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Electrophoresis 2015, 36, 405–412
Robert Goovaerts Tom Van Assche Marc Sonck Joeri Denayer Gert Desmet Department of Chemical Engineering, Vrije Universiteit Brussel, Brussels, Belgium
Received July 1, 2014 Revised August 18, 2014 Accepted August 18, 2014
Research Article
A micromixer with consistent mixing performance for a wide range of flow rates A micromixer with consistent mixing performance for a wide range of flow rates is presented. The mixer makes use of internally moving elements, i.e. steel balls that are located in dedicated mixing chambers. Movement is induced by a rotating magnetic field. To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. A mixing performance study for a range of flow rates along with pressure drop data is presented. The response of the moving elements in regard to the magnetic field is shown experimentally and shows the limitations of earlier modeling studies. Lastly, the estimated power input on the fluids was calculated and allows for a comparison with more well-known convective-type mixers. Keywords: Active mixing / Magnetic / Mixing performance / Passive mixing / Power dissipation DOI 10.1002/elps.201400314
1 Introduction Micromixers have been studied for over a decade. Numerous inventive designs have been made and several review papers have been written on the topic [1–4]. In general, two general classes of mixer types are proposed: passive and active micromixers. In passive mixers, the sole power input comes from the flow-generating pump. By smart design of the internal structure of the mixer, mixing performance can be dramatically enhanced. Passive mixers are typically operated under a certain flow rate range, since the behavior of the flow is dependent on both the internal mixer structure and the flow regime. Some mixers have been designed to work optimally at high internal velocities [5], whereas others are best operated at a lower flow rate regime [6–8]. Active mixers typically have multiple inputs to generate time-based changes in the flow profile which enhance mixing performance and as such have more variability in operating conditions. An interesting and well-studied principle is one where the flow is restructured initially so that axial dispersion, which is much more efficient than diffusion, is effectively generated [9–15]. This method offers good mixer performance, but the injection strategy is critical for the mixer performance and dependant on the flow rate. For high flow rates, the response time of the pumps may prove critical and thus lower the optimized injection profile which leads to lower mixing performance. An alternative strategy to restructure the flow is the introduction of an active element inside the mixing channel. To have some control of the stirring performance, outside control of this active element by magnetism is a viable strategy. Some numerical studies have
Correspondence: Robert Goovaerts, Pleinlaan 2, 1050 Elsene, Belgium E-mail: [email protected]
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been undertaken [16–18] and proved the effectiveness of this strategy. The active element (microstirrer) can be fixed to the channel [19], fixed in a chamber [20], or used as a suspension of magnetic particles [21]. Studies with small magnetic particles have been well covered. Electrofluids proved very effective in mixing [22, 23]. In-depth studies of the flow phenomena when these magnetic beads form chains have been investigated recently [24, 25] and the drag forces on the chain formation have been studied. To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. The mixer is composed of a series of mixing chambers, each filled (or not) with a (rotating) ball that can either move freely under the forces of the flow; or that can be rotated under the influence of an externally controlled applied magnetic field. It was preferred to work with a 1-mm-sized element so that sedimentation, which is an important problem with micron sized particles, has no meaningful effect. The study is also meant to investigate the effect of the flow rate on the response of the element to the external control, which has to our knowledge not been studied before. Lastly, the added cost for improving the passive mixer design is discussed by estimating the power dissipation generated in the mixer setup.
2 Materials and methods 2.1 Mixer design and setup As chip material, PMMA was chosen for a number of reasons: it is suited for mechanical operations, e.g. milling. The material can be bonded thermally and hence large head-loss
Colour Online: See the article online to view Fig. 6 in colour.
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Figure 1. The design of the micromixer.
resistant chips can be made which allow the user to work under a broad operating range (unlike PDMS). The material also is UV-VIS transparent, which allows for optical study of the flows. The microchip is composed of a bottom section with milled features and a top section that serves as lid. Prior to thermal bonding, steel balls were placed into the mixing chambers (one ball per chamber). Next, the lid section was clamped onto the bottom section and the assembly was placed into an oven during 30 (155°C) to allow for thermal bonding. Two inlet channels are joined in a Y-type entry section which leads to the mixing channel. This channel consists of a set of chambers that are interconnected by a single, straight channel with 500 m sides (length 1.5 mm between the chambers). The mixing chambers are designed as cylinders with a height and width of 1.5 mm. Inside these chambers, a steel ball with a diameter of 1 mm is placed (Fig. 1). The structures are produced in PMMA (Eriks-Baudouin, Hoboken, Belgium) by milling (CNC milling engraving machine, Datron, NH, USA). Leftover debris was removed by pressurized air prior to thermal bonding (155°C, 30 min). The mixer was placed between a magnetic stirrer (Cimarec 2, Barnstead Thermolyne, NH, USA) and an inverted microscope (see next section for a description of the fluorescence setup). To generate a stronger magnetic field by increasing the proximity, the lid of the magnetic stirrer was removed prior to placing it upside down on the mixer.
2.2 Fluorescence study The mixing performance was evaluated by dilution experiments. A FITC solution (10−5 M, Sigma-Aldrich, Bornem, Belgium) was prepared by dissolution in ultrapure water (Synergy UV Water Purification System, Millipore, MA, USA). Two syringe pumps (260D Syringe Pump, Teledyne ISCO, NE, USA) were connected to the mixer by fused silica capillaries (ID 182 m, OD 354 m, Polymicro Technologies, AZ, USA), which were placed into dedicated milled grooves and subsequently glued with a UV-curable glue (OrmoCore, microresist technology, Berlin, Germany). FITC and water were fed at equal flow rates to the mixer and entered the mixing channel via the Y-shaped entry section. For the detection of the fluorescence profile, an inverted microscope C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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(IX71, Olympus, Belgium) was used, equipped with a wide green filter cube set. Illumination with an Hg-vapor lamp (U-LH100HGAPO, Olympus) allowed for excitation at 505 nm and for emission around 515 nm. The mixing progress was visualized using an air-cooled CCD fluorescence camera (ORCA-ERC4742, Hamamatsu Photonics, Massy, France) mounted on the video adapter of the microscope. The video images were taken downstream each mixing chamber over the entire width of the channel and subsequently analyzed with the accompanying simple-PCI 5.1 software. The acquired fluorescence values (Xij ) (which are measures for the concentration of FITC) were averaged out (Xsignal ) to correct for local fluctuations of the fluorescence. To correct for background fluorescence contributions (due to channel roughness), the background fluorescence Xbackground was subtracted from Xsignal . The background fluorescence value for a given position did not change during experiments, indicating low to no deposition of the dye due to flushing steps (with ultrapure water) between experiments. Taking this background value into account, the average of the fluorescence values could be subsequently calculated, Eq. (1). To represent the mixing progress over the entire channel in a compact way, the standard deviation of the fluorescence values (Eq. (2)) was calculated and normalized between a value of 0 and 1 by dividing the actual standard deviation by the standard deviation at the inlet (nonmixed). This value was then subtracted from Eq. (1). This normalized value, from here on referred to as mixing quality ␣, Eq. (3), was used to display the mixing progress after each mixing chamber: n
=
=
(X signal − X background )
i=1
(1)
n n
2 X signal − X background − i=1
␣=1−
n . max
(2)
(3)
2.3 Pressure measurement study The syringe pumps provided a pressure readout (10 kPa precision), which allowed to measure the pressure losses over the setup for the whole flow rate range (0.01–10 mL/min). The pressure losses for the connections were measured separately to estimate the contribution of the mixer more accurately. The pressure losses were measured both in absence of the steel balls as well as in presence of the steel ball for varying rotation intensities (including no rotation). www.electrophoresis-journal.com
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Figure 2. (A) The concept of the low mixing performance zone as typically presented. (B) The separate contribution of mixing by diffusion and the added mixing by convection (indicative). For low Reynolds numbers diffusion dominates, for higher Reynolds numbers convection dominates.
3 Results and discussion 3.1 Mixing performance As mentioned in the introduction, passive (convective) type mixers suffer from a low mixing performance for Reynolds number around 1–20 [26–29]. The origin of this problem can be understood best when the individual mixing processes are considered. Given a fixed mixer design with a fixed but limited volume and operating at very low Reynolds numbers, the mixing will be complete since time for diffusion is large enough. At high Reynolds numbers, inducement of eddies will lead to a much higher interface between the fluids and mixing will be enhanced dramatically. In the intermediate range of Reynolds number, where the flow is not yet showing signs of turbulence and where the time for diffusion is limited, a zone of low mixing is apparent. Improvements to solve this problem have been suggested [6], but to the author’s knowledge, completely omitting the low mixing zone has not been solved yet [8]. In Fig. 2A, the occurrence of the low mixing zone is shown (conceptually) as it is typically presented. In Fig. 2B, it is shown how this behavior can be better understood by decoupling it into the inherently present diffusion (via x2 = 2Dmol t, with x the diffusion distance, Dmol the molecular diffusion coefficient, and t the time available for diffusion) and the added effects due to mixing. It is clear that the extra diffusion that is generated by the mixer is crucial for the width of the low mixing performance zone. Note that
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the contribution of the mixing by variation of the flow rate in reality is very much dependant on the mixer design and that the mixer performances as presented in Fig. 2B are indicative only. To overcome the low mixing performance zone, a mixer with an active element is suggested. This active element is responsive to an external magnetic field by induced magnetism. The element acts by altering the flow field, which is most apparent at higher Reynolds numbers (at low Reynolds number it merely increases the flow path and the diffusion interface slightly). However, since the structures do not contribute much to mixing in the low to medium Reynolds range, applying an external magnetic field allows inducing flow alterations and vastly increased mixing performance. In the absence of the steel balls, the mixer can be seen as a Y-type mixer with varying channel width and height. The mixing performance was very much dependant on the flow rate (Fig. 3A) and could be largely correlated to the impulse associated with the initial contact of both inlet flows at the Ycontacting section. This has been well documented and will not be studied further [27]. The initial contacting effect came into play here when flow rates of 2 mL/min were applied for each input flow. For lower flow rates, the main mixing mechanism appeared to be the diffusion at the interface between the two fluids (which remained located at their initial side of the channel). Given that the residence time was smaller when comparing, e.g. the flow rates of 0.1 and 1.0 mL/min and seeing similar mixing performance, some additional flow rate coupled effects may already have been at play, but overall they were too small to enhance the mixing performance to a desired level. In the presence of the steel balls, but in absence of a magnetic field, the steels balls contributed at low, medium and high flow rate to mixing, but with different importance. For low flow rates, no alterations of the flow path were expected other than the movement of the fluid around the elements. The sole addition to mixing here was a bending of the interface (and thus an increase of the contacting length) between the two fluids. At increasing flow rates however, additional mixing was seen when compared to the empty mixing chambers. The additional flow rate coupled effects were larger than in the absence of the elements. Mixing was now not mainly generated by initial contact at the Y-inlet section, but also by convective effects in the wake of the steels balls (Fig. 3B). This type of setup has been studied previously and different shapes have been considered [30–32]. While it certainly was an improvement to the empty chambers design, the low mixing performance at low flow rates was still apparent. In the presence of a magnetic field, the mixing performance profile looked very different. For both low and high rotating speeds (and almost irrespective of the flow rate), the mixing quality was very good after only a few chambers (Fig. 3C and D). It appeared that the second mixing input, namely the active effect of the mixer, solved the low mixing performance marking the low to medium Reynolds number region. This was verified by plotting the mixing performance for a mixer with two mixing chambers (Fig. 4A) www.electrophoresis-journal.com
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Figure 4. Comparison of mixing performance for a large Reynolds range. The mixing performance for the studied mixer for a mixer with two mixing chambers (A) and six mixing chambers (B).
Figure 3. Mixing performance in absence and presence of the moving element for three rotating speeds. (A) No active element, (B) active element with no rotation, (C) rotation intensity 3, (D) rotation intensity 9.
and six mixing chambers (Fig. 4B) in function of the Reynolds number. The results suggested that, while for the empty chambers and the nonactive elements a low mixing performance zone was clearly visible, such a zone was not present when the element was moving actively in response to the rotating external magnetic field. The result for two mixer volumes were plotted to show the effect of the mixer volume on the profile of the low mixing zone. Indeed, if the res C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
idence time was not crucial, one could increase the mixer volume dramatically and generate complete mixing solely by diffusion. To understand why this active effect influenced the mixing performance so dramatically, the flow behavior was visualized. While the flows entered the first mixing chamber separately and next to each other with a contacting zone in the middle of the mixing channel, the flow profile changed drastically after passing the mixing chamber. As was discussed in the introduction, mixing is much more effective if axial dispersion comes into play. This requires restructuring flows as segments flowing behind each other (axially) instead of next to each other. This restructuring is exactly what happened in the mixing chamber. In Fig. 5, the flow behavior before, inside and after the first mixing chamber is presented. The effect was similar for the following mixing chambers, but the first chamber offered the clearest visible appreciation of the effect. In addition, some mixing also occurs in the chambers. As discussed above; without extra input (no rotation of the magnetic stirrer) the flows moved around the steel ball, increasing the diffusion but overall mixing only to a small extent. For a good design of experiments, it would be interesting to apply the optimal rotating speed for a given flow rate. A number of modeling studies [16–18] have attempted to assess this, by optimizing the rotating speed to induce the highest possible mixing for a given Reynolds number. However, from the recorded displacement maps (Fig. 6), it could be seen that this is not straightforward. The movement of the active element did not follow the rotation of the magnetic stirrer as it was expected and the influence of a varying flow rate impacted the activity of the element. For the highest flow rates (Fig. 6C), the active element was pushed against the back-end www.electrophoresis-journal.com
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Table 1. Stirrer data
Stirring intensity
Stirring speed (rpm)
Stirrer power requirement (W)
2 4 6 8 10
60 125 350 700 1100
9.453 11.086 15.203 20.240 26.611
Table 2. Overview of the pressure losses as a function of the flow rate
Type
a-term
b-term
c-term
R2
Connections Chip Chip with active element Rotation intensity 3 Rotation intensity 6 Rotation intensity 9
0.0032 0.0084 0.0114 0.0143 0.0200 0.0130
0.6000 1.3756 1.3658 1.3561 1.3387 1.4094
0 0 0 0 0 0
0.9994 0.9999 0.9998 0.9998 0.9994 0.9993
A polynomial of second order (y = ax2 + bx + c) was used to fit the data
Figure 5. Effect of the active element on the flow profile. (A) The flow profile around a nonrotating element. (B) The flow profile at the outlet of the first mixing chamber for different positions of the rotating element (flow rate 1.0 mL/min). (C) The flow profile inside the mixing chamber during rotations (flow rate 0.2 mL/min).
of the chamber due to the flow impulse. For low (Fig. 6A) to medium flow rates (Fig. 6B), the movement of the active element seemed to be more random than orderly. In some cases, the steel balls moved in the opposite direction of the magnetic stirrer direction. It seemed that modeling and predicting the optimal stirring speed in function of the flow rate was not as straightforward as was expected. However, this was not problematic, since mixing was very good in all cases (also for the low rotation intensity). For the high flow rates, with a virtually fixed active element, the convective effects were large enough and no active element was required. For the low to medium flow rates, even with the unexpected activity, fluorescence studies confirmed that mixing was good in all cases.
3.2 Power dissipation In terms of power consumption, an optimal situation would be one where a large amount of mixing is performed at a low cost. An interesting study governing the power dissipation and more specifically the energetic efficiency of convectivetype micromixers was recently published [33]. Here it was C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
concluded that at best only 3% of the dissipated power is converted to mixing. This emphasizes the limits of passive type of micromixers and supports the use of an active element. To estimate the additional power consumption, there are two possible approaches: to work with an optimized setup and measure the power cost at the stirring unit or estimate the power input at the elements and assume the energetic efficiency to be as high as possible. In Table 1, the stirrer intensity data with the stirring speed of the externally rotating stirring bar magnet is presented, as well as the measured power requirement (by use of an amperometer). Since the magnetic rotor was much larger than the individual cells and was not optimized for the mixer, the external power requirement in this case is much higher than required. Because of the mismatching sizes of the magnetic stirrer unit and the mixer itself, no direct link between the power consumption of the stirrer unit and the actually received power of the magnetic balls could be calculated. Instead, the power dissipation was estimated indirectly in two different ways. The first way consisted of an experimental study where the pressure drop of the whole mixer setup was measured in presence and in absence of the active elements for different stirring intensities (and correcting for the connections). By multiplying the corrected pressure drop with the volumetric flow rate, the power consumption at the pumps was calculated. The results showed only marginal increase in the power consumption, the limiting aspect proved the limited head pressure readout. In Table 2, the equations for the (total/uncorrected) pressure loss data are presented. The second way to estimate the power dissipation was by calculating the displacement of fluid by the active element. Frames were taken every 111 ms and the center of the steel ball was determined for each frame. It was assumed www.electrophoresis-journal.com
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Figure 6. Displacement maps for a range of rotating speeds. The dots indicate the center of the elements; the lines correspond to the displaced distance per frame. Flow rate: (A) 0.10 mL/min, (B) 1.00 mL/min, and (C) 10.00 mL/min; rotation intensity (A1-B1-C1) 1, (A2-B2-C2) 5, and (A3-B3-C3) 10.
the ball made a straight displacement (which visual inspection of the flows seemed to confirm); this allowed calculating the distance that was moved per unit of time. By using the drag equation (with the drag coefficient CD estimated as 24/Re [30]), the power input from the element to the flow was calculated. To get a more correct approximation of the power dissipation, the impulse from the steel balls on the chamber wall was also taken into account:
Power input = FD × vrel + m × v
(4)
FD = 0.5 × CD × A × v 2 × .
(5)
With FD the drag force, vrel the relative (to the flow) velocity of the element, v the absolute velocity of the element, m the mass displaced per unit of time (mass flow rate for the steel ball), A the front surface of the element, and the density of the liquid that the element is moving through. To get the total power input, the power input of all steel balls was added. Since the relative flow velocity varies, the largest C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
possible flow velocity (the chamber inlet velocity) was taken to estimate the largest possible required power input. The specific power dissipation, which correlates the power input to the mixer volume, and is often used as a means to evaluate convective-type mixers [30, 33, 34], was calculated by dividing the power input by the mass of the liquid in the mixer. The results are shown in Table 3: εactive elements =
Power input . Vmixer × fluid
(6)
The values of the power dissipation increased sharply with increasing Reynolds number due to the higher relative velocity. For the highest flow rate, the elements were virtually fixed due to flow impulse and no power dissipation could be estimated. For a given flow rate, the stirrer intensity was of minor importance, which was also suggested in the displacement maps and the mixing analysis. It could therefore be argued to work under low rotation intensity conditions for optimal power to mixing efficiency. When comparing the power www.electrophoresis-journal.com
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Electrophoresis 2015, 36, 405–412 Table 3. Estimated power dissipation values (×10−3 ) of the active elements by contact with the flow for a range of rotation intensities and flow rates
Stirring intensity 1 2 3 4 5 6 7 8 9 10
Flow rate (mL/min) 0.1
0.2
0.4
1.0
2.0
4.0
10.0
1.0 1.6 1.6 0.7 0.7 0.9 1.3 0.6 0.9 1.5
26.8 24.1 23.5 23.1 18.3 15.8 30.5 28.5 22.9 37.8
76.6 171.4 149.7 134.5 144.8 116.8 146.7 49.2 142.3 199.5
1267.2 2543.6 1471.0 2598.7 2723.2 2042.2 2561.0 1952.8 2343.4 1924.5
18 899.1 10 775.3 18 743.5 21 295.1 11 013.2 12 581.5 15 679.4 20 754.5 20 072.7 19 451.4
39 549.6 144 306.0 162 389.0 169 999.6 169 921.9 89 418.3 170 077.3 127 765.2 170 980.5 154 404.1
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
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tensities. Displacement maps for variable rotation intensities and flow rates showed the limitations of earlier modeling studies. Depending on the strength of the inputs and the ratio of these, the displacement of the active element varies greatly. In terms of power input, the cost at the stirrer was not considered since an optimization of the design was not the purpose of this work. A next step is the characterization of the energetic efficiency for an optimized mixer design. The authors have declared no conflict of interest.
5 References ¨ [1] Hardt, S., Drese, K. S., Hessel, V., Schonfeld, F., Microfluid. Nanofluid. 2005, 1, 108–118. ¨ ¨ [2] Hessel, V., Lowe, H., Schonfeld, F., Chem. Eng. Sci. 2005, 60, 2479–2501.
Table 4. The estimated power dissipation caused by the total flow
Flow rate (mL/min)
flow
0.1 0.2 0.4 1.0 2.0 4.0 10.0
1.7 6.8 10.9 67.2 268.7 1071.4 7040.8
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dissipation values of the elements with the power dissipation generated by the flow (by using the data for nonrotating active elements, Table 4), it appeared that the added power dissipation by the active elements values was very low. For the lowest flow rates, where the steel balls can provide already effective mixing, this method offered thus a cheap means to increase mixing very effectively: εflow =
Pdrop × Flow rate . Vmixer × fluid
(7)
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4 Concluding remarks
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To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. Both the mixing performance as well as the power consumption was considered. The mixer proved to be a good solution for the low mixing performance zone that occurs in convective-type mixers. The rearrangement of the flow led the mixer to profit from axial dispersion rather than solely diffusion which was visualized with fluorescence dilution experiments. Since rearrangement of the flow suffices to generate very good mixing for a large Reynolds range, the required extra power input was limited. This was measured both experimentally by pressure drop experiments as well as modeled with displacement maps. This result was also supported by the good mixing results for both low and high rotation in-
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Robert Goovaerts Tom Van Assche Marc Sonck Joeri Denayer Gert Desmet Department of Chemical Engineering, Vrije Universiteit Brussel, Brussels, Belgium
Received July 1, 2014 Revised August 18, 2014 Accepted August 18, 2014
Research Article
A micromixer with consistent mixing performance for a wide range of flow rates A micromixer with consistent mixing performance for a wide range of flow rates is presented. The mixer makes use of internally moving elements, i.e. steel balls that are located in dedicated mixing chambers. Movement is induced by a rotating magnetic field. To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. A mixing performance study for a range of flow rates along with pressure drop data is presented. The response of the moving elements in regard to the magnetic field is shown experimentally and shows the limitations of earlier modeling studies. Lastly, the estimated power input on the fluids was calculated and allows for a comparison with more well-known convective-type mixers. Keywords: Active mixing / Magnetic / Mixing performance / Passive mixing / Power dissipation DOI 10.1002/elps.201400314
1 Introduction Micromixers have been studied for over a decade. Numerous inventive designs have been made and several review papers have been written on the topic [1–4]. In general, two general classes of mixer types are proposed: passive and active micromixers. In passive mixers, the sole power input comes from the flow-generating pump. By smart design of the internal structure of the mixer, mixing performance can be dramatically enhanced. Passive mixers are typically operated under a certain flow rate range, since the behavior of the flow is dependent on both the internal mixer structure and the flow regime. Some mixers have been designed to work optimally at high internal velocities [5], whereas others are best operated at a lower flow rate regime [6–8]. Active mixers typically have multiple inputs to generate time-based changes in the flow profile which enhance mixing performance and as such have more variability in operating conditions. An interesting and well-studied principle is one where the flow is restructured initially so that axial dispersion, which is much more efficient than diffusion, is effectively generated [9–15]. This method offers good mixer performance, but the injection strategy is critical for the mixer performance and dependant on the flow rate. For high flow rates, the response time of the pumps may prove critical and thus lower the optimized injection profile which leads to lower mixing performance. An alternative strategy to restructure the flow is the introduction of an active element inside the mixing channel. To have some control of the stirring performance, outside control of this active element by magnetism is a viable strategy. Some numerical studies have
Correspondence: Robert Goovaerts, Pleinlaan 2, 1050 Elsene, Belgium E-mail: [email protected]
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been undertaken [16–18] and proved the effectiveness of this strategy. The active element (microstirrer) can be fixed to the channel [19], fixed in a chamber [20], or used as a suspension of magnetic particles [21]. Studies with small magnetic particles have been well covered. Electrofluids proved very effective in mixing [22, 23]. In-depth studies of the flow phenomena when these magnetic beads form chains have been investigated recently [24, 25] and the drag forces on the chain formation have been studied. To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. The mixer is composed of a series of mixing chambers, each filled (or not) with a (rotating) ball that can either move freely under the forces of the flow; or that can be rotated under the influence of an externally controlled applied magnetic field. It was preferred to work with a 1-mm-sized element so that sedimentation, which is an important problem with micron sized particles, has no meaningful effect. The study is also meant to investigate the effect of the flow rate on the response of the element to the external control, which has to our knowledge not been studied before. Lastly, the added cost for improving the passive mixer design is discussed by estimating the power dissipation generated in the mixer setup.
2 Materials and methods 2.1 Mixer design and setup As chip material, PMMA was chosen for a number of reasons: it is suited for mechanical operations, e.g. milling. The material can be bonded thermally and hence large head-loss
Colour Online: See the article online to view Fig. 6 in colour.
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Figure 1. The design of the micromixer.
resistant chips can be made which allow the user to work under a broad operating range (unlike PDMS). The material also is UV-VIS transparent, which allows for optical study of the flows. The microchip is composed of a bottom section with milled features and a top section that serves as lid. Prior to thermal bonding, steel balls were placed into the mixing chambers (one ball per chamber). Next, the lid section was clamped onto the bottom section and the assembly was placed into an oven during 30 (155°C) to allow for thermal bonding. Two inlet channels are joined in a Y-type entry section which leads to the mixing channel. This channel consists of a set of chambers that are interconnected by a single, straight channel with 500 m sides (length 1.5 mm between the chambers). The mixing chambers are designed as cylinders with a height and width of 1.5 mm. Inside these chambers, a steel ball with a diameter of 1 mm is placed (Fig. 1). The structures are produced in PMMA (Eriks-Baudouin, Hoboken, Belgium) by milling (CNC milling engraving machine, Datron, NH, USA). Leftover debris was removed by pressurized air prior to thermal bonding (155°C, 30 min). The mixer was placed between a magnetic stirrer (Cimarec 2, Barnstead Thermolyne, NH, USA) and an inverted microscope (see next section for a description of the fluorescence setup). To generate a stronger magnetic field by increasing the proximity, the lid of the magnetic stirrer was removed prior to placing it upside down on the mixer.
2.2 Fluorescence study The mixing performance was evaluated by dilution experiments. A FITC solution (10−5 M, Sigma-Aldrich, Bornem, Belgium) was prepared by dissolution in ultrapure water (Synergy UV Water Purification System, Millipore, MA, USA). Two syringe pumps (260D Syringe Pump, Teledyne ISCO, NE, USA) were connected to the mixer by fused silica capillaries (ID 182 m, OD 354 m, Polymicro Technologies, AZ, USA), which were placed into dedicated milled grooves and subsequently glued with a UV-curable glue (OrmoCore, microresist technology, Berlin, Germany). FITC and water were fed at equal flow rates to the mixer and entered the mixing channel via the Y-shaped entry section. For the detection of the fluorescence profile, an inverted microscope C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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(IX71, Olympus, Belgium) was used, equipped with a wide green filter cube set. Illumination with an Hg-vapor lamp (U-LH100HGAPO, Olympus) allowed for excitation at 505 nm and for emission around 515 nm. The mixing progress was visualized using an air-cooled CCD fluorescence camera (ORCA-ERC4742, Hamamatsu Photonics, Massy, France) mounted on the video adapter of the microscope. The video images were taken downstream each mixing chamber over the entire width of the channel and subsequently analyzed with the accompanying simple-PCI 5.1 software. The acquired fluorescence values (Xij ) (which are measures for the concentration of FITC) were averaged out (Xsignal ) to correct for local fluctuations of the fluorescence. To correct for background fluorescence contributions (due to channel roughness), the background fluorescence Xbackground was subtracted from Xsignal . The background fluorescence value for a given position did not change during experiments, indicating low to no deposition of the dye due to flushing steps (with ultrapure water) between experiments. Taking this background value into account, the average of the fluorescence values could be subsequently calculated, Eq. (1). To represent the mixing progress over the entire channel in a compact way, the standard deviation of the fluorescence values (Eq. (2)) was calculated and normalized between a value of 0 and 1 by dividing the actual standard deviation by the standard deviation at the inlet (nonmixed). This value was then subtracted from Eq. (1). This normalized value, from here on referred to as mixing quality ␣, Eq. (3), was used to display the mixing progress after each mixing chamber: n
=
=
(X signal − X background )
i=1
(1)
n n
2 X signal − X background − i=1
␣=1−
n . max
(2)
(3)
2.3 Pressure measurement study The syringe pumps provided a pressure readout (10 kPa precision), which allowed to measure the pressure losses over the setup for the whole flow rate range (0.01–10 mL/min). The pressure losses for the connections were measured separately to estimate the contribution of the mixer more accurately. The pressure losses were measured both in absence of the steel balls as well as in presence of the steel ball for varying rotation intensities (including no rotation). www.electrophoresis-journal.com
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Figure 2. (A) The concept of the low mixing performance zone as typically presented. (B) The separate contribution of mixing by diffusion and the added mixing by convection (indicative). For low Reynolds numbers diffusion dominates, for higher Reynolds numbers convection dominates.
3 Results and discussion 3.1 Mixing performance As mentioned in the introduction, passive (convective) type mixers suffer from a low mixing performance for Reynolds number around 1–20 [26–29]. The origin of this problem can be understood best when the individual mixing processes are considered. Given a fixed mixer design with a fixed but limited volume and operating at very low Reynolds numbers, the mixing will be complete since time for diffusion is large enough. At high Reynolds numbers, inducement of eddies will lead to a much higher interface between the fluids and mixing will be enhanced dramatically. In the intermediate range of Reynolds number, where the flow is not yet showing signs of turbulence and where the time for diffusion is limited, a zone of low mixing is apparent. Improvements to solve this problem have been suggested [6], but to the author’s knowledge, completely omitting the low mixing zone has not been solved yet [8]. In Fig. 2A, the occurrence of the low mixing zone is shown (conceptually) as it is typically presented. In Fig. 2B, it is shown how this behavior can be better understood by decoupling it into the inherently present diffusion (via x2 = 2Dmol t, with x the diffusion distance, Dmol the molecular diffusion coefficient, and t the time available for diffusion) and the added effects due to mixing. It is clear that the extra diffusion that is generated by the mixer is crucial for the width of the low mixing performance zone. Note that
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the contribution of the mixing by variation of the flow rate in reality is very much dependant on the mixer design and that the mixer performances as presented in Fig. 2B are indicative only. To overcome the low mixing performance zone, a mixer with an active element is suggested. This active element is responsive to an external magnetic field by induced magnetism. The element acts by altering the flow field, which is most apparent at higher Reynolds numbers (at low Reynolds number it merely increases the flow path and the diffusion interface slightly). However, since the structures do not contribute much to mixing in the low to medium Reynolds range, applying an external magnetic field allows inducing flow alterations and vastly increased mixing performance. In the absence of the steel balls, the mixer can be seen as a Y-type mixer with varying channel width and height. The mixing performance was very much dependant on the flow rate (Fig. 3A) and could be largely correlated to the impulse associated with the initial contact of both inlet flows at the Ycontacting section. This has been well documented and will not be studied further [27]. The initial contacting effect came into play here when flow rates of 2 mL/min were applied for each input flow. For lower flow rates, the main mixing mechanism appeared to be the diffusion at the interface between the two fluids (which remained located at their initial side of the channel). Given that the residence time was smaller when comparing, e.g. the flow rates of 0.1 and 1.0 mL/min and seeing similar mixing performance, some additional flow rate coupled effects may already have been at play, but overall they were too small to enhance the mixing performance to a desired level. In the presence of the steel balls, but in absence of a magnetic field, the steels balls contributed at low, medium and high flow rate to mixing, but with different importance. For low flow rates, no alterations of the flow path were expected other than the movement of the fluid around the elements. The sole addition to mixing here was a bending of the interface (and thus an increase of the contacting length) between the two fluids. At increasing flow rates however, additional mixing was seen when compared to the empty mixing chambers. The additional flow rate coupled effects were larger than in the absence of the elements. Mixing was now not mainly generated by initial contact at the Y-inlet section, but also by convective effects in the wake of the steels balls (Fig. 3B). This type of setup has been studied previously and different shapes have been considered [30–32]. While it certainly was an improvement to the empty chambers design, the low mixing performance at low flow rates was still apparent. In the presence of a magnetic field, the mixing performance profile looked very different. For both low and high rotating speeds (and almost irrespective of the flow rate), the mixing quality was very good after only a few chambers (Fig. 3C and D). It appeared that the second mixing input, namely the active effect of the mixer, solved the low mixing performance marking the low to medium Reynolds number region. This was verified by plotting the mixing performance for a mixer with two mixing chambers (Fig. 4A) www.electrophoresis-journal.com
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Figure 4. Comparison of mixing performance for a large Reynolds range. The mixing performance for the studied mixer for a mixer with two mixing chambers (A) and six mixing chambers (B).
Figure 3. Mixing performance in absence and presence of the moving element for three rotating speeds. (A) No active element, (B) active element with no rotation, (C) rotation intensity 3, (D) rotation intensity 9.
and six mixing chambers (Fig. 4B) in function of the Reynolds number. The results suggested that, while for the empty chambers and the nonactive elements a low mixing performance zone was clearly visible, such a zone was not present when the element was moving actively in response to the rotating external magnetic field. The result for two mixer volumes were plotted to show the effect of the mixer volume on the profile of the low mixing zone. Indeed, if the res C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
idence time was not crucial, one could increase the mixer volume dramatically and generate complete mixing solely by diffusion. To understand why this active effect influenced the mixing performance so dramatically, the flow behavior was visualized. While the flows entered the first mixing chamber separately and next to each other with a contacting zone in the middle of the mixing channel, the flow profile changed drastically after passing the mixing chamber. As was discussed in the introduction, mixing is much more effective if axial dispersion comes into play. This requires restructuring flows as segments flowing behind each other (axially) instead of next to each other. This restructuring is exactly what happened in the mixing chamber. In Fig. 5, the flow behavior before, inside and after the first mixing chamber is presented. The effect was similar for the following mixing chambers, but the first chamber offered the clearest visible appreciation of the effect. In addition, some mixing also occurs in the chambers. As discussed above; without extra input (no rotation of the magnetic stirrer) the flows moved around the steel ball, increasing the diffusion but overall mixing only to a small extent. For a good design of experiments, it would be interesting to apply the optimal rotating speed for a given flow rate. A number of modeling studies [16–18] have attempted to assess this, by optimizing the rotating speed to induce the highest possible mixing for a given Reynolds number. However, from the recorded displacement maps (Fig. 6), it could be seen that this is not straightforward. The movement of the active element did not follow the rotation of the magnetic stirrer as it was expected and the influence of a varying flow rate impacted the activity of the element. For the highest flow rates (Fig. 6C), the active element was pushed against the back-end www.electrophoresis-journal.com
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Table 1. Stirrer data
Stirring intensity
Stirring speed (rpm)
Stirrer power requirement (W)
2 4 6 8 10
60 125 350 700 1100
9.453 11.086 15.203 20.240 26.611
Table 2. Overview of the pressure losses as a function of the flow rate
Type
a-term
b-term
c-term
R2
Connections Chip Chip with active element Rotation intensity 3 Rotation intensity 6 Rotation intensity 9
0.0032 0.0084 0.0114 0.0143 0.0200 0.0130
0.6000 1.3756 1.3658 1.3561 1.3387 1.4094
0 0 0 0 0 0
0.9994 0.9999 0.9998 0.9998 0.9994 0.9993
A polynomial of second order (y = ax2 + bx + c) was used to fit the data
Figure 5. Effect of the active element on the flow profile. (A) The flow profile around a nonrotating element. (B) The flow profile at the outlet of the first mixing chamber for different positions of the rotating element (flow rate 1.0 mL/min). (C) The flow profile inside the mixing chamber during rotations (flow rate 0.2 mL/min).
of the chamber due to the flow impulse. For low (Fig. 6A) to medium flow rates (Fig. 6B), the movement of the active element seemed to be more random than orderly. In some cases, the steel balls moved in the opposite direction of the magnetic stirrer direction. It seemed that modeling and predicting the optimal stirring speed in function of the flow rate was not as straightforward as was expected. However, this was not problematic, since mixing was very good in all cases (also for the low rotation intensity). For the high flow rates, with a virtually fixed active element, the convective effects were large enough and no active element was required. For the low to medium flow rates, even with the unexpected activity, fluorescence studies confirmed that mixing was good in all cases.
3.2 Power dissipation In terms of power consumption, an optimal situation would be one where a large amount of mixing is performed at a low cost. An interesting study governing the power dissipation and more specifically the energetic efficiency of convectivetype micromixers was recently published [33]. Here it was C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
concluded that at best only 3% of the dissipated power is converted to mixing. This emphasizes the limits of passive type of micromixers and supports the use of an active element. To estimate the additional power consumption, there are two possible approaches: to work with an optimized setup and measure the power cost at the stirring unit or estimate the power input at the elements and assume the energetic efficiency to be as high as possible. In Table 1, the stirrer intensity data with the stirring speed of the externally rotating stirring bar magnet is presented, as well as the measured power requirement (by use of an amperometer). Since the magnetic rotor was much larger than the individual cells and was not optimized for the mixer, the external power requirement in this case is much higher than required. Because of the mismatching sizes of the magnetic stirrer unit and the mixer itself, no direct link between the power consumption of the stirrer unit and the actually received power of the magnetic balls could be calculated. Instead, the power dissipation was estimated indirectly in two different ways. The first way consisted of an experimental study where the pressure drop of the whole mixer setup was measured in presence and in absence of the active elements for different stirring intensities (and correcting for the connections). By multiplying the corrected pressure drop with the volumetric flow rate, the power consumption at the pumps was calculated. The results showed only marginal increase in the power consumption, the limiting aspect proved the limited head pressure readout. In Table 2, the equations for the (total/uncorrected) pressure loss data are presented. The second way to estimate the power dissipation was by calculating the displacement of fluid by the active element. Frames were taken every 111 ms and the center of the steel ball was determined for each frame. It was assumed www.electrophoresis-journal.com
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Figure 6. Displacement maps for a range of rotating speeds. The dots indicate the center of the elements; the lines correspond to the displaced distance per frame. Flow rate: (A) 0.10 mL/min, (B) 1.00 mL/min, and (C) 10.00 mL/min; rotation intensity (A1-B1-C1) 1, (A2-B2-C2) 5, and (A3-B3-C3) 10.
the ball made a straight displacement (which visual inspection of the flows seemed to confirm); this allowed calculating the distance that was moved per unit of time. By using the drag equation (with the drag coefficient CD estimated as 24/Re [30]), the power input from the element to the flow was calculated. To get a more correct approximation of the power dissipation, the impulse from the steel balls on the chamber wall was also taken into account:
Power input = FD × vrel + m × v
(4)
FD = 0.5 × CD × A × v 2 × .
(5)
With FD the drag force, vrel the relative (to the flow) velocity of the element, v the absolute velocity of the element, m the mass displaced per unit of time (mass flow rate for the steel ball), A the front surface of the element, and the density of the liquid that the element is moving through. To get the total power input, the power input of all steel balls was added. Since the relative flow velocity varies, the largest C 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
possible flow velocity (the chamber inlet velocity) was taken to estimate the largest possible required power input. The specific power dissipation, which correlates the power input to the mixer volume, and is often used as a means to evaluate convective-type mixers [30, 33, 34], was calculated by dividing the power input by the mass of the liquid in the mixer. The results are shown in Table 3: εactive elements =
Power input . Vmixer × fluid
(6)
The values of the power dissipation increased sharply with increasing Reynolds number due to the higher relative velocity. For the highest flow rate, the elements were virtually fixed due to flow impulse and no power dissipation could be estimated. For a given flow rate, the stirrer intensity was of minor importance, which was also suggested in the displacement maps and the mixing analysis. It could therefore be argued to work under low rotation intensity conditions for optimal power to mixing efficiency. When comparing the power www.electrophoresis-journal.com
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Electrophoresis 2015, 36, 405–412 Table 3. Estimated power dissipation values (×10−3 ) of the active elements by contact with the flow for a range of rotation intensities and flow rates
Stirring intensity 1 2 3 4 5 6 7 8 9 10
Flow rate (mL/min) 0.1
0.2
0.4
1.0
2.0
4.0
10.0
1.0 1.6 1.6 0.7 0.7 0.9 1.3 0.6 0.9 1.5
26.8 24.1 23.5 23.1 18.3 15.8 30.5 28.5 22.9 37.8
76.6 171.4 149.7 134.5 144.8 116.8 146.7 49.2 142.3 199.5
1267.2 2543.6 1471.0 2598.7 2723.2 2042.2 2561.0 1952.8 2343.4 1924.5
18 899.1 10 775.3 18 743.5 21 295.1 11 013.2 12 581.5 15 679.4 20 754.5 20 072.7 19 451.4
39 549.6 144 306.0 162 389.0 169 999.6 169 921.9 89 418.3 170 077.3 127 765.2 170 980.5 154 404.1
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
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tensities. Displacement maps for variable rotation intensities and flow rates showed the limitations of earlier modeling studies. Depending on the strength of the inputs and the ratio of these, the displacement of the active element varies greatly. In terms of power input, the cost at the stirrer was not considered since an optimization of the design was not the purpose of this work. A next step is the characterization of the energetic efficiency for an optimized mixer design. The authors have declared no conflict of interest.
5 References ¨ [1] Hardt, S., Drese, K. S., Hessel, V., Schonfeld, F., Microfluid. Nanofluid. 2005, 1, 108–118. ¨ ¨ [2] Hessel, V., Lowe, H., Schonfeld, F., Chem. Eng. Sci. 2005, 60, 2479–2501.
Table 4. The estimated power dissipation caused by the total flow
Flow rate (mL/min)
flow
0.1 0.2 0.4 1.0 2.0 4.0 10.0
1.7 6.8 10.9 67.2 268.7 1071.4 7040.8
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dissipation values of the elements with the power dissipation generated by the flow (by using the data for nonrotating active elements, Table 4), it appeared that the added power dissipation by the active elements values was very low. For the lowest flow rates, where the steel balls can provide already effective mixing, this method offered thus a cheap means to increase mixing very effectively: εflow =
Pdrop × Flow rate . Vmixer × fluid
(7)
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To get better insight in differences between active and passive mixing, we studied a mixer that can operate in both regimes. Both the mixing performance as well as the power consumption was considered. The mixer proved to be a good solution for the low mixing performance zone that occurs in convective-type mixers. The rearrangement of the flow led the mixer to profit from axial dispersion rather than solely diffusion which was visualized with fluorescence dilution experiments. Since rearrangement of the flow suffices to generate very good mixing for a large Reynolds range, the required extra power input was limited. This was measured both experimentally by pressure drop experiments as well as modeled with displacement maps. This result was also supported by the good mixing results for both low and high rotation in-
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