Mixing enhancement of a novel C-SAR microfluidic mixer

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 338–345

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Mixing enhancement of a novel C-SAR microfluidic mixer Kexiang Chen 1 , Hui Lu 1 , Meng Sun, Li Zhu ∗ , Yiping Cui Advanced Photonics Center, Southeast University, Nanjing 210096, Jiangsu, China

a r t i c l e

i n f o

a b s t r a c t

Article history:

We proposed a three-inlet planar mixing geometry, named cascaded splitting and recombi-

Received 24 February 2017

nation (C-SAR). The C-SAR mixer works in a wide range of Reynolds number (34.6–150) with

Received in revised form 14 January

90% mixing efficiency; the mixing time is as short as sub-milliseconds and sample consump-

2018

tion is as low as a few microliters per second. The asymmetric arranged triangular baffles

Accepted 16 January 2018

in the mixing region introduce C-SAR, which transports the central fluid toward channel walls further than symmetric splitting and recombination (S-SAR), resulting in more effective mixing with fluids from side inlets; meanwhile, corner vortices and Dean’s vortices are

Keywords:

generated when fluids pass through sharp bends formed by triangular baffles or channel

Microfluidic mixer

edge with high speed, which creates chaotic advection and enhances mixing. Therefore, C-

Cascaded split and recombination

SAR greatly improves mixing efficiency compared with S-SAR. This easily fabricated C-SAR

Asymmetric planar geometry

rapid mixer is an attractive tool to study biomacromolecular dynamics.

Low sample consumption

© 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Sub-millisecond mixing time

1.

Introduction

Microfluidic technology has shown more and more attractions in the field of chemical engineering, biological engineering, and detection/analytical process because the diminutive scale of the flow channel increases the surface to volume ratio, which is beneficial for many applications, such as chemical synthesis, biosensing, and transport phenomena on the microscale (Jeong et al., 2010; Lee et al., 2011; Nge et al., 2013). The micromixer is an important component in a microfluidic system and usually used to manipulate reagents. Fast mixing is essential in many biochemistry analyses, such as cell activation, enzyme reaction and protein folding, which require rapid mixing reactants to trigger reactions (Nguyen and Wu, 2005; Hertzog et al., 2004; Kane et al., 2008; Zhu et al., 2011; Li et al., 2014). Therefore, the microfluidic mixer used for studying biochemical reaction kinetics has to meet following requirements: high mixing efficiency, short mixing time and

∗

low sample consumption because the yield of biochemistry samples is low and cost is high. However, flows in the microchannel are laminar so that mixing relies on molecular diffusion, which is a slow process. To address this challenge, various methods have been developed to enhance mixing (Hessel et al., 2005; Ward and Fan, 2015; Kathuria et al., 2013). Compared with active mixers, which use external fields (acoustic, electric, magnetic) to accelerate mixing, passive mixers are inexpensive, easy to fabricate and integrate with microfluidic systems, so that passive mixers are being used in most microfluidic applications. Passive mixers use the geometry of the mixing chamber to produce a specific flow pattern which promotes mixing. Hydrodynamic focusing mixer can achieve a few microseconds mixing time by focusing sample to a very narrow ribbon to reduce diffusion lengths while consuming femtomole sample (Knight et al., 1998; Hertzog et al., 2004; Yao and Bakajin, 2007). However because of the tiny sample volume inside the

Corresponding author. E-mail address: [email protected] (L. Zhu). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.cherd.2018.01.032 0263-8762/© 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

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Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 338–345

mixer, the design can only be used with high sensitive probes, such as fluorescence, not for low sensitive probes, e.g. light absorbance or Raman measurement. Splitting and recombination (SAR) and chaotic advection (Kathuria et al., 2013; Jeong et al., 2010; Lee et al., 2016; Nge et al., 2013; Nguyen and Wu, 2005; Hessel et al., 2005; Ward and Fan, 2015) are another strategies to enhance mixing. SAR splits a fluid into many streams and increases the contact surface between the fluids, consequently improves diffusion based mixing; meanwhile, SAR generates lateral movements and promotes mixing. The chaotic advection forces a change in flow direction that exponentially increases the interaction surface, so that enhances mixing while maintaining low flow rates (Kathuria et al., 2013; Lin, 2015). A lot of mixer geometries have been proposed based on SAR and chaotic advection. Lin et al. placed small cylindrical obstacles in the channel and achieved a mixing time of 20 ␮s with a mass flow speed of 20 ␮L/s (Lin et al., 2003). Kane et al. fabricated a 2D-serpentine mixer with 200 ␮s mixing time and 300 ␮L/min flow rate (Kane et al., 2008); Egawa et al. made the alcove mixer and obtained 22 ␮s mixing time at 20 ␮L/s (Egawa et al., 2009). These mixers realize rapid mixing at pretty high flow rates and result in high pressures inside channel. For example, the pressure in the serpentine mixer is larger than 200 psi (Kane et al., 2008). Therefore, the above mixers are all made of silicon to withstand high pressures. But fabrication of hard materials like silicon or glass is a difficult process and costs a lot. Polydimethylsiloxane (PDMS) is currently the most popular polymeric material for microfluidics in use in academic laboratories due to its low cost, ease of fabrication and optical transparency. Li et al. proposed a PDMS-glass hybrid Zigzag ultrarapid micromixer with a mixing time of 5.5 ␮s at 8.67 ␮L/s flow rate (Li et al., 2014). However, significant pressure drop in the mixer may cause the system instable (Kathuria et al., 2013). Wang et al. embedded triangular obstacles symmetrically in the Y mixer to generate SAR and enhanced mixing. The mixer can work at low Reynold number (Re = 1.0) with 85.5% mixing efficiency, but mixing length is pretty long, corresponding to slow mixing time (Wang et al., 2014). Recently, several researchers found that unbalanced geometries could effectively improve the performance of SAR mixer (Ansari and Kim, 2010; Sheu et al., 2012; Hossain and Kim, 2014; The et al., 2015). The et al. fabricated a shifted trapezoidal blades (STB) mixer which has asymmetric 3D geometrical structure (The et al., 2015). STB mixer had stable mixing efficiency over 80% for Reynolds number values in the range from 0.5 to 100; the highest mixing efficiency value (95%) was achieved at Re = 40. However, manufacturing 3D structure is a complex process. Inspired by unbalanced structures, we designed and fabricated an asymmetric planar geometry in the 3-inlet mixer, and named it cascaded splitting and combination (C-SAR) mixer. It has 90% mixing efficiency over a wide range of Reynolds number (34.6–150) and achieves sub-milliseconds mixing time with low sample consumption.

2.

Mixer design

The geometry and dimensions of the mixing region in the C-SAR micromixer are shown in Fig. 1(a). The top channel supplies the sample and the two sides supply buffer. The two solutions are mixed when they flow through the mixing region. Fully mixed solution exits through the bottom chan-

nel. The mixing region consists of five mixing units and each mixing unit (shown in Fig. 1(b)) is composed of four rows of triangular baffles which are arranged asymmetrically. The fluids are split by the first and second triangular baffles in cascade (Fig. 2(a)), so that the sample is delivered toward the channel wall further and has more chances to mix with buffer from side channels. Compared with the symmetrical arrangement of obstacles (S-SAR) (Fig. 2(b)), C-SAR induces more transverse movement of fluids and results in more effective mixing. In addition, vortices are created when fluids flow through sharp bends formed by the channel edge or triangle baffles, which enhances mixing further (details shown in Results and discussion).

3.

Methods

3.1.

Numerical simulation

The physical modes, laminar flow and transport of diluted species, in Comsol Multiphysics package based on finite element method (FEM) were applied to simulate mixing effects in three-dimensional model. The governing equations are presented as Eqs. (1)–(3): T

(u · ∇)u = ∇ · [−PI + (∇u + (∇u) )] + F

(1)

∇ · u = 0

(2)

∇ · (−D∇ci ) + u · ∇ci = R

(3)

where  denotes the fluid density (kg/m3 ); u represents the velocity vector (m/s); P is the pressure (Pa);  equals the dynamic viscosity (Pa s); T is the viscous stress tensor; F is the body force term (N/m3 ); I is the identity matrix; D equals the diffusion coefficient (m2 /s); R is a source term, respectively. Among them,  is set to 1000 kg/m3 ;  is 0.001 Pa s; the pressure of the outlet is set to 0 Pa; the sample is Rhodamine B and D = 0.4 × 10−9 m2 /s (Culbertson et al., 2002; Gendron et al., 2008). The flow rate ratio of the central inlet and side inlets is 1:5:5. The concentration of sample is set to 1 mol/m3 in the central inlet and 0 in side inlets. The Reynolds number is calculated as Re =

vDh 

(4)

where  is the fluid density; v is the average velocity in the channel; Dh is the hydraulic diameter of the channel, numerically equal to 4 times the ratio of the area to perimeter. The bigger the Reynolds number indicates the greater effect of the inertia force. The dependence of mixing efficiency on Reynolds number (9–150) was analyzed. Mixing time is equal to the volume of the mixing region divided by the total flow (Li et al., 2014): t=

Vmix vT

(5)

where Vmix is the volume of the mixing region; vT is the total flow. Mixing times versus flow rates are shown in Table S1. The mixing efficiency M is used to quantitatively evaluate the performance of the proposed C-SAR mixer, and it is obtained by: M=1−

(6)

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Fig. 1 – (a) Geometry of the C-SAR micromixer; (b) geometry of one mixing unit.

Fig. 2 – Schematics of mixing: (a) C-SAR; (b) S-SAR.

where  is the standard deviation of the concentration at outlet cross-section and is defined as

  N   1  ci − c¯ 2 = c¯

N

corners. The mesh refinement is also shown in Supplemental Files.

(7)

i=1

where c¯ is the mean concentration, N is the total sampled points at the outlet cross-section, ci is the concentration value at sampled point i. To minimize numerical diffusion and optimize computational time (Hossain et al., 2009; The et al., 2015; Lin, 2015), the mesh independence test with an element number ranging from 7.32 × 105 to 3.18 × 106 were implement. Concentration along central line at exit channel cross-section and the standard deviation with various mesh refinements are shown in Supplemental Files. Beyond the total element number of 2.4 × 106 , the difference of concentration profiles was negligible which indicated obtained result was independent of mesh. Therefore, 2.4 × 106 was selected as the optimal element size. The mesh type was free tetrahedral and was refined at sharp

3.2.

Experiments

3.2.1.

Chip fabrication

The devices were made of polydimethylsiloxane (PDMS) using the replica molding technique. Molds were fabricated at the Suzhou Wenhao Chip Technology Co., Ltd. The chip fabrication processes were as follows: (1) The mixture of pre-polymer of PDMS and curing agent with mass ratio of 10:1 was poured on the mold for 8 h to remove bubbles; (2) After been baked at 65 ◦ C for at least 3 h, the PDMS replica was peeled from the mold with designed pattern in it, then been punched inlet and outlet with 0.5 mm diameter; (3) After being cleaned by oxygen plasma, the PDMS replica and a piece of PDMS coverslip were bonded together. To achieve permanent bonding, the chip was put in oven (65 ◦ C) for 3 h. The fabricated C-SAR chip is shown in Fig. 3 and the size is 1.5 cm × 2.5 cm.

Chemical Engineering Research and Design 1 3 2 ( 2 0 1 8 ) 338–345

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Fig. 3 – Mold and photograph of the C-SAR microfluidic chip.

Fig. 4 – (a) Top view of streamlines in the first mixing unit; (b) velocity profile and transverse components at cross-sections C1.1 –C1.4 ; (c) concentration distributions of sample at cross-section C1.1 –C1.4 , the velocity transverse components are also displayed.

3.2.2.

Evaluation of mixing efficiency

There are a number of approaches to characterize and evaluate the performance of mixing (Aubin et al., 2010; Kukukova et al., 2009; Alberini et al., 2014). In this work, a dye dilution based method was undertaken. Rhodamine B and deionized water (DI water) were employed as sample and buffer. They were pumped into central and side channels respectively by two syringe pumps (Model: LSP04-1A, LongerPump, China) through hoses connected to needles which were inserted in inlets. The images of mixing process were recorded and combined together because the field of view of the camera (UI-1465LE-C-BG, uEye, Germany) was not wide enough. The color intensity profile of recorded images was used to evaluate the mixing efficiency. A homogeneous profile represents a

perfect mixing. The mixing efficiency was quantitatively calculated by the standard deviation of color intensities along the cross section in the exit channel. First, the images were converted into gray scale. Second, to minimize the effect of the background noise, the intensity of each pixel was normalized by the Eq. (8) (Ansari et al., 2010):

Ini =

Ii − Ibg Idarkest − Ibg

(8)

where Ini is the normalized intensity value of each pixel; Ii is the intensity value of each pixel; Ibg and Idarkest are intensities of background and the darkest pixel along the cross section, respectively. The measured mixing efficiency M and standard

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Fig. 5 – (a) Mixing concentration profile in the C-SAR mixer; (b) concentration distributions of sample at cross-sections C1 –C7 (z = 0); (c) concentration of sample along the central line of the mixing channel (x = 0, z = 0). deviation  of the normalized intensities were calculated using Eqs. (9) and (10).

  N   1  Ini − ¯In 2 = N

i=1

¯In

M=1−

(9)

(10)

where ¯In is the average value of normalized intensity in the calculation area. Evaluation experiments were performed five times and the error bar was the standard deviation of five measurements.

4.

Results and discussion

4.1. Mixing mechanisms and efficiency of C-SAR micromixer Fig. 4(a) is the top view of streamlines in the first mixing unit; red represents sample and black is buffer. C-SAR introduces more lateral motions which transport sample toward outside of the channel to mix with buffer; meanwhile, corner vortices are generated by fluids passing through corners formed by triangular baffles and channel edge with high speed, which introduce transverse movements of fluids and promote mixing (Fig. 4(a)). The velocity field profile and trans-

Fig. 6 – Comparison of mixing efficiencies between C-SAR mixer and S-SAR mixer. verse components at four cross-sections 20 ␮m passing each triangular baffle in the first mixing unit at Re = 47.1 are shown in Fig. 4(b). The inset gives the relative position of velocity field and the mixer geometry. Fig. 4(c) shows transverse components and how they work on sample transportation. The flow-separation regions in Fig. 4(b) and (c) are created by corner vortices in Fig. 4(a). Besides, rotational movements generated in the cross-sectional plane, known as Dean’s vortices (Vanka et al., 2004), driving fluids from the midplane of the channel toward the outer channel wall are also displayed in Fig. 4(b)

Fig. 7 – The distribution of Rhodamine B in the C-SAR mixer at Reynolds number 47.1.

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center of channel. The concentration is decreased to 10% after fluids leave the mixing region. Mixing efficiencies at cross-section C6 are calculated using Eqs. (6) and (7) and shown in Fig. 6. Compared with S-SAR mixer with similar feature sizes, the mixing efficiency of CSAR is greatly improved. It keeps above 90% in a wide range of Reynolds numbers (34.6–150). The detail analysis of S-SAR is shown in Supplemental Files.

4.2.

Fig. 8 – Simulated and experimental mixing efficiencies of C-SAR mixer versus Reynolds number.

and (c). Therefore, opposing movements of fluids introduced by 3 mechanisms, C-SAR, corner vortices and Dean’s vortices, and their interactions, greatly enhance mixing at the boundary of sample and buffer (shown in Fig. 4(c)). The concentration distribution of sample in the whole channel is shown in Fig. 5(a). Fluids have been fully mixed after they leave the mixing region. The lateral concentration distributions at seven cross-sections are shown in Fig. 5(b). The intensities decrease while the full width at half maximum (FWHM) increase with fluids flowing, which shows the concentration distribution in the channel is more and more uniform. Fig. 5(c) shows the rapid decrease of the concentration at the

Experimental results

Mixing performance of the C-SAR mixer was tested by DI water diluting Rhodamine B and the whole mixing process is presented vividly in Fig. 7. Reynolds number corresponding to this experiment was 47.1. The two solutions started mixing at the intersection of three inlets due to hydrodynamic focusing. Then the sample solution was led to channel walls during cascaded splitting by triangular baffles and the increased transverse movements enhanced mixing. Meanwhile, vortices were created when fluids were passing through corners formed by the channel edge and triangle baffles and promoted mixing. The actual mixing efficiencies of the C-SAR mixer were calculated using Eqs. (9) and (10). The experimental results are perfectly consistent with the predicted values (Fig. 8). Mixing efficiencies keep above 90% from Re = 34.6 to Re = 150. Images of mixing effect at various Reynolds number are shown in Supplemental Files.

Fig. 9 – Mixing efficiency versus base angle of triangular baffles: (a) T1 ; (b) T2 .

Fig. 10 – Streamlines formed by different h1 values.

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Fig. 11 – (a) Mixing efficiency versus size of T3 ; (b) streamlines at different T3 size. Base lengths of T3 are 100, 150, 200, 250 ␮m respectively, from left to right.

4.3.

Sizes optimization

Triangular baffles T1 and T2 (Fig. 1) are used to split central inlet fluid and introduce transvers flow movement to increase mixing. Therefore, the size and arrangement of T1 and T2 will influence the mixing efficiency. It is reasonable that the sharper the base angles of triangular baffles, the more central fluid is transported outward to mix with fluids from side inlets and consequently increase the mixing efficiency (Wang et al., 2014). The mixing efficiency versus base angle of triangular baffles at Re = 47.1 is shown in Fig. 9. The distance between two baffles (h1 ) determines whether the cascaded splitting effect could happen. Fig. 10 shows that more and more central channel streamlines (red) are guided to the side by T2 with the distance continuously reducing (50–12.5 ␮m). The size of the feature in the channel wall (T3 ) has important impact on the mixing. On the one hand, the sharper the angle contributes more to introduce transverse flow movements; on the other hand, the sharper the angle (longer base of T3 in Fig. 11(a)) makes the smaller the space between channel wall and baffles, which leads to higher speed when fluid pass through the corners formed by triangular baffle and channel edge and generates stronger vortices. As a result, mass transport is boosted and mixing is greatly enhanced. The influence of the size of T3 on mixing effect is shown in Fig. 11. Although sharp base angles of features and small distance between triangular baffles benefits mixing efficiency, we choose sizes shown in Fig. 1, because small size and sharp angle are difficult to fabricate and 90% mixing efficiency is good enough.

5.

Conclusion

In conclusion, we developed a novel C-SAR micromixer and characterized its mixing performance. The mixer is made of PDMS with standard replica molding method. Because of the asymmetric arrangement of triangular baffles in the mixing region, the SAR is in cascade and the sample from the center channel is further transported to sides, which enhances effective mixing with buffer from side channels; meanwhile, vortices are created when high speed fluids flow through sharp bends formed by triangle or channel edge, which boosts mixing efficiency greatly. The C-SAR mixer can work in a wide range of Reynolds number (34.6–150) with mixing efficiency more than 90%; meanwhile, the concentration of sample is reduced to 10%, which meets the requirement of protein/DNA refolding kinetics study (Hertzog et al., 2004; Zhu et al., 2013;

Ansari et al., 2010). At Re = 135, the sample flow rate is 2 ␮L/s and corresponding mixing time is 1 ms; at Re = 189, the sample consumption is 3 ␮L/s and mixing time is reduced to 670 ␮s (SF, Table S1). Therefore, the C-SAR micromixer is an attractive analytical tool to study biomacromolecule dynamics because it is balanced for low sample consumption and fast mixing, and also easy to manufacture and implement.

Acknowledgements This work is supported by the National Natural Sciences Foundation of China (61378045, 61535003), the Natural Science Foundation of Jiangsu Province (BK20131297), and Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of the People’s Republic of China.

Appendix A. Supplementary data Supplementary data associated with cle can be found, in the online https://doi.org/10.1016/j.cherd.2018.01.032.

this artiversion, at

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