Microfluid Nanofluid DOI 10.1007/s10404-015-1610-4

RESEARCH PAPER

A labyrinth split and merge micromixer for bioanalytical applications Ioanna N. Kefala1 · Vasileios E. Papadopoulos1 · Georgia Karpou1 · George Kokkoris1 · George Papadakis1 · Angeliki Tserepi1 

Received: 7 January 2015 / Accepted: 4 June 2015 © Springer-Verlag Berlin Heidelberg 2015

Abstract  A planar split and merge (SAM) passive micromixer with labyrinthine microchannels is proposed to efficiently mix biomolecular solutions by combining several advantages of existing micromixer designs in one realization. First, to demonstrate the labyrinth-SAM micromixer advantages, it is compared with three passive micromixers of different geometries, i.e., a zigzag, a spiral, and a linear one, with respect to their mixing efficiency, by means of a computational study. The geometrical specifications are imposed from flexible printed circuit (FPC) technology which is used for their fabrication and the diffusion coefficient from the applications to be implemented, i.e., the mixing of biochemical reagents. The computations include the numerical solution of continuity, Navier–Stokes, and mass conservation equations in 3d. It is demonstrated that the labyrinth-SAM micromixer exhibits the highest mixing efficiency. Specifically, compared to a linear micromixer, which shows a mixing efficiency of 0.328, the spiral micromixer improves the mixing efficiency by 8 %, the zigzag by 11 %, and the SAM by 92 %; the diffusion coefficient of the biomolecules is 10−10 m2/s, the Reynolds number is 0.5, and the volume of each micromixer is 2.54 μl. Second, the proposed SAM micromixer is realized simply and inexpensively, with a small footprint, implementing FPC technology, commonly available in the production lines of printed circuit board manufacturers. Finally, its mixing efficiency is experimentally evaluated by means of fluorescence

* George Kokkoris [email protected] * Angeliki Tserepi [email protected] 1



Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, Athens, Greece

microscopy, while it is further validated for enzymatic digestion of DNA. The latter is achieved even within 30 s of sufficient mixing of DNA and enzyme solutions through the SAM. Despite the numerous works on micromixers, the labyrinth-SAM is a novel design of an efficient passive micromixer. The efficiency together with its simplicity, which is manifested by (a) the planar (and not complex three-dimensional) geometry, (b) the two-inlet, instead of multiple-inlet, configuration, (c) the small number of fabrication steps, and (d) the compatibility with mass production, makes the proposed micromixer a good candidate for integration in bioanalytical miniaturized platforms. Keywords  Micromixer · Split and merge · Split and recombine · Simulation · LoC · FPC technology

1 Introduction The vision of integrating several functions of a (bio)chemical analysis laboratory on a chip (lab-on-a-chip, LoC) drives the research, design, and development of microfluidic devices. Microfluidic devices are being developed to play an important role in sample manipulations, such as transport, mixing, separation, and/or reactions. These functions are necessary for the operation of LoC systems, the total performance of which depends on the efficient operation of its components. For instance, a well-designed micromixer can reduce the analysis time and the footprint of a LoC system (Ottino and Wiggins 2004). In particular, micromixers are important in LoC systems where efficient interaction between molecules, e.g., chemical reactions, is required. When designing micromixers, the objective is the rapid mixing between at least two liquid flows. Micromixers can be classified into two categories:

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active and passive ones (Lee et al. 2011; Mansur et al. 2008). Passive are the micromixers which do not require external energy (besides the energy required for the pumping of the fluid) as opposed to the active ones that use the disturbance generated by an external field for the mixing process. Even though the active micromixers are usually more effective than the passive ones (Alam and Kim 2012; Fu and Lin 2007; Mansur et al. 2008), they entail more complex and expensive fabrication processes, and their integration with other microcomponents is more tedious. In addition, active micromixers have higher cost for active control, and typically higher power consumption, compared to the passive ones. Furthermore, some active mixing mechanisms such as ultrasonic waves or high-temperature gradients can damage biological samples, making them unsuitable for the bioanalytical process to be performed (Capretto et al. 2011; Nguyen 2008). Due to the miniaturized dimensions of a micromixer, the flow is governed by low Reynolds number (Re): Turbulence is absent and hence the mixing process is induced by molecular diffusion and chaotic advection. A micromixer generates chaotic advection when advection occurs not only in the direction of the flow but in other directions as well (Capretto et al. 2011), increasing the interfacial area and decreasing the diffusion path. Several designs of passive micromixers have been proposed in the literature such as Y- or T-shaped and multiinlet channels with parallel or serial lamination (Gobby et al. 2001; Hessel et al. 2003). The multi-lamination approach increases the mixing efficiency by decreasing the diffusion path and increasing the interfacial area between the mixing streams. The introduction of gas or liquid bubbles into the flow (Song et al. 2003) or the use of hydrodynamically focused mixing streams (Knight et al. 1998) also improves mixing. Other designs focus on creating flow perturbation by barriers (posts) (Ali Asgar et al. 2007; Jeon and Shin 2009) or grooves (Afzal and Kim 2014; Kee and Gavriilidis 2008; Stroock et al. 2002) or by using channels with a suitably varying cross section (Fu et al. 2014; Wang et al. 2012), enhancing chaotic advection. A well-designed and one of the most studied chaotic micromixers is the herringbone micromixer (Stroock et al. 2002) which is composed of herringbone grooves on the floor of the microchannel. Alternative designs based on chaotic advection, such as designs with zigzag channels (Jeon and Shin 2009), helical flow patterns, expansion units (Sudarsan and Ugaz 2006), logarithmic spirals (Scherr et al. 2012), and split and merge (or recombine) geometries (Bhopte et al. 2010), or even complex 3d geometries (Vladimir and Mohammad 2013), have been also proposed. The motivation of this work is the design of a simple, planar, passive micromixer for bioanalytical applications, such as the enzymatic digestion of DNA. For a successful

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Microfluid Nanofluid

digestion, a sufficient/rapid mixing of the enzyme with the DNA is required. However, the enzymes, and generally the biomolecules, have very low diffusion coefficients, varying from 10−9 to 10−11 m2/s (Ottino and Wiggins 2004), which renders mixing very slow and the design of a rapid micromixer a challenging problem. In the present work, a passive labyrinth micromixer which is based on the principle of split and merge (SAM) or split and recombine (SAR) is proposed that combines several of the advantages of individual micromixer designs in one realization. More specifically, the SAM micromixers decrease the diffusion path and increase the contact area by splitting and rejoining the flow; the novel feature of the proposed micromixer is its labyrinthine geometry, which additionally induces a higher-concentration gradient and as a consequence a higher diffusive flux at the interfacial (contact) area, improving the mixing efficiency. Several aspects of the geometry and inlet velocity (or Re) are investigated, and the mixing efficiency of the labyrinth-SAM is compared through a computational study to that of three different commonly realized designs of passive micromixers, i.e., a zigzag, a spiral, and a linear micromixer. Concerning the fabrication technology, microfluidics has seen the development of new fabrication methods, which is an important aspect of the potential for commercialization of microfluidics. Very recently, commercially available, photosensitive dry films, such as TMMF (from TOK Ltd) or PA (from JSR), have revolutionized the massive fabrication of polymer microfluidics and LoC systems (Imec 2013; Wangler et al. 2011). In particular, dry-film photoresist laminates used with standard photolithography for the fabrication of microfluidic structures have excellent functional characteristics, can be laminated with processing speed much higher than for spin-coating processes, and show a potential for mass production of microfluidic devices and LoC. In this work, the proposed labyrinthSAM design is implemented with commercial dry-film photoresist (from DuPont), routinely used as a coverlay to encapsulate circuitry in flexible printed circuit (FPC) technology. The proposed technology allows the integration of microfluidic devices with heterogeneous components: electronic circuits, sensors, and microheaters (Moschou et al. 2013) that can be utilized for on-chip detection and control in a cost-effective manner, following the current trend in LoC technology (Aracil et al. 2015; Kim et al. 2011; Wu et al. 2010). To the best of our knowledge, the use of this dry-film resist proposed by our team (Papadopoulos et al. 2014) and implemented in this work as structural material of microfluidic devices is very rare in the literature. Finally, the performance of the labyrinth-SAM is evaluated for mixing of fluorescein with water by means of fluorescence microscopy. In addition, the realized mixer

Microfluid Nanofluid

is implemented for enzymatic digestion of DNA, requiring sufficient mixing of DNA fragments with restriction enzymes. The rest of the paper is structured as follows: In Sect. 2, the mathematical model is presented. In Sects. 3 and 4, the designs and simulation results are described, respectively. In Sect. 5, the fabrication process is described and realized devices are shown. The experimental evaluation of the micromixer by means of fluorescence microscopy and its validation for enzymatic digestion of DNA is described in Sect. 6. The last section includes the conclusions.

2 Mathematical model All studied micromixers consist of a channel with two inlets and one outlet. The solvent is fed to one inlet and the solution to the other. The mathematical model describes the fluid flow and the diffusion of species in the channel. It consists of the continuity equation (1)

∇ ·u=0 and the Navier–Stokes equation

ρu · ∇u = −∇p + µ∇ 2 u

(2)

where u is the vector of fluid velocity, ρ, μ, and p, are the density, dynamic viscosity, and pressure of the fluid, respectively. The model includes also the mass conservation equation of the solute (e.g., the enzyme in a DNA digestion process)

∇ · (−D∇C) + u · ∇C = 0

(3)

where C and D are the concentration and diffusion coefficient of the solute in the solution. No slip condition for the velocity and zero derivatives for the concentration are considered at the walls of the micromixer. Fully developed parabolic profiles of the velocity are considered at the inlets, whereas zero derivatives of both velocity and concentration in the outflow direction are considered at the outlet. The density and the dynamic viscosity of the solution are those of water at 20 °C. The equations are solved in 3d by the finite volume method with ANSYS Fluent (ANSYS, Inc., Canonsburg, PA). The performance of the micromixer is evaluated by the mixing efficiency, n (Nguyen 2008), at a vertical-to-flow cross section   2 N  1  Ci − C¯  n=1− (4) N C¯ i=1

C¯ is the expected concentration of the solute at full mixing and Ci is the local concentration at point i of the cross section. N is the number of points in the cross section. Essentially, the points are the nodes of the mesh at the cross section.

3 The proposed design and conditions of the numerical evaluation The design of the proposed labyrinth-SAM micromixer is shown in Fig. 1a. It consists of concentric rings where the flow splits and merges while moving from the outer channels to the inner ones. The specifications regarding the channel dimensions stem from the fabrication technology (see Sect. 5). The height of the channel is 60 μm, equal to the thickness of the photo-imageable dry film (Papadopoulos et al. 2014) where the channel will be formed. The minimum width of the channels is 150 μm, appropriate for a reproducible lithographic result. The labyrinth-SAM micromixer has two inlets with channel width equal to 150  μm, merging in a 300-μm-wide main channel, and a total volume of 2.54 μl. The labyrinth-SAM micromixer efficiency is evaluated through a computational study and compared to that of three micromixers of the same volume: The first one (Fig. 1b) is a composition of two spirals with two turns joined at the center of the micromixer with two mirrored semicircles (Schönfeld and Hardt 2004). The second one (Fig. 1c) is a zigzag geometry with a 60° angle (Jeon and Shin 2009). The third micromixer is a linear one (Fig. 1d). The curved channel of the spiral micromixer (Fig. 1b) develops a flow interfacial stretching and a secondary flow due to the action of centrifugal forces (Schönfeld and Hardt 2004). The flow stretching is actually a shift of the maximum in the velocity profile toward the outer channel wall, whereas the secondary flow refers to the Dean vortices that can be quantified by the Dean number  Dh K = Re (5) Rc where Dh is the characteristic channel dimension, and Rc is the radius of curvature. Κ increases as Re and/or the characteristic channel dimension increases and/or as Rc decreases. There is a critical value for K equal to 140–150; above this value, Dean vortices become more effective improving further the mixing (Jiang et al. 2004). The zigzag geometry (Fig. 1c) creates, along with Dean vortices, continuous sudden changes of the flow direction, thus improving the mixing. In the labyrinth-SAM design (Fig.  1a), the flow stretching and the secondary flow are combined with splitting and merging of the flow, targeting more efficient mixing. All four micromixers are compared under the same flow conditions, i.e., the same volumetric flow rates. It is pointed out that all micromixers have the same volume, the same channel depth, and the same main channel width, therefore

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Fig. 1  Computer-aided design (CAD) of the micromixer with a lab- ▸ yrinth-SAM geometry, b spiral geometry, c zigzag geometry (only a part is shown, the total footprint length is 87.7 mm), and d linear geometry (only a small part of the straight channel is shown; the total length is 140.7 mm). The numbers in a show the regions where the fluorescence images are taken during the experimental evaluation of the labyrinth-SAM (cf. Sect. 6.1; Fig. 12)

the same total arclength along the channel axis (~140 mm, equal to the total length of the linear channel). The diffusion coefficient of the solute (biomolecules) is considered equal to 10−10 m2/s.

4 Simulation results and discussion For the numerical solution, meshes with hexahedral elements are built for all geometries. For mesh-independent solutions, approximately 25 millions of elements are required for the spiral, the zigzag, and labyrinth-SAM micromixers, and almost 16 millions of elements are required for the linear micromixer. The procedure for the mesh independency of the solution involves the continuous doubling of the elements, until the solution (velocity and concentration) shows small difference from the previous one; in particular, the densification of the mesh stopped when the difference of the mixing efficiency between successive solutions was less than 2.5 %. Figure 2 shows the concentration contours at the middle height of the microchannel of the four micromixers for a volumetric flow rate of 2.7 μl/min at each inlet, i.e., a total rate of 5.4 μl/min at the outlet (Re = 0.5). Τhe calculated mixing efficiencies at the outlet cross section of the micromixers are shown in Fig. 3: It is 0.630 for the labyrinthSAM, 0.365 for the zigzag, and 0.355 for the spiral. The labyrinth-SAM micromixer provides significantly higher mixing efficiency than the other two designs. Compared to the linear micromixer, the spiral improves mixing by 8 %, the zigzag by 11 %, and the labyrinth-SAM by 92 %. The time required for the mixing efficiencies of Fig. 3 is the ratio of volume over the volumetric flow rate, i.e., 2.54/5.4 min or ca. 28 s. Three potential mechanisms can account for the improved mixing efficiency of the labyrinth-SAM micromixer: the formation of Dean vortices due to the curved channels, the decrease in the mixing length by splitting the flow-stream, and the induction of a high-concentration gradient at the merging junctions [see areas (A)–(D) in Fig. 2a], creating gradually a lamination type flow. Regarding the last one, the geometry of the labyrinth-SAM induces a greater concentration gradient at the junctions compared to the normal split and merge case. In order to

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◂Fig. 2  Concentration contours at the middle microchannel height of

four micromixers: a labyrinth-SAM, b spiral, c zigzag, and d linear. Regions (A)–(D) in a are the merging areas from the second (the first is out of the labyrinth) to the last junction, respectively; the concentration profiles at these regions are shown in Fig. 5

demonstrate this, the labyrinth-SAM micromixer is compared with a similar SAM micromixer with linear channels (linear-SAM, see Fig. 4). The linear-SAM has the same volume with the labyrinth-SAM, and the distances between the splits and merges are the same as in the labyrinth-SAM. The linear-SAM splits and merges the flow without creating high-concentration gradients as the labyrinth-SAM does. This is demonstrated in Fig. 5a, b, where the concentration contours at the middle microchannel height of the two micromixers are shown. The concentration profiles along the line normal to the flow at the four merging junctions are shown in Fig. 5c. It is seen that in all four merging areas, higher-concentration gradients occur for the labyrinth-SAM, a feature which enhances mixing. Figure  5b, c also shows the formation of extra, compared to the linear-SAM, concentration gradients normal to the flow direction; essentially, a type of lamination occurs, while in linear-SAM the concentration profiles follow a monotonic behavior. The calculation results show that the linear-SAM provides significantly lower mixing efficiency (0.308), even lower than the linear micromixer (see Fig. 3). This is justified, given that the curved parts of the linear-SAM do not induce Dean vortices (K is from 1.89 to 3.95): In addition, the linear micromixer allows for more contact time between the two flow-streams compared to the linear-SAM. In order to increase K and improve the mixing efficiency of the linear-SAM, a higher flow velocity is required. The results of Fig. 3 also show that the mixing efficiency of the spiral and zigzag micromixers are close to that of the linear micromixer. The reason for the smaller than expected increase in the mixing efficiency is again the low K values

Fig. 3  Comparison of micromixers in terms of their mixing efficiency [Eq. (4)] at the outlet (diffusion coefficient of the biomolecule is 10−10 m2/s, Re is 0.5)

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(A)

(B)

(C)

(D)

Fig. 4  CAD design of the linear-SAM micromixer. (A), (B), (C), and (D) indicate the four merging areas of the linear-SAM micromixer

Merging area A

Merging area B

Merging area C

Merging area D

(a) Fig. 5  Concentration contours at the four merging areas [(A)–(D)] at the middle microchannel height of a the labyrinth-SAM and b the linear-SAM micromixer. c The concentration profiles along the line normal to the flow at the four merging junctions: the labyrinth-SAM creates higher-concentration gradients at each merging junction com-

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(b)

(c)

pared to the linear-SAM. It also creates extra concentration gradients normal to the flow direction. At each position along the lines, twentytwo concentration values are shown corresponding to equidistant heights from the bottom of the microfluidic channel; the concentration profiles are almost independent from the height

Microfluid Nanofluid

ranging from 0.06 to 0.23 (Schönfeld and Hardt 2004). Indeed, an increase in the flow velocity, e.g., by increasing the volumetric flow rate (see Sect. 4.2), and/or an increase in Dh, e.g., by increasing the depth of the channel (this would require the use of a thicker film for the fabrication of the channel), would increase K and hence the mixing efficiency of all micromixers. In this case, the % difference in the mixing efficiency between the linear and the zigzag (or spiral) micromixers is expected to be greater than the calculated 8 % (see Sect. 4.2).

While keeping the volume of the labyrinth-SAM and the volumetric flow rate constant, further improvement in the mixing efficiency can be achieved if the width of the channels is decreased; to maintain the same volume and volumetric flow rate, the depth of the channels should be increased by the same factor. The decrease in the channel width will decrease the diffusion path, and the increase in the channel depth will increase the interfacial area between the mixing streams, thus enhancing the mixing performance of the micromixer.

4.1 Modifications of the labyrinth‑SAM design for further improvement of the mixing efficiency

4.2 The effect of Re on the mixing efficiency

For improving the mixing efficiency of the labyrinthSAM geometry, several modifications are explored (Fig.  6). The first modification (Fig. 6a) increases the length and time that the two-inlet flow-streams travel in contact before the first split. The aim is to utilize the high initial concentration gradient at the contact area of the flow-streams before splitting. The labyrinth-SAM micromixer with a longer channel length (longer labyrinth-SAM) before the first split is shown in Fig. 6a. Calculations show a slight increase (~3.7 %) in the mixing efficiency from 0.630 to 0.653. However, increasing the length before the first split increases the total volume of the micromixer by 0.74 μl. The mixing efficiency becomes equal to 0.505, i.e., lower compared to that of the basic design of the labyrinth-SAM micromixer, when it is reduced to the volume of 2.54 μl (volume of the basic design). The aim of the second modification (Fig. 6b) is to utilize the high initial concentration gradient of two flow-streams: It decreases the length and time that the two-inlet flowstreams travel separately before the first junction. Essentially, the difference with the basic design of the labyrinthSAM (see Fig. 1a) is the position of the inlets: The inlets are in the center of the labyrinth, and the flow is reversed. The calculations show that the labyrinth-SAM with reversed flow (reverse labyrinth-SAM) exhibits a slightly (~2.5 %) higher mixing efficiency (0.645) compared to the basic design of the labyrinth-SAM. The total volume of the micromixer remains the same. The aim of the third modification (Fig. 6c) is the same as of the previous two. In this case, the aim is achieved by non-symmetric splitting of the flow-stream: The widths of the channels after the split are not equal to each other (i.e., 150 μm); the width of the first is double compared to the second (i.e., 200 and 100 μm). However, the main channel is still 300 μm, and the total volume is the same as in the basic design. The calculations show that the mixing efficiency for the non-symmetric labyrinth-SAM micromixer is 0.704, i.e., 11.9 % higher compared to the basic design.

Up to this point, the comparison of the micromixer designs was made under the same flow conditions corresponding to a low Re (0.5). Even though the experimental conditions at which the labyrinth-SAM will operate support this very low Re, Re in a much wider regime (up to 160) is chosen for comparing the designs (Fig. 7). Re increases by increasing the velocity at the inlets from 0.005 m/s (Re = 0.5) to 1.6 m/s (Re  = 160). By increasing Re, two competitive phenomena regarding mixing take place: The time that the flow-streams are in contact decreases and K increases. The first reduces while the second enhances the mixing efficiency. The calculations show that the mixing efficiency first decreases up to a minimum and then increases with Re for both the labyrinth-SAM (Fig. 1a) and the reverse labyrinthSAM (Fig. 6b). This critical value for Re is equal to 80 for the labyrinth-SAM and equal to 60 for the reverse labyrinth-SAM. At this critical value, the effect of Dean vortices dominates over the decrease in the contact time. The zigzag micromixer performs much better than the other three designs at middle and high Re, while the spiral micromixer gives very low mixing efficiency even at high Re. The mixing efficiency of the spiral micromixer increases at high Re, but it is not sufficiently effective due to its small curvature which leads to low K values. 4.3 Proposed design It is clear from the above analysis that the labyrinth-SAM operates better than alternative designs (linear, zigzag, and spiral designs) with the same volume and under the same operating conditions, corresponding to a very low Re (0.5). At higher Re, the zigzag design is favorable due to the enhancement of the secondary flow. However, given that the operating conditions of the application of interest are in the very low Re regime, the labyrinth-SAM design is proposed. Modifications in the labyrinth-SAM geometry affect slightly the mixing efficiency; the only remarkable improvement (by ~10 %) is observed for the nonsymmetric labyrinth-SAM (Fig. 6c). However in that case,

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Microfluid Nanofluid

◂Fig. 6  CAD design of the SAM-labyrinth micromixer with a the

extended entrance length, b the inlets positioned at the center of the micromixer, and c asymmetric splits. d The mixing efficiency of the basic design of labyrinth-SAM and its modifications shown in a, b, and c

(a)

(b)

the minimum width of the channel is 100 μm, marginally below the resolution capability of the photosensitive dry resist implemented for the micromixer fabrication. In addition, reduction in the channel width renders the channel susceptible to clogging by impurities. Furthermore, as noted above, for the results presented in Sect. 4, the diffusion coefficient of the solute was 10−10 m2/s, i.e., a typical value for biomolecules. In case that the diffusion coefficient of the biomolecule is greater (or lower) than that, the mixing efficiency for all micromixers will increase (or decrease). The mixing efficiency for a labyrinth-SAM of volume of 2.54 μl is 0.630 (in ~28 s). For more efficient mixing, sequential joining of 2 units of the basic design or the addition of 2 more external circles in the labyrinth is proposed; the mixing efficiency of the former configuration is 0.87 (in ~56 s) and that of the latter is 0.82 (in ~60 s). Alternatively, by decreasing the flow velocity, the mixing efficiency will be improved; for flow velocity equal to 0.002 or 0.001 m/s, the mixing efficiency is 0.80 (in ~70 s) or 0.90 (in ~140 s), respectively. A final note can be made here; although the proposed labyrinth-SAM performs much better than similar easy-tofabricate micromixers, it is inferior compared to the wellknown herringbone micromixer. Specifically, a herringbone micromixer compatible with our technology and fabrication materials (minimum dimension is equal to 150 μm) and with a total volume of 0.50 μl performs similarly to the labyrinth-SAM with a volume of 2.54 μl. However, its fabrication would be more complicated, involving an additional lithographic step for the formation of the herringbone patterns on the microchannel bottom.

(c)

(d)

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Fig. 7  Mixing efficiency versus Reynolds number for labyrinthSAM, reverse labyrinth-SAM, spiral, zigzag, and linear micromixers

Microfluid Nanofluid

5 Micromixer fabrication A commercially available printed circuit board (PCB) substrate and a photo-imageable polyimide(PI)-based dry film (Dupont™, Pyralux® PC1000 series) are used for the fabrication of the microchannel. These materials are chosen for their excellent functional characteristics, their compatibility with mass production, and their capability to easily form integrated devices. The DuPont™ Pyralux® PC is routinely used in the FPC industry as a coverlay to protect circuitry. Its implementation as a structural material for microfluidics

Fig. 10  Micromixer with the custom-made chip holder enabling fluidic interfacing

Fig. 8  Process flow for the fabrication of the labyrinth-SAM micromixer

has been proposed recently by our group (Papadopoulos et al. 2014). The process flow for the micromixer fabrication is shown in Fig. 8. The fabrication starts with lamination of the Pyralux® PC1000 on the PCB substrate (after removal of the copper layer, not useful in this work), using a roll laminator operating at 85 °C and medium pressure. Subsequently, the substrate is pre-baked at 120 °C, UV-exposed, and developed in a 1 % w/w aqueous sodium bicarbonate solution (Na2CO3), so as to form the microfluidic network. Then, the substrate is hard-baked at 160 °C for 2 h in an oven. To allow injection of fluid samples, holes are drilled at the microchannel inlet and outlet. Finally, the microfluidic network is sealed through lamination with polyolefin film (StarSeal Advanced Polyolefin Film, STARLAB International GmbH) at 70 °C to form enclosed microchannels; the polyolefin film is suitable for optical detection, due to its high transparency and low auto-fluorescence. An image of the fabricated labyrinth-SAM micromixer is shown in Fig. 9.

6 Experimental evaluation of the micromixer 6.1 Mixing of fluorescein with water in the micromixer

Fig. 9  Fabricated labyrinth-SAM micromixer

The labyrinth-SAM micromixer is experimentally evaluated first by means of fluorescence microscopy. A fluorescence microscope (Axioscope 2 Plus epifluorescence microscope by Carl Zeiss, Germany) equipped with a Micropublisher 3.3 RTV (Qimaging) digital camera is used. The objective is 10×/0.3. The two solutions used to evaluate the efficiency of the micromixer are distilled water (dH2O) and an aqueous solution of 3 × 10−5 M fluorescein. The diffusion coefficient

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◂ Fig. 11  Fluorescence images at different junctions of the labyrinth-

SAM micromixer: a first junction, b A (in Fig. 2a), c B (in Fig. 2a) and d C (in Fig. 2a), as well as at e the last merge (D in Fig. 2a). The normalized fluorescence intensity values (void circles) along the lines drawn in Fig. 11a–e are shown in Fig. 11f–j, together with the simulation results (cross filled circles) along the same lines; the diffusion coefficient is 4.9 × 10−10 m2/s. The simulation results refer to concentration profiles at twenty-two equidistant heights from the bottom of the microfluidic channel; the concentration profiles are almost independent from the height

of fluorescein in water is 4.9 × 10−10 m2/s (Ying Li et al. 2012), i.e., in the range of values for biomolecules. To perform the evaluation tests, fluidic interfacing is necessary. In particular, a custom-made, plexiglass chip holder fabricated in-house to be compatible with commercially available Upchurch® Nanoport fittings is used (Fig. 10). The two solutions are injected in the inlets with a volumetric flow rate of 2.7 μl/min each, by means of a syringe pump (Chemyx Inc, Fusion 200). A band-pass excitation filter at 485 nm and a band-pass emission filter at 534 nm are used for the visualization. The software used for the image capture is ImagePro Plus (Media Cybernetics, Inc., USA). During injection of aqueous solution of fluorescein and distilled water, a first set of fluorescence images at the four junctions of the labyrinth [see noted regions (A)–(D) in Fig. 2a] as well as at the first junction of the two inlets were taken and are shown in Fig. 11a–e. The values of fluorescence intensity along the lines shown in Fig. 11a–e were extracted using ImagePro Plus. The points exactly at the walls where the fluorescence intensity is high were not included in the lines. Subsequently, during injection of distilled water (dH2O) in both inlets, a second set of images were taken at the same regions. The values of fluorescence intensity were extracted along the same lines as for the first set and were considered as background noise. Therefore, they were subtracted from the corresponding values of the first set. After removing the background noise, the values were calibrated using the intensity values from the image of the first junction of the two inlets, where there was no mixing yet, and then normalized in the interval [0, 1]. The normalized fluorescence intensity values along the lines shown in Fig. 11a–e are depicted in Fig. 11f–j. In the latter, simulation results along the same lines are shown. The diffusion coefficient in this case is that of fluorescein, i.e., 4.9 × 10−10 m2/s, and not 10−10 m2/s as in the results presented in Sect. 4. Despite the noise in the experiments, the fluorescence measurements are in good agreement with the simulation results at the merging areas of the labyrinth-SAM. The mixing efficiency [Eq. (4)] of several cross sections (see points 0–11 of Fig. 1a) along the channel axis was also calculated using the normalized fluorescence intensity values. The last cross section corresponds

Fig. 12  Mixing efficiency from experimental data and computational results at several points along the labyrinth-SAM micromixer. The numbers on x axis correspond to the positions defined in Fig. 1a

to the outlet of the micromixer. Figure 12 shows the mixing efficiency at these cross sections compared with the corresponding computational results. 6.2 Enzymatic digestion of DNA in the micromixer In addition to mixing of fluorescein with water, the evaluation of the micromixer is also based on its performance for digestion of a PCR product with a restriction endonuclease (enzyme). A 635-bp DNA was produced by PCR using bacterial genomic DNA (Salmonella enterica) and the following primers: (1) 5′-GACACCTCAAAAGCAGCGT-3′ and (2) 5′-AGACGGCGATACCCAGCGG-3′. The 635-bp DNA can be digested with the restriction endonuclease DdeI into two fragments of 342 and 293 bp, respectively. It should be noted that it is necessary to include, within the DNA and enzyme solutions, 1.5 % PEG 8000 and 2 mg/ ml BSA, to prevent sample loss on the microchannel walls due to the high surface-to-volume ratio of the microdevice (Yang et al. 2002). Our purpose is to evaluate the capability of the labyrinth-SAM micromixer to effectively mix a PCR product with a restriction endonuclease solution at room temperature that would lead to digestion of DNA and to compare its performance with that of a linear micromixer. Initially, a fraction of a PCR reaction containing an amplified 635 bp product is loaded on the micromixer from the first inlet and the enzyme solution from the second inlet, and both are driven through the SAM micromixer using a peristaltic pump. The flow rate along the main channel of the micromixer is 10 μl/min. Five microliters of DNA–enzyme mix is collected from the exit within 30 s, and it is placed on ice and then is immediately loaded on a gel for estimation of the degree of digestion. The gel analysis reveals partial digestion of the DNA with a ratio of cut/uncut DNA equal to 0.72 or 1.8 times higher than the ratio obtained without the micromixer (Fig. 13a, b). This result indicates sufficient mixing of the reagents ensuring rapid DNA digestion at room temperature within the microdevice.

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Microfluid Nanofluid

Fig. 13  Gel images of a partially digested 635 bp DNA fragment after 30-s incubation without mixing in an Eppendorf tube and b after passing through the micromixer for 30 s. c Undigested (lane 2) and partially digested (lanes 3 and 4) 635 bp fragment in a linear (lane 3) and a labyrinth-SAM (lane 4) micromixer. The mixing and digestion (without incubation) are performed at room temperature. In the first lane of all three images, a DNA ladder is shown

In a second experiment, 20 μl of DNA–enzyme mix are collected from the exit of the labyrinth-SAM and the linear micromixer within 2.5 min, and they are placed on ice and then immediately loaded on a gel. The gel analysis (Fig. 13c) reveals partial digestion of the DNA with a ratio of cut/uncut DNA equal to 2.13 and 1.03, for the labyrinth-SAM and linear micromixers, respectively. This result indicates a 2.09 times higher mixing efficiency for the labyrinth-SAM compared to the linear micromixer, in agreement with the simulation results (Fig. 3). Although, as discussed in Sect. 4.3, a double labyrinth-SAM or a smaller flow velocity would be required for complete on-chip DNA digestion, this result validates the model and shows that the developed micromixer is indispensable as a simple, small footprint component of LoC systems for diagnostic purposes.

7 Conclusions Aiming at the design and realization of an efficient, passive planar micromixer with simple and cost-efficient fabrication process for biochemical applications, a zigzag, a spiral, and a SAM micromixer with labyrinthine microchannel are compared through numerical calculations. The comparison is performed under the same conditions, while the geometrical specifications of the micromixer are imposed by the FPC technology which is used for the micromixer fabrication. For a diffusion coefficient equal to 10−10 m2/s (typical for biomolecules), for Re equal to 0.5, and for a total volume of 2.54 μl, the labyrinth-SAM outperforms the rest; its mixing efficiency is 0.630, whereas it is 0.365 and 0.355 for the zigzag and the spiral micromixers, respectively. The

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mixing performance of the labyrinth-SAM micromixer is enhanced by the greater concentration gradient at the junctions (merging areas) compared to the linear-SAM case. Due to the low Reynolds number (0.5), the Dean number is low for the zigzag and spiral geometries. As a consequence, their mixing efficiency is close to that of the linear micromixer. The proposed labyrinth-SAM micromixer is realized with FPC technology on a PCB substrate: The channels of the micromixer are formed on photo-imageable PI-based dry film. It is amenable to mass production and can be used in microanalytical platforms easily integrated with other microfluidic devices and sensors. The labyrinth-SAM micromixer is experimentally evaluated by means of fluorescence microscopy. In particular, mixing of distilled water and an aqueous solution of fluorescein is performed in the micromixer. The fluorescence intensity measurements compare well with the simulation results and validate the model. In addition, the labyrinthSAM micromixer is implemented for DNA digestion at room temperature after mixing of reagents through the micromixer. DNA digestion is demonstrated even after 30 s which manifests sufficient mixing in the labyrinth-SAM micromixer. The superiority of the latter over other micromixer designs of the same volume is clearly demonstrated, in agreement with simulation results, for accelerating a bioanalytical process, without compromising ease and simplicity of fabrication. Finally, although there are a lot of publications on micromixers in the literature, the labyrinth-SAM is a novel design of an efficient and simple passive micromixer, an advantageous candidate for integration in bioanalytical miniaturized platforms. Its simplicity is based on (a) planar (and not complex three-dimensional) geometry, (b)

Microfluid Nanofluid

two-inlet, instead of multiple-inlet, configuration, (c) small number of fabrication steps, and (d) its compatibility with mass production, which makes the micromixer a cost-efficient one. Acknowledgments  This work was partly supported by the GSRT projects “SYNERGASIA 2011-Converging Lamb wave sensors with microtechnologies towards an integrated Lab-on-chip for clinical diagnostics-LambSense” (11Syn_5_502) and “DoW-DNA on waves: an integrated diagnostic system” (LS7-276, program “Supporting post-doctoral researchers,” Ministry of Education, Lifelong Learning, and Religious Affairs); the source of funding is the European Social Fund (ESF)—European Union and National Resources. The fluorescence experiments were performed at the Immunoassays and Immunosensors Laboratory of the Institute of Nuclear and Radiological Sciences and Technology, Energy and Safety of NCSR “Demokritos”; the authors would like to thank Drs. P. S. Petrou and S. E. Kakabakos for their guidance on fluorescence measurements. The enzymatic digestion experiments were performed at the Biosensors Laboratory of the Dept. of Biology, Univ. Crete and IMBB-FORTH, Crete, and the authors are thankful to Prof. E. Gizeli for that. In addition, the authors would like to thank Dr. D. Moschou for useful discussions and Dr. D. Papageorgiou for his help on the fabrication of the chip holder.

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