Design and analysis of the cross linked dual helical micromixer for rapid mixing at low Reynolds numbers

Transcription

1 DOI /s RESEARCH PAPER Design and analysis of the cross linked dual helical micromixer for rapid mixing at low Reynolds numbers Keyin Liu Qing Yang Feng Chen Yulong Zhao Xiangwei Meng Chao Shan Yanyang Li Received: 18 June 2014 / Accepted: 31 January 2015 / Published online: 11 February 2015 Springer-Verlag Berlin Heidelberg 2015 Abstract We demonstrated rapid and stable fluid micromixing at low Reynolds numbers in an easily fabricated and geometrically simple three-dimensional cross-linked dual helical (CLDH) micromixer. Mixing mechanism of the CLDH channels was investigated with numerical simulations. The split and recombine (SAR), chaotic advection, and flow impact mixing effects were integrated and improved in the passive mixer with CLDH channels. A new SAR mixing effect dominated by flow collision was involved in the mixer in which a cycle of CLDH mixer can achieve two SAR mixing courses which is more effective than conventional SAR mixers. A geometric optimization method of studying the mass flow rate of flow streams was proposed to obtain the optimized structure, which can be applied to optimizing passive mixers with crossed or overlapped channels. The CLDH mixer shows a stable and excellent mixing capability in an extra short length for a wide low Re range; 99 % mixing degree can be achieved in four cycles (i.e., 320 μm) for < Re < 30. This rapid and robust micromixer will contribute to a flexible application in microfluidic systems. Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. K. Liu Q. Yang (*) F. Chen (*) Y. Zhao X. Meng C. Shan Y. Li State Key Laboratory for Manufacturing System Engineering and Key Laboratory of Photonics Technology for Information of Shaanxi Province, School of Electronics and Information Engineering, Xi an Jiaotong University, Xi an , People s Republic of China yangqing@mail.xjtu.edu.cn F. Chen chenfeng@mail.xjtu.edu.cn Keywords Microfluidics Passive mixer Cross-linked dual helical channels Mixing improvement 1 Introduction Microfluidic systems are widely used for analytical chemistry, biomedical assay, and biochemical synthesis (Chin et al. 2011; Jeong et al. 2010). Compared with conventional large-scale facilities, microfluidic devices have significant advantages to conduct biomedical research and clinical applications, such as less volume of sample consumption, increased accuracy, and faster analytical process. As an essential component of microfluidic systems, micromixing devices are used to homogenize samples or reactants. Active and passive mixing methods have been employed to enhance the mixing of fluids in microfluidic systems. Active mixers can achieve fast and effective mixing (Yang et al. 2001; Azimi et al. 2011; Bottausci et al. 2007). However, the fabricating process is complicated. And the complex electro/magnetism operations may result in side effects for the assay process. Two main passive mixing concepts, namely split and recombine (SAR) and chaotic advection, have been applied in microfluidic mixers (Long et al. 2009; Lim et al. 2011; MacInnes et al. 2007; Kim et al. 2005; Stroock et al. 2002; Johnson et al. 2002). Such passive mixers are designed to promote an efficient diffusion with complex multilayer or three-dimensional (3D) channels, either by increasing the interfacial area between fluids or by decreasing the distance over which diffusion takes place. Although numerous passive mixers have been designed, most of them merely realize effective mixing for a certain range of Reynolds number (Re) in several millimeters (Fang and Yang 2009; SadAbadi et al. 2013; Lee and Lee

2 ; Chen and Meiners 2004; Nimafar et al. 2012; Lee et al. 2007). For example, Zhang et al. (2012) reported a passive mixer based on capillary to realize 99 % mixing in 61.7 mm for Re 0.3; Tofteberg et al. (2010) reported a lamination mixer in a planar channel system realizing ~80 % mixing in four cycles (1.5 mm) for Re 1; Hong et al. (2004) reported a passive mixer with modified Tesla structures to achieve effective mixing in 7 mm for Re < 10. The mixing length of SAR mixers grows with the flow velocity, and efficient mixing is often achieved for Re < 1. Three-dimensional mixing in chaotic advection mixers requires a relatively high Reynolds number, i.e., Re > 1, to induce lateral motions which act as an internal agitator to force the flow to fold and split. Therefore, passive mixers that combine SAR and chaotic advection effects can achieve ideal mixing for a wide range of Re. However, the flexible design of complex mixing structures has been limited by the fabrication methods, among which the two-dimensional (2D) photolithography and patterning process has been the main approach. The reported designs are based on conventional planar SAR and chaotic advection structures that can only achieve fully mixing in millimeters (Chung et al. 2008; Shih and Chung 2008; Bhagat et al. 2007; Schönfeld et al. 2004; Kim et al. 2005). For example, Xia et al. (2005, 2006) reported passive chaotic mixers using two-layer crossing channels to achieve effective mixing in ~12 mm for 0.01 < Re < 1. In this study, we propose a cross-linked dual helical (CLDH) mixer, which is consisted of double helical channels rotating in opposite directions to create repeated crossing regions. The mixing mechanism of CLDH channels was investigated by numerical analysis. Compared with conventional SAR structures, a new SAR process was achieved with flow collision. Flow streams were stretched, split and folded by flow collision, and recombined in the crossing regions. Chaotic advection mixing effect was enhanced with the sharply twisting streams on the basis of helical flow and flow collision. The separation distance between the double helical channels was investigated as the main factor that affects the mixing performance. And, optimal mixer geometries were derived from the simulation results by studying the mass flow rate of repelling flow and straight flow. The femtosecond laser was employed to fabricate the CLDH channels in fused silica. The mixing process was testified by mixing two fluorescent dye solutions. The uniqueness in our research is that a new SAR process to achieve two SAR mixing courses in one cycle, chaotic advection, and flow impact mixing effects is integrated in the CLDH mixer, which enables a stable and excellent mixing capability in an extra short length for a wide low Re range. The proposed geometric optimization method of studying the mass flow rate of flow streams can be extended to studying passive mixers with crossed or overlapped channels. Fig. 1 Schematic of the cross-linked dual helical micromixer 2 Materials and methods 2.1 Design of the CLDH micromixer Inspired by the combination of SAR and chaotic advection mixing effects, the CLDH mixer was designed on the basis of cross-linked double helical channels, as shown in Fig. 1. 3D serpentine and helical structures have been designed to induce a chaotic mixing effect in passive mixers (Liu et al. 2000; Lee et al. 2007; Jani et al. 2011). Recently, we have studied a 3D helical mixer of chaotic advection to achieve effective mixing for Re > 1 based on the femtosecond laser fabrication technology (Liu et al. 2013; He et al. 2012; Bian et al. 2012; Qu et al. 2012). But fast mixing of fluids over lower Res with the 3D helical channels remains a difficult task due to the dominance of molecular diffusion. The mixing component of the CLDH mixer is the double helical channels which rotate in opposite directions to create repeated crossing regions. The conversely rotating double helical channels are designed to take full advantages of chaotic advection. Flow streams are split by flow collision and recombined repeatedly flowing through the crossing regions, which enables a new SAR mixing effect. Meanwhile, the SAR mixing effect is improved with flow impact in the crossing regions, which has been verified in the modified Tesla structures (Hong et al. 2004). 2.2 Numerical simulation To demonstrate the 3D mixing mechanism, numerical simulations were carried out using commercially available finite element analysis software (COMSOL Multiphysics 4.3). Two streams of liquid water with a relative species concentration of 1 and 0 were injected into the mixer through the inlets; the velocity and concentration fields were obtained by solving the incompressible

3 Navier Stokes and convection diffusion equations in the stationary mode. Dynamic simulations were also conducted to trace the inert particles flowing in the CLDH channels. Detailed information of the simulation process is included in the supplementary material. A dynamic mixing index σ is employed to evaluate the mixing performance based on the simulation results (Cerbelli et al. 2008): ( Ci C a A C a )V z da σ = 1 (1) A V zda where C i is the concentration value, A is the crosssectional area, V z is the axial velocity, and C a equals A C iv z da/ A V zda. As the mixing process develops, the concentration value C i will approach the average value C a at each point in the concentration sections. Thus, it shows that the fluids mix well when the value of σ gets closer to 1; in contrast, as σ gets closer to 0, the mixing becomes worse. The average inlet velocity was controlled to investigate the dependency of the mixing performance on the Reynolds number: 171 PDMS-based microfluidic systems. Two fluorescent dye solutions (fluorescein sodium and rhodamine B) were used in the mixing test. The volumetric flow rate was controlled using a syringe pump. 3 Results and discussion 3.1 Comparative analysis To study the mixing performance of the CLDH mixer, simplified CLDH, helical, and straight mixers were modeled and simulated, as shown in Fig. 2. The T-shaped inlet structure was simplified into two symmetrical semicircle inlet surfaces. The geometric parameters of the CLDH mixer and helical mixer are set as helical diameter D = 60 μm, helical pitch P = 80 μm, number of cycle = 2.5, and separation of double helical channels H = 15 μm. The CLDH mixer is smoothly connected at the inlet and outlet with a half-cycle helical channel (helical diameter D = 75 μm) and a straight channel (length = 15 μm). The channel Re = ρυd h µ (2) where υ denotes the fluid velocity, ρ is the density, µ is the viscosity, and d h is the hydraulic diameter of the channel. The averaged Lyapunov exponent ( λ) was employed to show the chaotic degree of flow in the CLDH channel according to Xia s formula (Xia et al. 2006): λ i = 1 x ln δ i(x) δ i (0) (3) where x is one cycle of the CLDH mixer (including two crossing regions), which was set as 1, δ i (0) is the initial separation of the ith pair of neighboring particles, and δ i (x) is the separation after one cycle of the CLDH mixer. 3,000 pairs of neighboring particles were released at the inlets, and their Poincaré trajectories were captured after one cycle of the CLDH mixer. Detailed simulation information is included in the supplementary material of dynamic simulations. The averaged value of λ ( λ) was then calculated to reflect the overall chaotic degree of CLDH channel. 2.3 Experiments The CLDH channels were fabricated in fused silica by the improved femtosecond laser wet etching (FLWE) technology (Liu et al. 2013; He et al. 2012; Chen et al. 2013). Detailed information of the fabricating process is included in the supplementary material. The fabricated chip was sealed by bonding with a polydimethylsiloxane (PDMS) block (Liu et al. 2013). This glass PDMS interface design will enable a flexible application of the CLDH mixer in Fig. 2 Models of a the CLDH micromixer, b helical micromixer and c straight micromixer. The channel diameter d i is 30 μm. The straight mixer has a channel length that is equivalent to the helical one

4 172 Figure 3b shows the mixing index of the CLDH mixer, helical mixer, and straight mixer for < Re < 30. At lower Res (Re < 0.075), the mixing result of the helical mixer is almost the same as the straight mixer; and increase in Re leads to drop in the mixing effect, in which the laminar flow and diffusing effect contributes to the mixing process. As Re increases above ~1, the helical channel induces chaotic advection, and the mixing in the helical mixer is enhanced compared with the straight mixer. In contrast, the CLDH mixers show a relatively stable mixing ability; the mixing index of the CLDH mixer with split injection is above 0.92 for all Re values, and the mixing index of the CLDH mixer with parallel injection is ~0.8 for < Re < 30. Figure 4 shows the slice plots of velocity magnitude field in the one-cycle CLDH mixer (helical diameter D = 60 μm, helical pitch P = 80 μm, and separation Fig. 3 Mixing effect of the micromixers. a Overall and outlet concentration field at Re = 0.3, b mixing index of the outlet varies with Re for the CLDH mixer, helical mixer and straight mixer length of the straight mixer is 515 μm, which is equivalent to the helical one. Two injection methods were applied to the CLDH mixer, which are split injection and parallel injection. The inlet concentration of inlet surfaces is defined as [C inlet = 1 (x 0), C inlet = 0 (x < 0)] for the split injection and [C inlet = 1 (y 0), C inlet = 0 (y > 0)] for the parallel injection, as shown in Fig. 3a. In order to maintain the same sectional average velocity, the average inlet velocity is set as 0.01 m s 1 for the helical mixer and straight mixer and 0.02 m s 1 for the CLDH mixer. The concentration distribution of the four mixers is shown in Fig. 3a. As the Reynolds number remains a low level (Re = 0.3), the mixing is mainly dominated by molecular diffusion rather than convection. The helical and straight mixers realize similar mixing indexes of ~0.55, while the CLDH mixers show much better mixing results. The mixing effect of the CLDH mixer can be further improved by the split injection method; the mixing index of split and parallel injection is 0.94 and 0.79, respectively. The injected solutions are evenly distributed into the double helical channels with split injection for pre-mixing before entering the first crossing region. In contrast, the two streams are actually separately introduced into the helical channels with parallel injection. Fig. 4 Slice plots of the velocity magnitude field in the CLDH mixer. The streamlines and arrows show the flow direction. The streamline radius expression is determined by the velocity magnitude; the arrow length is determined by the flux magnitude

5 H = 20 μm). The repeated crossing regions of double helical channels induce flow collisions and splits continually in the mixer. The flow streams in the double helical channels intersect and impact each other entering the crossing region; as the flow collision develops, there occur two patterns of fluid behavior, i.e., repelling flow and straight flow; subsequently, the four streams of repelling and straight flow recombine in the downstream helical channels. The SAR course is accomplished after flowing through a single crossing region. That means a cycle of CLDH mixer can achieve two SAR mixing courses which is more effective than conventional SAR mixers. As discussed above, the SAR effect in the CLDH mixer can improve the mixing result at lower Res (Re < 1). The helical channels promote the chaotic advection to accelerate mixing as Re increases above 1. Meanwhile, the curvature diameter of repelling flow is less than the helical diameter; thus, better chaotic advection can be achieved with the smaller curvature diameter of curved flow (Verma et al. 2008). In addition, the chaotic advection and mixing effect can be largely improved with flow impact in the crossing regions, which has been verified in the modified Tesla structures (Hong et al. 2004). Therefore, the CLDH mixer can realize a stable mixing for a wide Re range. To better understand the mixing mechanism of the CLDH mixer, we define the relative mass flow rate as: A ξ = out VC i da (4) A in VC i da where C i is the concentration value, A out is the outlet surface area, A in is the inlet surface area, and V is the normal velocity that is perpendicular to the surface. Here, we specify the mixing process in one crossing region and downstream half-cycle helical channels as a mixing course and assume that the mixing process is fully developed in one mixing course to a certain level (0 100 %). Then, the mixing effect after a mixing course can be estimated by a formula which reflects the mixing degree: 173 where N is the mixing course number which equals the crossing region number. For the CLDH mixer with split injection, the mixing degree can be estimated as: ( θ = 1 1 2ξ in γ in where (1 2ξ in γ in) represents the pre-mixing effect of split injection (ξ in 0.5). Thus, the mixing performance of the CLDH mixer in Fig. 3b can be well explained by formulas 6 and 7. The mixing efficiency coefficient γ is determined by the combined mixing effect of SAR and chaotic advection, which can be maintained in a high level for a wide range of Re. As ξ (ξ 0.5) is specified by the structure of crossing region and γ is maintained in a high level, the mixing degree is largely determined by the number of crossing region N. That is why the CLDH mixers display a stable mixing performance for different Re values. The slight changes of mixing index are caused by the variations of γ and ξ, because the SAR and chaotic advection mixing effects vary with Reynolds number and ξ can also be influenced by the flow velocity. However, the mixing index of CLDH mixer with parallel injection is lower than that of the helical mixer for Re > 10, because the mass flow rate ξ is relative little and species distribution in the double helical channels is uneven. 3.2 Structural analysis ) N i=1 ( ) 1 2ξ i γ i To achieve an optimal mixing effect, geometric parameters of the CLDH mixer have to be optimized. From formulas 6 and 7, we can conclude that mixing effect of the CLDH mixers is determined by three parameters (taking no account of the split injection), which are mixing efficiency coefficient γ, relative mass flow rate ξ, and the number of crossing region N. As γ is determined by the combined (7) λ = 2ξ γ where γ (0 < γ < 1) is the mixing efficiency coefficient that represents the mixing ratio in one mixing course, ξ is the relative mass flow rate of one crossing region, which represents the minimum mass flow rate of the double helical channels ((ξ = min(ξ out1, ξ out2 )), ξ out1 + ξ out2 = 1). Thus, the mixing degree of the CLDH mixer with two flow streams being separately injected into the double helical channels (i.e., parallel injection) can be estimated as: (5) θ = 1 N i=1 ( 1 2ξ i γ i ) (6) Fig. 5 Dependency of the mass flow rate of straight flow and repelling flow on the ratio of separation to channel diameter (H/d i ) at Re = 0.3

6 174 Fig. 6 a Influence of the ratio of separation to channel diameter (H/di) on the mixing index of the outlet at Re = 0.3. b Concentration and flow distribution of the CLDH channels with 0.5, 1.0 and 1.5 cycles for H/di = The streamlines and arrows show the flow direction. The streamline radius expression is determined by the velocity magnitude; the arrow length is determined by the flux magnitude mixing effect of SAR and chaotic advection, we can refer to reported results of helical channels and SAR mixers to improve γ (Yasui et al. 2011; Therriault et al. 2003; Verma et al. 2008; Lim et al. 2011). Here, we focused our study on the relative mass flow rate ξ. The optimal mixing result of the CLDH mixer can be realized as ξ gets to 0.5. Since the geometric configuration of every crossing region is the same and the velocity distribution in the double helical channels is similar, ξ can be estimated with a half-cycle CLDH mixer: ξ = min(ξr, ξs ), where ξr represents the mass flow rate of repelling flow, ξs represents the mass flow rate of straight flow (ξr + ξs = 1), as shown in Fig. 5. The separation distance of double helical channels is likely to be the main factor affecting the mixing results. When the helical channels fully overlap (H = 0), a decreased agitation effect is expected due to laminar flow. 13 Fig. 7 Influence of the ratio of separation to channel diameter (H/di) on the pressure drop between the inlet and outlet at Re = 0.3

7 175 Fig. 8 Optimal ratio of separation to channel diameter (H/d i ) varies with a the helical diameter D and b the helical pitch P When the helical channels are shifted (separation distance H < channel diameter d i ), there occur the repelling flow and straight flow, and a strong agitation effect is enabled. As the separation distance increases to the value of channel diameter, the double helical channels overlap no more. Thus, an optimal separation distance is expected to achieve the best agitation effect. Figure 5 shows the simulation results of mass flow rate ξ r and ξ s with a half-cycle CLDH mixer. The geometric parameters of the CLDH mixer are set as helical diameter D = 60 μm, helical pitch P = 80 μm, and number of cycle = 0.5. Two streams of solution (concentration c = 1 and 0) are injected into the mixer through the inlets with an average velocity of 0.01 m s 1. The mass flow rate ξ of outlet A and B represents the mass flow rate of repelling flow ξ r and straight flow ξ s, respectively. The mass flow rate value varies with the ratio of separation to channel diameter (H/d i ). Mass flow rate lines of ξ r and ξ s intersect and reach 0.5 as the H/d i value approaches We also studied the influence of flow velocity on the mass flow rate and found that the mass flow rate is little changed for < Re < 30. The optimal H/d i value derived from Fig. 5 was verified by evaluating the mixing index. As shown in Fig. 6a, the best mixing result of the half-cycle CLDH mixer is achieved as the ratio of H/d i gets to ~0.82, which is precisely the same as Fig. 5. However, the optimal H/d i value varies with the cycle number of CLDH channels. As the number of cycle increases, the optimal H/d i value decreases and approaches ~0.7. This phenomenon is caused by the non-uniform concentration distribution of species in the crossing regions, as shown in Fig. 6b. The concentration fields for the two outlets of the half-cycle CHDH mixer are asymmetrical. The flow streams of asymmetrical concentration distribution after the first crossing region are injected

8 176 As the helical diameter D is increased or helical pitch P is decreased, the crossing region area and crossing angle of double helical channels increases. It results in the enhancement of flow collision which forces more fluid to move backward and induces increased repelling flow. Thus, the mass flow rate of repelling flow is increased. Based on the simulation results, an optimized CLDH mixer was modeled, and the geometric parameters were set as the helical diameter D equals 60 μm, helical pitch P equals 80 μm, and separation distance H equals 21 μm (ratio of H/d i = 0.7). The mixing results show that the optimized CLDH mixer with parallel injection can achieve 99 % mixing degree in four cycles (320 μm) and 95 % mixing in three cycles (240 μm) for < Re < 30, as shown in Fig. 9. And the mixing index lines for 0.03 < Re < 30 are very similar. Thus, the mixing degree of formula 6 can be simplified as: θ 1 ( 1 2ξ γ ) N (8) Fig. 9 Mixing effect of the optimized four-cycle CLDH mixer: fully (99 %) mixing can be achieved in four cycles of the CLDH mixer for 0.03 < Re < 30 into the downstream second crossing region, as shown in Sect. 1 of the one-cycle mixer. It causes an uneven species distribution in the repelling flow and straight flow after the second crossing region, as shown in Fig. 6b, in which less and smaller arrows indicate less species in the flow. To compensate the uneven species distribution, the repelling flow has to be enhanced by decreasing the H/d i value. However, the influence of non-uniform concentration distribution on the mixing effect decreases with more cycles (number of cycle >1.5), because the concentration fields after 1.5 cycles are more uniform than upstream ones. The separation distance of double helical channels also influences the pressure drop of flow, as shown in Fig. 7. The pressure drop between the inlet and outlet increases with the H/d i value, which means it needs a larger pumping power to maintain a constant flow as the separation distance of double helical channels increases. Influence of the helical diameter D and helical pitch P on the mass flow rate ξ was also studied. As shown in Fig. 8a, the helical pitch P is controlled constant at 80 μm while varying the helical diameter D. From the results, we can find that the optimal ratio of H/d i increases with helical diameter. But the optimal ratio of H/d i decreases with helical pitch, as shown in Fig. 8b where the helical diameter D is controlled constant at 60 μm while varying the helical pitch. That is attributed to the variation of crossing region dimension which affects the flow collision intensity. where the flow rate ξ is estimated as 0.5, the mixing efficiency coefficient γ is estimated as 0.44, and N is the crossing region number. Figure 10 shows the dynamic simulation results of inert particle trajectories which flow through the CLDH channel. As 99 % mixing degree can be achieved in four cycles, the time duration that the particle trajectories fully develop in four cycles can be estimated as the mixing time, as shown in Fig. 10a. The mixing time is <200 ms as the flow velocity increases above 0.01 m s 1 (i.e., Re > 0.3). From the Poincaré maps of the particle trajectories, we can find that the chaotic advection is not fully developed for Re < 3, which is consistent with the averaged Lyapunov exponent ( λ), as shown in Fig. 10a. The chaotic advection flows are largely improved as Re increases, that λ increases to 1.3 and chaotic particle trajectories are observed in the Poincaré maps at Re = 30. However, the indication of chaotic mixing effect for Re < 3 can be identified that the averaged Lyapunov exponent λ remains constant at ~ 0.9. The crosssectional profiles of particle trajectories clearly indicate the SAR process in the CLDH mixer. The diffusion distance decreases with the crossing region number in an exponential form, as shown in Fig. 10b d. Figure 11 shows the fabricated CLDH mixer embedded in fused silica and mixing results. Fine features of the construction and surface geometry are observed from the SEM cross-sectional images of the channel, and uniform sections and smooth inner surface are achieved (Fig. 11a). The smooth inner surface of the channel will facilitate the fluid flow. Two streams of solution were injected into the CLDH channels separately in the mixing test at Re = 2.5. The mixing results were recorded using a fluorescein microscope (Leica DM4000), which is equipped with a

9 177 Fig. 10 Poincaré maps of the particle trajectories at different sections. The color is a logical expression indicating which inlet the particles have been released from. a The mixing time and the averaged Lyapunov exponent λ for different Res. Cross-sectional profiles of particle trajectories for b Re = 0.003, c Re = 3, and d Re = 30 constant color intensity control module (CCIC). To obtain a harmonious fluorescence image, the mass concentration of fluorescein sodium and rhodamine B solution was modified to 0.35 and 1 mg ml 1, respectively. Figure 11b shows the mixing results using the blue excitation, under which the two fluorescent dye solutions show a balanced fluorescent intensity. From the color variation, fully mixing is observed in four cycles of the CLDH channel; the injected green and

10 178 Fig. 11 a Fabricating results of the CLDH micromixer, b mixing results of fluorescein sodium solution and rhodamine B solution under the blue excitation, c simulation results of particle trajectories at Re = 2.5, d mixing results of fluorescein sodium solution and rhodamine B solution under the ultraviolet excitation at Re 2.5 red solutions turn into a homogeneous yellow tone flowing through the CLDH channel. To further review the mixing mechanism, the ultraviolet excitation was used, under which the fluorescence intensity of rhodamine B was restrained to a relative lower level compared with that of fluorescein sodium. Therefore, the optical contrast of red and green light was employed to reveal the mixing process, as shown in Fig. 11d. The SAR effect can be clearly observed from the dark red flow streams, which is in close agreement with the simulation results of particle trajectories, as shown in Fig. 11c, d and the partial enlarged views. Flow streams are separated and recombined when flowing through the crossing regions, which enables an improved SAR mixing effect in the CLDH channel. The dark red flow streams also indicate that the SAR effect contributes a main role in accelerating the mixing process, since inert particles were used in the simulation of particle trajectories. The confocal microscope (Olympus Fluoview FV1000) was also used to observe the mixing process of the fluorescein sodium solution and rhodamine B solution, as shown in Fig. 12. Fluorescent images are obtained slice by slice and stacked subsequently to observe the total color intensity. The helical channel of fluorescein sodium solution overpasses that of rhodamine B solution at the first crossing region from the microscopically viewing angle. Thus, more green flow streams are observed to be split into the double helical channels in the upper slices and less in the lower slices than the red flow, which is consistent with the simulation results. From the scanned fluorescent slices, we can find that the SAR process is achieved in the CLDH channel and fully mixing can be realized in four cycles of the CLDH mixer. More information about the confocal microscoping results can be gained in the supplementary material and videos. Compared with conventional SAR structures, flow streams in the CLDH channels are split by flow collision rather than obstacles or gaskets in the channel, which can simplify the channel structure and eliminate the dead area of flow. The flow impact in crossing regions can dramatically improve the secondary flow and mixing result, which has been validated in the modified Tesla structures by Hong

11 179 Fig. 12 Confocal microscoping images of scanned fluorescent slices from bottom to top of the mixer and the stacking result of intensity projection. More information and dynamic observation can be obtained in supplementary material and videos et al. (2004). Similar passive mixers using two-layer overlapping channels have also been reported to realize species exchange of flow in the channels (Kim et al. 2005; Xia et al. 2005, 2006; Fang et al. 2011). But the planar twolayer channels are connected to each other without crossing regions, in which the flow splitting caused by collision is not in dominance. The SAR effect in two-layer channels is not obviously improved compared to conventional SAR structures that each mixer unit can only achieve one SAR operation. Meanwhile, species redistribution or exchange of the SAR process is uneven and incomplete with the connected two-layer channels. The species exchange is mainly caused by the mass diffusion and flow rotation in the overlapping areas of the two-layer channels, which is even much less effective than conventional SAR mixers (Fang et al. 2011). Typically, one cycle of the CLDH mixer (one mixing unit) can achieve two SAR mixing courses, which is more effective than reported SAR mixers. In addition, the 3D helical channels can induce steady and continuous chaotic advection for moderate Res (Re > 1), while straight bridges in the planar two-layer mixers do not contribute to chaotic advection. The dead area of flow is also not eliminated in square corners of the two-layer channels. 4 Conclusions In conclusion, a 3D passive mixer with CLDH channels for rapid mixing of liquid at low Res was designed and analyzed in this study. The mixing mechanism of CLDH mixers was studied by the numerical simulation and theoretical formulas. With the typical structure, two flow patterns of repelling flow and straight flow are induced in the fluid; SAR and chaotic advection mixing effects are integrated and improved in the CLDH mixer. Optimal geometric parameters were gained for the CLDH mixer according to the numerical analysis results. The simulation and experimental results show that fully mixing (99 % degree) can be achieved in four cycles (320 μm) over a wide range of low Re ( ) with the CLDH channel. The mixing efficiency can be further optimized according to reported studies (Yasui et al. 2011; Therriault et al. 2003; Verma et al. 2008; Lim et al. 2011), including decreasing helical diameter to improve Dean number, reducing channel diameter to decrease the diffusion distance and diminishing helix angle. The geometric optimization method of studying the mass flow rate of flow streams can be the guidelines for optimizing passive mixers with crossed or overlapped channels. Meanwhile, fast prototyping of true 3D microfluidic systems with a more compact structure can be achieved by combing the glass PDMS assembling design and the femtosecond laser fabrication technology. Acknowledgments This work is supported by the National Science Foundation of China under the Grant Nos and , the Special-funded program on national key scientific instruments and equipment development of China under the Grant No. 2012YQ and collaborative innovation center of Suzhou nano science and technology in China. 13

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