A Revised Paper Submitted to the
Microfluidics and Nanofluidics
Formation of Recirculation Zones in a Sudden Expansion
Microchannel with a Rectangular Block Structure over a Wide
Reynolds Number Range
by
Chien-Hsiung Tsai 1, Cheng-Peng Yeh 2, Che-Hsin Lin 3,4, Ruey-Jen Yang2* and Lung-Ming Fu5*
1Department of Vehicle Engineering,
National Pingtung University of Science and Technology, Pingtung 912, Taiwan 2Department of Engineering Science,
National Cheng Kung University, Tainan 701, Taiwan 3Department of Mechanical and Electro-mechanical Engineering,
4Advanced Crystal Opto-electronics Research Center, National Sun Yat-sen University, Kaohsiung 804, Taiwan
5Department of Materials Engineering,
National Pingtung University of Science and Technology, Pingtung 912, Taiwan,
Corresponding author: Prof. Lung-Ming Fu e-mail: [email protected]
Tel: +886-8-7703202-7553 Tel Fax: +886-7740552 Corresponding author: Ruey-Jen Yang
e-mail: [email protected] Tel: +886-932-840730 Tel Fax: +886-946-526044 Lung-Ming Fu – Professor
Che-Hsin Lin – Professor Ruey-Jen Yang – Professor Chien-Hsiung Tsai – Professor Cheng-Peng Yeh – Graduate Student
Source: Microfluidics and Nanofluidics, Vol.12, No.1-4, pp.213-220 Date of Publication: 2012-01
ISSN: 1613-4982 Publisher: Springer Verlag DOI: 10.1007/s10404-011-0864-8
Formation of Recirculation Zones in a Sudden Expansion
Microchannel with a Rectangular Block Structure over a Wide
Reynolds Number Range
Chien-Hsiung Tsai 1, Cheng-Peng Yeh 2, Che-Hsin Lin 3,4, Ruey-Jen Yang2* and Lung-Ming Fu5*
1Department of Vehicle Engineering,
National Pingtung University of Science and Technology, Pingtung 912, Taiwan
2Department of Engineering Science,
National Cheng Kung University, Tainan 701, Taiwan
3Department of Mechanical and Electro-mechanical Engineering, 4Advanced Crystal Opto-electronics Research Center,
National Sun Yat-sen University, Kaohsiung 804, Taiwan
5Department of Materials Engineering,
National Pingtung University of Science and Technology, Pingtung 912, Taiwan, Abstract
This paper involves computational and experimental investigations into the flow of a Newtonian fluid through a sudden expansion microchannel consisting of a rectangular block. The results elucidate that the Reynolds number and aspect ratio has a significant impact on the sequence of vortex growth downstream of the expansion channel. The experimental flow visualization results are found to be in good agreement with the numerical predictions of the local fluid dynamics. The simulation results also draw the Re－γ (Reynolds number－aspect ratio) flow pattern map to classify how the flow structures vary with Reynolds number, for example, the resulting flow structures can be classified as five types progressively. The findings in this study provide designers with valuable guidelines for improving the design and operation of the proposed microfluidic rectifier.
1. Introduction
Developments in the field of microfluidics over the past decade have caused a rapid increase in their application in chemical and biological analysis (Fu et al. 2007; Wen et al. 2009; Sun et al. 2010; Oh et al. 2010; Yeh et al. 2010; Hou et al. 2011; Wang et al. 2011; Chang et al. 2011). These devices have emerged as a powerful toolset for miniaturization, automation of fluid handling and fluid analysis (Fu et al. 2004; Fu et al. 2008; Zhang et al. 2009; Lin et al. 2009; Fu et al. 2009; Hong et al. 2010; Wu et al. 2010; Tofteberg et al. 2010; Yang et al. 2010; Rosenauer et al. 2011; Zhao and Yang 2011), significantly reducing reagent consumption, and the time and cost involved in diagnostic procedures. For these reasons, understanding the basic phenomena and flow characteristics in prototypical configurations, such as sudden expansion channels, is critical.
Early experimental studies of liquid flow through a microscale planar channel (Tsai et al. 2008; Hou et al. 2009; Kang and Li 2009; Kennedy et al. 2009; Zhu et al. 2009; Chen and Wang. 2009; Xuan et al. 2010; Movahed and Li 2011; Li et al. 2011; Cheng et al. 2011), demonstrated that the friction coefficients were somewhat higher than those predicted by classical theories for traditional large-scale channel flow. Oliveira (2003) performed a 2-D planar expansion of the 1:3 expansion ratio simulations to investigate the flow field for a range of Reynolds number ranging from
0 to 100, and showed that the flow becomes asymmetric above a critical Reynolds number, Rec ≈ 54. Later, Revuelta (2005) also presented a numerical investigation of an incompressible viscous jet through a channel with a large expansion ratio. They indicated that the critical Reynolds number depends significantly on the expansion ratio. However, the simulation results presented above only considered the two-dimensional geometry. In modeling microchannel flows, two-dimensional (2-D) and three-dimensional (3-D) numerical methods impose different assumptions. For example, 2-D simulations assume that the depth (i.e., the z-direction) of the microchannel geometry is infinite. In 2007, Tsai et al. (2007) indicated that the 2-D simulation method could only be applied to predict the flow behavior in sudden expansion microchannels with high aspect ratios. In addition, they numerically examined the flow of Newtonian fluids through micro-fabricated planar expansions and demonstrated that even though the microfluidic device may have a planar geometry, the flow becomes locally 3D near the expansion region.
Recently, the author’s group (Chen et al. 2010) propose a high performance microfluidic rectifier utilizing self-induced virtual valves in a sudden expansion channel. An embedded block structure is used to enhance the formation of vortices at the sudden expansion channel. The effective hydraulic diameter of the microchannel is reduced due to the formation of the vortices and it hence increases the flow
resistance of the microchannel. Flow rectification can be achieved without using any moving part. The rectification performance indexes (diodicity, Di) reach as high as 1.5 and 1.76 for experimental results, respectively. The performance of the developed microfluidic rectifier beats the performance of other valveless rectifiers utilizing Tesla valves, simple nozzle/diffuser structures or cascaded nozzle/diffuser structures. Tesla valve structure (Truong and Nguyen 2003) and the nozzle/diffuser structure (Yang et al. 2006; Yang et al. 2008) are two common schemes to realize a valveless flow rectifier. This kind of valve uses the flow resistance differences for the forward flow and the reverse flow. Simple structure and no moving part are the major advantages of these microfluidic flow rectifiers. However, the rectify performance (diodicity) of these approaches is relatively low. Tesla designed a classic valveless flow rectifier, named Tesla valve in 1920 (Tesla 1920). A serpentine side channel was used to produce the pinch effect during reverse flow such that the flow resistance was increased. Alternatively, Forster and Bardell (1995) reported a diffuser valve which could provide equivalent flow rectification performance in compare with a Tesla valve. Only the angle of the diffuser was needed to be consider, the design and the geometry of the diffuser valve were much simpler than Tesla valve. Recently, Wang reported a microfluidic flow rectifier composed of a nozzle and a diffuser structures (Wang et al. 2007). Separation vortices of different size were induced in the valve structure both at
forward and reverse flow, there induced vortices in the microchannel caused different flow resistances in the opposite flow directions. Flow rectification can be achieved without using a moving part with this approach. However, the rectification performance index of this simple structure was pretty low. The diodicity of this valve was only 1.1 – 1.3. Grosiman reported a flow rectifier composing of a cascade nozzle/diffuser structure (Groisman and Quake 2004). Several triangular nozzle/diffuser structures were cascade linked to increase the flow resistance differences between the two flows in opposite directions. The diodicity of this flow rectifier was up to a factor of 2 while using a viscous non-Newtonian fluid as the liquid sample. Similarly, Nguyen used a viscoelastic fluid of polyacrylamide to test the rectification performance of the cascade diffuser(Nguyen 2008). Results showed that the measured diodicity of this system was up to 1.8. However, the diodicity value of this valve was only 1.1 while using pure water as the sample fluid.
Numerical and experimental investigations in the present study are used to evaluate the performance of the proposed microfluidic rectifier that designed by the authors (Chen et. al. 2010). Especially focus on how the embedded block structure greatly enhances the performance of the rectifier. It is known that the performance of such devices is influenced by the onset of flow separation. However, the correlation between the characteristics of recirculation and the location
of a block structure placed downstream of the expansion channel is not yet clear. The aims of this study are: (1) to investigate the size of the recirculation zone for various distances between the contraction channel and the rectangular block with a constant expansion ratio (contraction channel width / expansion channel width) and aspect ratio (contraction channel depth / width) for Re = 40; (2) to study the pattern of vortex development and growth for various Reynolds numbers in the range from Re = 0 to Re = 365; and (3) to identify the flow pattern map when varying the aspect ratio, which illustrates the flow structures and their location in the Re－γ parameter space.
2. Experimental Section
The sudden expansion microchannels were fabricated on soda-lime glass substrates using standard photolithographic techniques (Lin et al. 2008; Lee et al. 2009). To reduce the complexity and expense of the fabrication process, a 3-μm thick AZ4620 (Clariant, Somerville, NJ, USA) positive photoresist layer was used in place of a metal layer as an etching mask to define the required microfluidic structures. The exposed substrate was etched using a buffered oxide glass etching (BOE) technique without agitation at room temperature. The microchannels were formed using a modified BOE with an etching rate of 0.9 μm/min. The substrates were then thermally bonded with drilled upper substrates in a sintering oven at a temperature of 580 for ℃
10 min to form the sealed sudden expansion microchannels. Finally, a Teflon tube of 500-μm inner diameter and 1.5-mm outer diameter was attached to the fluid-inlet hole on the upper substrate using epoxy glue. Figure 1(a) and 1(b) illustrates the 3-D geometry and an optical microscope image of the sudden expansion microchannel considered respectively. The set of channels was approximately designed to a 1:3 (0.2 mm: 0.6 mm) contraction-expansion ratio, and the channel lengths of contraction and expansion were 1 mm and 2 mm, respectively.
Figure 2 shows the schematic presentation of the experimental setup for this study. The experiments were performed under a lab-built PIV (particle image velocimeter) system composed of a 100-W fluorescent microscope (Model E400 Nikon, Kanagawa, Japan) for fluorescence excitation and a shutter controllable CCD (Model DSC-190, Sony, Tokyo, Japan) camera for capturing the experimental images. The image-capturing rate was 30 fps with the resolution of 640 × 480 pixels. To
obtain better experimental images using the PIV system, the sample fluid containing DI water doped with the green fluorescent microspheres (5-μm diameter, Duke Scientific Corp., Palo Alto, CA, USA) was used in this study. The sample fluid was driven into the microchip device using a programmable syringe pump (200 series, KD Scientific, Holliston, MA, USA) via the Teflon tubing. The experimental images acquired by the CCD were recorded via a high-speed image acquisition interface
(DVD PKB, V-gear, Taiwan). Note that all experimental results obtained in the five tests for each sample were then averaged in order to obtain a mean value for analysis purposes.
3.Numerical modeling
When modeling the flow field characteristics within the sudden expansion microchannel, the present simulations make two fundamental assumptions: (1) a steady state was assumed, and (2) the fluid flow satisfied the continuity equation and the Navier–Stokes momentum equation. In addition, the model was simplified by assuming that the fluid is incompressible. The governing equations can be expressed as follows: 0 u= ⋅ ∇ (1) u u u⋅∇ =−∇p+μ∇2 ρ (2)
where ρ, μ, p, and u are the fluid density, viscosity, pressure and flow velocity vector (u=uxˆ+vyˆ+wzˆ), respectively. In the study, the fluid properties of the DI water, ρ
and μ, are specified as 1,000 kg/m3 and 0.001 kg/m-s, respectively.
Figure 1(a) presents a schematic illustration of the computational domain for the 3-D sudden expansion microchannel used in the present simulations. As shown, a rectangular block structure with the dimensions of 200 μm and 100 μm (width and
length) is placed downstream of the sudden expansion channel. Appropriate conditions are specified at the boundary cells to correctly reflect the physical phenomena of the flow field. In the upstream section, the plug-flow is imposed. A reference pressure for the outlet at the downstream section of the computational domain is specified. The symmetric boundary condition is employed at the centerline of the microchannel, which means a zero-gradient in the direction normal to the boundary. For the boundary conditions at the channel walls, a non-slip condition is assumed in this study. This is reasonable because the water flowing through the hydrophilic channels has been shown to have a very small or negligible slip length (Tandon and Kirby 2008; Bouzigues et al. 2008).
The simulations were performed using the FLUENT CFD software. FLUENT employed the finite volume method through which the conservation principles were applied to a control volume. In this method, the governing differential equations were integrated for each control volume to yield a set of algebraic equations that ensured all quantities were conserved on a control volume basis. These algebraic equations were then solved through numerical means to obtain the unknown quantities. Due to the discrete nature of the algebraic equations, all quantities at the center of each control volume were averaged over the control volume. The first order upwind scheme was chosen for the spatial discretization of the convection term of each governing equation.
The pressure and velocity fields were decoupled using the semi-implicit method for a pressure-linked equation (SIMPLE) (Patankar, 1980).
In order to get the high resolution of the vortices, the grid comprised around six hundred thousand orthogonal hexagonal cells. The convergence is declared when the normal residual is lower than 1×10-6.
4. Results and discussion
As the Reynolds number increased, the recirculation size also increased progressively. Initially, the simulation and experiment consider the case of the flow phenomena within a microchannel with an expansion ratio of 3 (outlet width/inlet width = 0.6mm/0.2mm) and Re values of 8 and 40. In the expansion channel, a rectangular block structure with dimensions of 0.2 × 0.1 mm (width × length) was placed downstream of the expansion channel at a distance of 0.2mm, as shown in Fig. 3. Figure 3 presents the numerical and experimental results of the steady-state flow field in the microchannel. At low Reynolds numbers (Re = 8), fluid elements downstream of the expansion plane begin to reattach to the channel wall as soon as they exit the contraction channel (Figure 3 (a)). As the Reynolds number increases (Re = 40), the inertial effects result in the development of a separation vortex. As shown in Figure 3b, two pairs of flow vortices are induced in the corner and behind the block structure,
respectively, while the Re is above a certain value. It should be noted that the streak lines and recirculation sizes measured experimentally are symmetric about the centerline of the device.
4.1. Influence of the sudden expansion channel with a rectangular block structure
on the size of recirculation zone
From the above observations, we can see that the two pairs of separation vortices were formed in the channel when the Reynolds number increases to Re = 40. The results presented above only considered the case when the block structure was placed downstream of the expansion channel a distance of 0.2 mm. However, in practice, the size of the recirculation zone depends not only on the Reynolds number, but also on the position of the block structure as shown in Figure 4(a)~(d) for a fixed flow rate at four different distances. For the constant Reynolds number (Re = 400), the figures compare the experimental and numerical streamline distributions at a depth of 40 μm in a sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1/5 at varying positions for the block structure. Comparing the four sets of results, it is evident that the vortex structures extended and gradually increased in size as the distance of the block downstream of the expansion channel increased, whereas the size of the vortices behind the block structure was insensitive to distance. This is because the fluid inertia was constrained by the rectangular block, and therefore the corner recirculation region
shrank in size as the distance between the block and the contraction channel was reduced. By contrast, the recirculation zone was enlarged. While the distance was long enough, the vortex size was not sensitive to the location of the block structure for a constant Reynolds number. To clearly understand the correlation between the recirculation size and the relative position of the block, Figure 5 presents the size of the recirculation zone for the different distances between the contraction channel and the rectangular block with a constant expansion and aspect ratio for a Reynolds number of 400. The experimental images were processed by image analysis using ImagePro software (MediaCybernetics Inc., USA) to draw the grids. The line size of each grid is 50 μm. Therefore, the number of grids occupied by the recirculation zone can be obtained estimating the sizes of circulation zone. The results presented in Figure 5 confirm that the size of the circulation zone did not change when the block structure placed in the downstream of expansion channel was greater than 1 mm. Overall, a good qualitative agreement was observed to exist between the experimental results and the numerical predictions in every case.
4.2. A sequence of vortex growth associated with Reynolds number and the aspect
ratio of the sudden expansion channel
To better understand the flow structure in the current device, a sequence of experimental and computed streamlines are shown in Figure 6 for increasing flow
rates in a sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1/5, within which the block structure was placed 0.8 mm downstream of the expansion channel. Figure 6 presents the effect of inertia on the sequence of vortices formed downstream of the expansion as the Reynolds number increased. At low flow rates, the fluid behavior is akin to that of creeping flow in the sense that there is no flow separation. As we increase the Reynolds number (Re ≈ 100), the inertial effects result in the development of recirculating lip vortices (see Figure 6(a)). The recirculation grows with the fluid inertia, and at Re ≈ 265 it already extends to the side-wall. Furthermore, a flow separation vortex is induced behind the rectangular block, as shown in Figure 6(b). The strength and size of the recirculations increase as the Reynolds number is continuously increased to a value of around 430, as indicated in Figure 6(c), and we find that a small eddy occurred on the lateral side of the block structure. Eventually, a combination of recirculations develops around the rectangular block, which was observed for a Reynolds number as high as Re ≈ 465 (see Figure 6(d)).
With the objective of performing a systematic study of the effect of the aspect ratio on the flow structure, we have carried out an extensive set of simulations and classified the patterns of the flow within the expansion channel at increasing Reynolds numbers. These calculations were performed for the block structure placed
downstream of the expansion plane at a distance of 300 μm. The resulting flow structures were classified as “no recirculation (I)”, “lip recirculation (II)”, “corner recirculation and rear-block vortex (III)”, “full corner recirculation, rear- and lateral-block vortices (IV)” and “full corner recirculation and combination of recirculations around the block (V)”. The flow pattern map in Figure 7 illustrates these flow structures and their location in the Re－γ parameter space. In the lower
region of Figure 7, representing low Re, no visible recirculation formed downstream of the expansion channel. By contrast, at a high Reynolds number, two pairs of large recirculating structures located on the corner and block regions are observed, respectively. Between these two regions, a sequence of vortex growth is distinguished. Independent of the spatial structure of the flow, an enhancement in recirculation with increasing fluid inertia is seen for all aspect ratios that were considered. As shown in Fig.7, the threshold value of Reynolds number for each types are decreased dramatically when aspect ratio increase. The effect of the microchannel wall with small aspect ratio on dissipating the flow inertia force is the main reason. Generally, the vortices formation in a simple sudden expansion channel is categorized as the function of Reynolds number. However, Tsai et al. (2007) show that the aspect ratio is another important parameter in addition to the Reynolds number. The present results also confirm this strongly dependence in an expansion channel with a block
embedded for microfluidic rectifier.
5. Conclusions
This study presents a series of numerical simulations for Newtonian fluid flow through a sudden expansion micro-geometry device containing a rectangular block over a range of aspect ratios and Reynolds numbers. The simulation results are in good agreement with those observed in experiments. The numerical calculations enable all of the parameters to be varied over a wider range of conditions than are possible in the experiments, thus complementing the experimental work and guiding future device design. The results revealed that the size of corner recirculation is affected by the distance between the rectangular block and the contraction channel for a constant Reynolds number. While the distance is long enough, the recirculation size is not sensitive to the location of the block structure. Moreover, it has been shown that the Re－γ (Reynolds number－aspect ratio) flow pattern map, the resulting flow
structures can be classified as “no recirculation”, “lip recirculation”, “corner recirculation and rear-block vortex”, “full corner recirculation, rear- and lateral-block vortices”, and “full corner recirculation and combination of recirculations around the block”. The results presented in this study are of value to designers when rapidly exploring the consequences of changes to the geometric parameters governing the
flow in microfluidic devices, such as non-moving-part microvalves or micromixers.
Acknowledgement
The authors would like to thank the financial support provided by the National Science Council in Taiwan.
Figure Captions
Figure 1 (a) Schematic illustration of the 3-D geometry and (b) optical transmission microscope image of a 1:3 sudden expansion microchannel containing a rectangular block.
Figure 2 Schematic illustration of experimental setup.
Figure 3 Comparison of experimental (top) and numerical (bottom) streamline distribution in sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1 at different Re: (a) Re = 8 and (b) Re = 40. (Rectangular blocks located 200 μm downstream of expansion channel) Figure 4 Comparison of experimental (top) and numerical (bottom) streamline
distribution in sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1/5 at varying distances between the contraction channel and the rectangular block: (a) x = 300 μm, (b) x = 600 μm , (c) x = 800 μm and (d) x = 900 μm. (Re = 400)
Figure 5 The size of recirculation zone varies with the position of the rectangular block downstream of the expansion channel with an expansion ratio of 3, an aspect ratio of 1/5, and a Reynolds number of 40.
Figure 6 The effect of inertia on a sequence of vortex growth obtained downstream of the expansion channel for water flowing through a 1:3 sudden expansion microchannel with an aspect ratio of 1/5 at different Reynolds number: (a) Re ≈ 100, (b) Re ≈ 265, (c) Re ≈ 430 and (d) Re ≈ 465. (Rectangular block located 800 μm downstream of expansion channel)
Figure 7 Flow pattern map: (I) no recirculation; (II) lip recirculation; (III) corner recirculation and rear-block vortex; (IV) full corner recirculation, rear- and lateral-block vortices; and (V) full corner recirculation and combination of
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Figure 1 (LM Fu)
Figure 1. (a) Schematic illustration of the 3-D geometry and (b) optical transmission microscope image of a 1:3 sudden expansion microchannel containing a rectangular block.
Figure 2 (LM Fu)
Figure 3 (LM Fu)
Figure 3. Comparison of experimental (top) and numerical (bottom) streamline distribution in sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1 at different Re: (a) Re = 8 and (b) Re = 40.
Figure 4 (LM Fu)
Figure 4. Comparison of experimental (top) and numerical (bottom) streamline distribution in sudden expansion microchannel with an expansion ratio of 3 and an aspect ratio of 1/5 at varying distances between the contraction channel and the rectangular block: (a) x = 300 μm, (b) x = 600 μm , (c) x = 800 μm and (d) x = 900 μm. (Re = 400)
Figure 5 (LM Fu)
Figure 5. The size of recirculation zone varies with the position of the rectangular block downstream of the expansion channel with an expansion ratio of 3, an aspect ratio of 1/5, and a Reynolds number of 400. (Note that the results represent the average values obtained from five separate experiments for each sample.)
Figure 6 (LM Fu)
Figure 6. The effect of inertia on a sequence of vortex growth obtained downstream of the expansion channel for water flowing through a 1:3 sudden expansion microchannel with an aspect ratio of 1/5 at different Reynolds number: (a) Re ≈ 100, (b) Re ≈ 265, (c) Re ≈ 430 and (d) Re ≈ 465. (Rectangular block located 800 μm downstream of expansion channel)
Figure 7 (LM Fu)
Figure 7. Flow pattern map: (I) no recirculation; (II) lip recirculation; (III) corner recirculation and rear-block vortex; (IV) full corner recirculation, rear- and lateral-block vortices; and (V) full corner recirculation and combination of recirculations around the block. (Rectangular block located 300 μm downstream of expansion channel)
