorescent microspheres (Duke Scientific Co.) was added to 0.1%PW at a volume ratio of 0.1:1. These fluorescent microspheres served as tracing particles for the streak flow experiments.
determined using the viscometer Contraves LS 40 (controlled rate mode). The diffusion coefficient of the dye in water was determined by Wu et al. (2004) as D = 1.5 · 10–9 m2/s. Since diffusion coefficient is inversely proportional to viscosity (Einstein 1956), we estimated that D = 3.0 · 10–12 m2/s for 1% PGW.
2.3 Rheological property measurements
We employed a microchannel with a depth of 150 lm and an abrupt contraction of 1,000:125:1,000 lm to introduce the convergent/divergent flow. The length of the contraction was 1,000 lm. Side streams were introduced into the central mainstream through two side channels, each at either side of the main channel. The side channels were 1,000 lm in width and were located 3,000 lm upstream from the centerline of the contraction. The channel structures were realized in a silicon/ glass chip, see Fig. 1. The microchannels and through holes were etched in two steps using the deep reactive ion etching (DRIE) technique. First, the access holes were etched to a depth of about 400 lm. Next, the microchannels were etched to a depth of 150 lm and the holes were etched through the wafer. The entire silicon
Table 1 lists the rheological properties of the fluid. All the fluid properties were determined with the additives. Relaxation time (k) was computed from the ratio of storage modulus (G¢) and loss modulus (G†). The values of G¢ and G† were determined under shear stress in a frequency oscillation test (Rheometrics Scientific—ARES—Advanced Rheometric Expansion). The steady shear viscosities were determined using a strain controlled—steady rate sweep test with shear rates in the range of 0:1 c_ 100 s1 : Due to the dilute viscosity of 0.1% PW, its k could not be determined with our facility and its value was taken from Rodd et al. (2004). The viscosity of 0.1% PW was
2.4 Device fabrication and setup
Fig. 1 Configuration of silicon-glass chip
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wafer was then anodically bonded to a Pyrex glass wafer. The silicon/glass stack was then diced into 10 · 10 mm test chips. A polymeric holder was designed and fabricated as the micro/macro fluidic interface. 2.5 Imaging techniques All experimental results were collected at different time intervals in the same experiment. Our image acquisition system was reported in details earlier (Wu et al. 2004). A Mercury lamp worked as the illumination source. The optical system consisted of an inverted microscope (Model ECLISPE TE2000-S) with a set of epi-fluorescent attachments. The image acquisition devices consists of an interline transfer CCD camera (HiSense MkII), a FlowMap system hub with last-infirst-out (LIFO) capability and a commercial camcorder (Sony, DCR-DVD803E). The resolution of the CCD camera is 1,344 · 1,024 pixels with 12 bits grayscale. The recorded images were digitally transferred (in BMP format) to a personal computer for further analysis (using MATLAB). For each flow rate, the flow field images in the same experiment were visualized using the green fluorescent dye (mainstream) and the red fluorescent microspheres (side streams). The images of the streams were capFig. 2 Viscoelastic fluids flow in microchannels with 8:1 contraction ratio at two different flow rates, a, b _ 1ml=h and c, d Q¼ _ 12ml=h Q¼
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Microfluid Nanofluid (2007) 3:101–108
tured by switching the epi-fluorescent attachments of the microscope. Both green and red filters have a bandwidth of 25 nm. The separated florescent bands of the red particles (540/610 nm) and of the green dye (490/520 nm) allowed the clear discrimination of the sample fluids.
3 Results and discussions With reference to the mainstream fluid (1% PGW) properties, experiments were performed over a range of De and Re (23.2
