- Email: [email protected]
Configurable AC electroosmotic pumping and mixing
Microelectronic Engineering 90 (2012) 47–50
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Configurable AC electroosmotic pumping and mixing Neophytos Loucaides a,⇑, Antonio Ramos b, George E. Georghiou a a b
University of Cyprus, Department of Electrical and Computer Engineering, Cyprus University of Seville, Department of Electronics and Electromagnetism, Spain
a r t i c l e
i n f o
Article history: Available online 19 April 2011 Keywords: AC electroosmosis Pumping Mixing Microfluidics Lab-on-Chip
a b s t r a c t In this paper configurable AC electroosmotic array devices are investigated for the purpose of combined pumping and mixing in microcapillaries. The method relies on grouping similar electrodes together in terms of applied voltage, in order to create configurable asymmetries in periodic electrode arrays. Novel designs and excitation patterns are examined for the electrode arrays and the results are evaluated in both absolute and relative terms compared to previously proposed array patterns. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction AC electroosmotic flow [1,2] has been recently used in the pumping of fluids in capillaries, due to several advantages over DC electroosmosis. The main advantage is that the use of low AC voltage can reduce or eliminate Faradaic currents, which in turn reduces or eliminates the generation of bubbles and new species in the liquid. An important set of pumping systems that have been proposed and demonstrated, are the ones that utilise asymmetries in the electric field, created by electrode structures in capillaries in order to produce a directional AC electroosmotic net flow of fluid [3]. Asymmetries in this type of pumping systems can be introduced in many ways, such as by the shape of the electrodes [4] or their properties. A field of great interest in Lab-on-Chip devices is the use of electric fields to interact with an electrolyte in order to induce a mixing effect. Such methods include AC electrothermal fluid motion [5], AC electroosmosis for mixing of fluids [6], or even for combined pumping and mixing. Several designs have been proposed in order to achieve the latter (combined) effect, such as asymmetric electrode arrays [7] or diagonal/herringbone shapes [8]. Furthermore, devices have also been proposed that create a mixing effect by rotation of the flow [9]. The concept of configurable asymmetry in ACEO pumpingdevices has recently been introduced [10]. This allows modification of the system asymmetry by electrode grouping in terms of excitation. Here, new modes for mixing and pumping, implemented on a configurable array, are investigated, analysed and compared with modes previously proposed in the literature. These can be realised ⇑ Corresponding author. E-mail address: [email protected] (N. Loucaides). 0167-9317/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2011.04.007
on a single array resulting in a much more versatile and functional system. 2. Theory AC electroosmotic flow is caused by the interaction of the tangential electric field over an electrode, with the charge in the double layer over that electrode. The system of interest is one of three parallel co-planar electrodes, which is repeated periodically, such as the one in Fig. 1 [10]. This is achieved by applying the same voltage V applied ¼ V 0 cosðxtÞ to one group of electrodes (say 1 and 2) and the opposite voltage V applied ¼ V 0 cosðxtÞ to another group (electrode 3 in this case), so that a geometric asymmetry is created. In this way one can configure the direction of the asymmetry in a system by regrouping the electrodes, for example in this case by grouping electrodes 2 and 3 together at an applied voltage V applied ¼ V 0 cosðxtÞ and setting electrode 1 at V applied ¼ V 0 cosðxtÞ. The model used here to simulate the operation of the system is one based on the Debye–Huckel theory for the double layer and is valid for low voltages only [11]. 2.1. Electrical problem In order to obtain the required electric field, Laplace’s equation for the potential is solved:
r2 / ¼ 0
ð1Þ
where / is the electric potential. This is solved with the following boundary condition on the electrode [12]:
r~ n:r/ep ¼
/ep V applied Z DL
ð2Þ
48
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50 Table 1 Electrolyte properties used in the simulations. Property
Value
Fluid viscosity (g)
1 103 Pa s 80
Relative permittivity of medium ðr Þ Permittivity of free space ð0 Þ Debye length ðkDebye Þ Conductivity (r) Diffusion constant (D) Voltage ðV 0 Þ Frequency (f)
8:8542 1012 F m1 3 108 m 1:23 mS m1 1010 m2 s1 2V 250 Hz
2.3. Mixing problem Fig. 1. Schematic of the configuration and operation of the configurable system (not to scale) [10]. The arrows and streamlines indicate the fluid flow direction.
where /ep is the potential at the outer edge of the electrical double layer, r the fluid electrical conductivity, V applied the value of the voltage applied at the electrodes, Z DL ¼ ix1CDL the impedance of the double layer, C DL ¼ k the capacitance of the double layer (if the size Debye of the compact layer is negligible), x the angular frequency of the electric field and kDebye the Debye length on the electrode surface. The boundary condition used for all the electrodes is given by Eq. (2) implemented as a weak contribution on the boundary using a testð/Þð/V applied Þ test function (given by r/ ¼ ) (the applied voltage Z DL r V applied is different for each electrode depending on the grouping chosen). The inlet and outlet boundaries of the domain have periodic boundary conditions and the rest of the boundaries are set to a homogeneous Neumann boundary condition ~ n r/ ¼ 0, where ~ n is the vector normal to the surface.
2.2. Fluid flow problem The Navier–Stokes equations are solved, neglecting the inertial terms, to find the resulting fluid flow (under no external forces on the fluid):
gr2~ u rp ¼ 0
ð3Þ
r ~ u¼0
ð4Þ
where g is the fluid viscosity, ~ u the fluid velocity and p the fluid pressure. This has the following boundary condition for the fluid velocity on the surface of the double layer (which coincides with the electrode surface in the model geometry):
uslip ¼
4g
K
2 @ /ep V applied @x
The problem of interest here is the mixing of two species entering at the inlet under diffusion and convection in the channel due to ACEO. This is described by the following equation:
@c u:rc þ r:ðDrcÞ ¼ ~ @t
where c is the concentration, D the diffusion constant and ~ u the fluid velocity with x–y components u and v, respectively. The concentration at the inlet is set to c ¼ 0 for half the channel inlet cross section while the other half is set to c ¼ 1 as shown in Fig. 2. The outlet is set to convective flux while the rest of the boundaries are set to insulation (zero species flux). 3. Results The first setup examined is a pure pumping system using AC electroosmotic pumping and employing a configurable asymmetric electrode array. The array is shown in Fig. 2, where the width of the channel is assumed to be much greater than the height and therefore can be considered infinitely wide. The part shown is one of eight identical segments (in a real device the number can be much larger) which are simulated as a device. The electrodes are numbered 1, 2, 3, . . . , 24 for the top array and 25, 26, 27, . . . , 48 for the bottom one for reference. In conventional asymmetric arrays electrodes 2 and 3 for example would form a single electrode. The electrodes in Fig. 2 are such that each array has length 140 lm, electrodes 1 and 3 have length 20 lm and electrode 2 has length 40 lm while the interelectrode gaps have length 2 lm. The channel height in Fig. 2 is 200 lm. The setup presented here offers more flexibility in terms of the modes that can be realised on a single device. The first mode examined is the pure pumping mode, where the arrays are excited with AC voltage and 1 is in antiphase with 2 and 3, 4 is in antiphase with
ð5Þ
where K is the ratio of the diffuse double layer potential drop over the total double layer potential drop. The parameter K ¼ C SternCStern þC
diffuse
is
given by the ratio between the total capacitance and the diffuse double layer capacitance, and has been found experimentally for the system of interest here to be approximately 0:25 [12]. The properties of the system are summarised in Table 1. The boundary condition at the surface of the electrodes is u ¼ uslip , where V applied is different for each electrode, while the side boundaries are set to periodic boundary conditions and the boundaries at the interelectrode gaps are set to a no-slip condition. Both the electrical and fluid flow problems are solved numerically using the method of finite elements with Comsol Multiphysics.
ð6Þ
Fig. 2. Periodic segment of the array.
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50
49
Table 2 Electrode excitation table. (P) indicates a three electrode array pumping in the forward (right) direction, (P) an array pumping in the backward (left) direction and (S) an array where the two edge electrodes are in antiphase with the centre electrode. Mode/array position
Excitation
1/top 1/bottom 2/top 2/bottom 3/top 3/bottom 4/top 4/bottom
(P)(P)(P)(P)(P)(P)(P)(P) (P)(P)(P)(P)(P)(P)(P)(P) (P)(P)(P)(P)(P)(P)(P)(P) (P) (P)(P) (P) (P) (P)(P) (P) (P)(P)(P)(P)(P)(P)(S)(P) (P)(P)(P)(P)(P)(P)(S)(P) (P)(P)(P)(P) (P)(P)(P)(P) (P)(P) (P)(P)(P)(P) (P)(P) Fig. 4. Concentration plot in mode 2.
5 and 6 and so on. Therefore, the excitation mode for the wholearray is given in Table 2, where (P) indicates a three electrode array excitation pattern to induce pumping in the positive (to the right) direction. The result from this mode is shown in Fig. 3. It can be seen here that the mixing is very limited and can be attributed mostly to the diffusion of the species and to a small extent to the ACEO pumping array. In order to introduce significant mixing, other modes are tested. The best performing mode by Yoon et al. [7] is therefore examined. This is given by an alternating (P) and (P) excitation pattern which means pumping in the reverse direction on the top array, while the bottom array is always in a pumping (P) mode. The excitations are shown in Table 2. The results for the second mode are shown in Fig. 4. It can be seen that the mixing is now more than for the pure pumping mode. The novelty in the proposed design is that while in [7] these two modes have to be realised on different setups, here they can be realised on the same device simply by changing the voltage on the electrodes. Furthermore, novel modes are also possible. Another pumping–mixing mode tested is mode 3 where the electrode excitations are as in Table 2. Here another excitation pattern for the three electrode array is also defined, where the two outer electrodes such as 1 and 3 are in antiphase with the middle one, resulting in an enhanced mixing effect. This pattern is termed (S) for symmetric. The results for this mode are shown in Fig. 5. It can be seen that the mixing at the outlet is almost perfect in this case. Another possible mode (mode 4) is shown in Fig. 6, for which the excitations are shown in Table 2. The performance of the previously presented modes is usually evaluated by using the index ex defined in Eq. (7) and evaluated at the exit of the channel [13]. However, this index does not take into account the pumping performance at all, and the pumping is usually adversely affected by any changes in the excitation that depart from pure pumping mode. Therefore, a normalised index exn is defined in Eq. (8) where the pumping performance is also taken into account.
Fig. 3. Concentration plot in pure pumping mode, mode 1.
Fig. 5. Concentration plot in mode 3.
Fig. 6. Concentration plot in mode 4.
R jcðyÞ c1 jdy 100 ex 1 R jc0 c1 jdy ! R R jum :dyj jcðyÞ c1 jdy R exn R 100 1 jc0 c1 jdy up :dy
ð7Þ ð8Þ
Here um is the x-velocity at the outlet for the mode under examination, up is the x-velocity outlet for the pure pumping mode, cðyÞ the concentration distribution at the outlet, c1 the concentration distribution at the perfectly mixed state (equal to 0.5) [13] and c0 is the concentration at the inlet. It can be deduced that ex is equal to 100% when perfect mixing is achieved and therefore the higher this index is, the better the mixing performance. In exn the previous index is scaled by a ratio that accounts for the change in pumping performance associated with the change in mixing performance. This index still indicates performance, but even at perfect mixing this is not 100% (unless there is no deterioration in pumping performance). The performance of the different modes is assessed by the two indexes as shown in Table 3. It can be clearly seen that
50
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50
Table 3 Performance indexes. Mode
ex ð%Þ
exn ð%Þ
1 2 3 4 5 pumping 5 mixing
14 45.6 92.7 34.9 62.9 87.4
14 22.8 7.9 21.7 62.9 62.1
Fig. 8. Concentration plot in mode 5.
tation. Therefore, configurable ACEO arrays can be used in devices for pumping and mixing which can be very efficient, flexible, low power and very robust. 4. Conclusions
Fig. 7. Array configuration in mode 5.
while mode ex may give very good mixing performance, the exn index can be less than for the pure pumping mode, such as mode 3. All the modes presented here can be realised on a single array, therefore demonstrating the power of the technique presented in [10]. Furthermore, the modes can be alternated in real time, therefore offering great prospects for controlling the mixing in real time. Subsequently, a fifth mode is tested in which the swirls are created perpendicularly to the flow direction and therefore the device has to be simulated in three dimensions. The geometry and electrode setup are as in Fig. 7, with the electrodes and interelectrode gaps having the same dimensions as before, the channel width is 200 lm and the channel height is 100 lm, where an electrode array is placed only at the bottom of the channel and not at both the bottom and top as in the previous setups. In this setup, the arrays coloured red (electrodes 7, 8, 9) and blue (electrodes 31, 32, 33) are in antiphase, while the rest are in normal pumping mode. Therefore, a mixing effect is created as shown in Fig. 8. From Table 3 it can be seen that while the mixing performance is better in the combined mixing and pumping mode, the normalised performance is approximately the same as in pumping mode (the flow rate for the three-dimensional mode is calculated by integrating over the outlet area in two dimensions). However, it is demonstrated here that even with a planar array in a channel with significant height, the mixing can be enhanced by just switching two of the electrode arrays from their default pumping mode exci-
The method of configurable geometric asymmetry is applied to the problem of combined pumping and mixing using AC electroosmosis. A number of excitation modes are present here that can be realised on a single device. This demonstrates the flexibility of the method. Furthermore, novel excitation modes are tested and evaluated in comparison to pure pumping and other excitation modes previously proposed in the literature. It is found that it is possible to design modes with very good mixing performance, but there is always a trade off in pumping performance and the desired efficiency index can be used to select the mode to be utilised for a given application. Furthermore, a three-dimensional device is tested and it was found that with even simple switching of two electrodes, significant mixing can be achieved. References [1] A. Ramos, H. Morgan, N.G. Green, A. Castellanos, J. Phys. D 31 (1998) 2338– 2353. [2] A. Ramos, H. Morgan, N.G. Green, A. Castellanos, J. Colloid Interface Sci. 217 (1999) 420–422. [3] A. Ajdari, Phys. Rev. E 61 (2000) R45–R48. [4] A.B.D. Brown, C.G. Smith, A.R. Rennie, Phys. Rev. E 63 (2001) 016305. [5] M. Sigurdson, D. Wang, C. Meinhart, Lab Chip 5 (2005) 1366–1373. [6] W.Y. Ng, S. Goh, Y.C. Lam, C. Yang, I. Rodriguez, Lab Chip 9 (2009) 802–809. [7] M.S. Yoon, B.J. Kim, H.J. Sung, Int. J. Heat Fluid Flow 29 (2008) 269–280. [8] B.J. Kim, S.Y. Yoon, H.J. Sung, C.G. Smith, J. Appl. Phys. 102 (2007) 074513. [9] Y. Huang, X.W.J. Yang, F. Beckerand, P. Gascoyne, J. Hematother. Stem Cell Res. 8 (1999) 481–490. [10] N. Loucaides, A. Ramos, G.E. Georghiou, Microfluid. Nanofluid. 3 (2007) 709– 714. [11] P. Garcia-Sanchez, A. Ramos, N. Green, H. Morgan, IEEE Trans. Dielectr. Electr. Insul. 13 (2006) 670–677. [12] N.G. Green, A. Ramos, A. Gonzalez, H. Morgan, A. Castellanos, Phys. Rev. E 66 (2002) 026305–026311. [13] D. Li, Electrokinetics in Microfluidics, Academic Press, 2004.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Configurable AC electroosmotic pumping and mixing Neophytos Loucaides a,⇑, Antonio Ramos b, George E. Georghiou a a b
University of Cyprus, Department of Electrical and Computer Engineering, Cyprus University of Seville, Department of Electronics and Electromagnetism, Spain
a r t i c l e
i n f o
Article history: Available online 19 April 2011 Keywords: AC electroosmosis Pumping Mixing Microfluidics Lab-on-Chip
a b s t r a c t In this paper configurable AC electroosmotic array devices are investigated for the purpose of combined pumping and mixing in microcapillaries. The method relies on grouping similar electrodes together in terms of applied voltage, in order to create configurable asymmetries in periodic electrode arrays. Novel designs and excitation patterns are examined for the electrode arrays and the results are evaluated in both absolute and relative terms compared to previously proposed array patterns. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction AC electroosmotic flow [1,2] has been recently used in the pumping of fluids in capillaries, due to several advantages over DC electroosmosis. The main advantage is that the use of low AC voltage can reduce or eliminate Faradaic currents, which in turn reduces or eliminates the generation of bubbles and new species in the liquid. An important set of pumping systems that have been proposed and demonstrated, are the ones that utilise asymmetries in the electric field, created by electrode structures in capillaries in order to produce a directional AC electroosmotic net flow of fluid [3]. Asymmetries in this type of pumping systems can be introduced in many ways, such as by the shape of the electrodes [4] or their properties. A field of great interest in Lab-on-Chip devices is the use of electric fields to interact with an electrolyte in order to induce a mixing effect. Such methods include AC electrothermal fluid motion [5], AC electroosmosis for mixing of fluids [6], or even for combined pumping and mixing. Several designs have been proposed in order to achieve the latter (combined) effect, such as asymmetric electrode arrays [7] or diagonal/herringbone shapes [8]. Furthermore, devices have also been proposed that create a mixing effect by rotation of the flow [9]. The concept of configurable asymmetry in ACEO pumpingdevices has recently been introduced [10]. This allows modification of the system asymmetry by electrode grouping in terms of excitation. Here, new modes for mixing and pumping, implemented on a configurable array, are investigated, analysed and compared with modes previously proposed in the literature. These can be realised ⇑ Corresponding author. E-mail address: [email protected] (N. Loucaides). 0167-9317/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2011.04.007
on a single array resulting in a much more versatile and functional system. 2. Theory AC electroosmotic flow is caused by the interaction of the tangential electric field over an electrode, with the charge in the double layer over that electrode. The system of interest is one of three parallel co-planar electrodes, which is repeated periodically, such as the one in Fig. 1 [10]. This is achieved by applying the same voltage V applied ¼ V 0 cosðxtÞ to one group of electrodes (say 1 and 2) and the opposite voltage V applied ¼ V 0 cosðxtÞ to another group (electrode 3 in this case), so that a geometric asymmetry is created. In this way one can configure the direction of the asymmetry in a system by regrouping the electrodes, for example in this case by grouping electrodes 2 and 3 together at an applied voltage V applied ¼ V 0 cosðxtÞ and setting electrode 1 at V applied ¼ V 0 cosðxtÞ. The model used here to simulate the operation of the system is one based on the Debye–Huckel theory for the double layer and is valid for low voltages only [11]. 2.1. Electrical problem In order to obtain the required electric field, Laplace’s equation for the potential is solved:
r2 / ¼ 0
ð1Þ
where / is the electric potential. This is solved with the following boundary condition on the electrode [12]:
r~ n:r/ep ¼
/ep V applied Z DL
ð2Þ
48
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50 Table 1 Electrolyte properties used in the simulations. Property
Value
Fluid viscosity (g)
1 103 Pa s 80
Relative permittivity of medium ðr Þ Permittivity of free space ð0 Þ Debye length ðkDebye Þ Conductivity (r) Diffusion constant (D) Voltage ðV 0 Þ Frequency (f)
8:8542 1012 F m1 3 108 m 1:23 mS m1 1010 m2 s1 2V 250 Hz
2.3. Mixing problem Fig. 1. Schematic of the configuration and operation of the configurable system (not to scale) [10]. The arrows and streamlines indicate the fluid flow direction.
where /ep is the potential at the outer edge of the electrical double layer, r the fluid electrical conductivity, V applied the value of the voltage applied at the electrodes, Z DL ¼ ix1CDL the impedance of the double layer, C DL ¼ k the capacitance of the double layer (if the size Debye of the compact layer is negligible), x the angular frequency of the electric field and kDebye the Debye length on the electrode surface. The boundary condition used for all the electrodes is given by Eq. (2) implemented as a weak contribution on the boundary using a testð/Þð/V applied Þ test function (given by r/ ¼ ) (the applied voltage Z DL r V applied is different for each electrode depending on the grouping chosen). The inlet and outlet boundaries of the domain have periodic boundary conditions and the rest of the boundaries are set to a homogeneous Neumann boundary condition ~ n r/ ¼ 0, where ~ n is the vector normal to the surface.
2.2. Fluid flow problem The Navier–Stokes equations are solved, neglecting the inertial terms, to find the resulting fluid flow (under no external forces on the fluid):
gr2~ u rp ¼ 0
ð3Þ
r ~ u¼0
ð4Þ
where g is the fluid viscosity, ~ u the fluid velocity and p the fluid pressure. This has the following boundary condition for the fluid velocity on the surface of the double layer (which coincides with the electrode surface in the model geometry):
uslip ¼
4g
K
2 @ /ep V applied @x
The problem of interest here is the mixing of two species entering at the inlet under diffusion and convection in the channel due to ACEO. This is described by the following equation:
@c u:rc þ r:ðDrcÞ ¼ ~ @t
where c is the concentration, D the diffusion constant and ~ u the fluid velocity with x–y components u and v, respectively. The concentration at the inlet is set to c ¼ 0 for half the channel inlet cross section while the other half is set to c ¼ 1 as shown in Fig. 2. The outlet is set to convective flux while the rest of the boundaries are set to insulation (zero species flux). 3. Results The first setup examined is a pure pumping system using AC electroosmotic pumping and employing a configurable asymmetric electrode array. The array is shown in Fig. 2, where the width of the channel is assumed to be much greater than the height and therefore can be considered infinitely wide. The part shown is one of eight identical segments (in a real device the number can be much larger) which are simulated as a device. The electrodes are numbered 1, 2, 3, . . . , 24 for the top array and 25, 26, 27, . . . , 48 for the bottom one for reference. In conventional asymmetric arrays electrodes 2 and 3 for example would form a single electrode. The electrodes in Fig. 2 are such that each array has length 140 lm, electrodes 1 and 3 have length 20 lm and electrode 2 has length 40 lm while the interelectrode gaps have length 2 lm. The channel height in Fig. 2 is 200 lm. The setup presented here offers more flexibility in terms of the modes that can be realised on a single device. The first mode examined is the pure pumping mode, where the arrays are excited with AC voltage and 1 is in antiphase with 2 and 3, 4 is in antiphase with
ð5Þ
where K is the ratio of the diffuse double layer potential drop over the total double layer potential drop. The parameter K ¼ C SternCStern þC
diffuse
is
given by the ratio between the total capacitance and the diffuse double layer capacitance, and has been found experimentally for the system of interest here to be approximately 0:25 [12]. The properties of the system are summarised in Table 1. The boundary condition at the surface of the electrodes is u ¼ uslip , where V applied is different for each electrode, while the side boundaries are set to periodic boundary conditions and the boundaries at the interelectrode gaps are set to a no-slip condition. Both the electrical and fluid flow problems are solved numerically using the method of finite elements with Comsol Multiphysics.
ð6Þ
Fig. 2. Periodic segment of the array.
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50
49
Table 2 Electrode excitation table. (P) indicates a three electrode array pumping in the forward (right) direction, (P) an array pumping in the backward (left) direction and (S) an array where the two edge electrodes are in antiphase with the centre electrode. Mode/array position
Excitation
1/top 1/bottom 2/top 2/bottom 3/top 3/bottom 4/top 4/bottom
(P)(P)(P)(P)(P)(P)(P)(P) (P)(P)(P)(P)(P)(P)(P)(P) (P)(P)(P)(P)(P)(P)(P)(P) (P) (P)(P) (P) (P) (P)(P) (P) (P)(P)(P)(P)(P)(P)(S)(P) (P)(P)(P)(P)(P)(P)(S)(P) (P)(P)(P)(P) (P)(P)(P)(P) (P)(P) (P)(P)(P)(P) (P)(P) Fig. 4. Concentration plot in mode 2.
5 and 6 and so on. Therefore, the excitation mode for the wholearray is given in Table 2, where (P) indicates a three electrode array excitation pattern to induce pumping in the positive (to the right) direction. The result from this mode is shown in Fig. 3. It can be seen here that the mixing is very limited and can be attributed mostly to the diffusion of the species and to a small extent to the ACEO pumping array. In order to introduce significant mixing, other modes are tested. The best performing mode by Yoon et al. [7] is therefore examined. This is given by an alternating (P) and (P) excitation pattern which means pumping in the reverse direction on the top array, while the bottom array is always in a pumping (P) mode. The excitations are shown in Table 2. The results for the second mode are shown in Fig. 4. It can be seen that the mixing is now more than for the pure pumping mode. The novelty in the proposed design is that while in [7] these two modes have to be realised on different setups, here they can be realised on the same device simply by changing the voltage on the electrodes. Furthermore, novel modes are also possible. Another pumping–mixing mode tested is mode 3 where the electrode excitations are as in Table 2. Here another excitation pattern for the three electrode array is also defined, where the two outer electrodes such as 1 and 3 are in antiphase with the middle one, resulting in an enhanced mixing effect. This pattern is termed (S) for symmetric. The results for this mode are shown in Fig. 5. It can be seen that the mixing at the outlet is almost perfect in this case. Another possible mode (mode 4) is shown in Fig. 6, for which the excitations are shown in Table 2. The performance of the previously presented modes is usually evaluated by using the index ex defined in Eq. (7) and evaluated at the exit of the channel [13]. However, this index does not take into account the pumping performance at all, and the pumping is usually adversely affected by any changes in the excitation that depart from pure pumping mode. Therefore, a normalised index exn is defined in Eq. (8) where the pumping performance is also taken into account.
Fig. 3. Concentration plot in pure pumping mode, mode 1.
Fig. 5. Concentration plot in mode 3.
Fig. 6. Concentration plot in mode 4.
R jcðyÞ c1 jdy 100 ex 1 R jc0 c1 jdy ! R R jum :dyj jcðyÞ c1 jdy R exn R 100 1 jc0 c1 jdy up :dy
ð7Þ ð8Þ
Here um is the x-velocity at the outlet for the mode under examination, up is the x-velocity outlet for the pure pumping mode, cðyÞ the concentration distribution at the outlet, c1 the concentration distribution at the perfectly mixed state (equal to 0.5) [13] and c0 is the concentration at the inlet. It can be deduced that ex is equal to 100% when perfect mixing is achieved and therefore the higher this index is, the better the mixing performance. In exn the previous index is scaled by a ratio that accounts for the change in pumping performance associated with the change in mixing performance. This index still indicates performance, but even at perfect mixing this is not 100% (unless there is no deterioration in pumping performance). The performance of the different modes is assessed by the two indexes as shown in Table 3. It can be clearly seen that
50
N. Loucaides et al. / Microelectronic Engineering 90 (2012) 47–50
Table 3 Performance indexes. Mode
ex ð%Þ
exn ð%Þ
1 2 3 4 5 pumping 5 mixing
14 45.6 92.7 34.9 62.9 87.4
14 22.8 7.9 21.7 62.9 62.1
Fig. 8. Concentration plot in mode 5.
tation. Therefore, configurable ACEO arrays can be used in devices for pumping and mixing which can be very efficient, flexible, low power and very robust. 4. Conclusions
Fig. 7. Array configuration in mode 5.
while mode ex may give very good mixing performance, the exn index can be less than for the pure pumping mode, such as mode 3. All the modes presented here can be realised on a single array, therefore demonstrating the power of the technique presented in [10]. Furthermore, the modes can be alternated in real time, therefore offering great prospects for controlling the mixing in real time. Subsequently, a fifth mode is tested in which the swirls are created perpendicularly to the flow direction and therefore the device has to be simulated in three dimensions. The geometry and electrode setup are as in Fig. 7, with the electrodes and interelectrode gaps having the same dimensions as before, the channel width is 200 lm and the channel height is 100 lm, where an electrode array is placed only at the bottom of the channel and not at both the bottom and top as in the previous setups. In this setup, the arrays coloured red (electrodes 7, 8, 9) and blue (electrodes 31, 32, 33) are in antiphase, while the rest are in normal pumping mode. Therefore, a mixing effect is created as shown in Fig. 8. From Table 3 it can be seen that while the mixing performance is better in the combined mixing and pumping mode, the normalised performance is approximately the same as in pumping mode (the flow rate for the three-dimensional mode is calculated by integrating over the outlet area in two dimensions). However, it is demonstrated here that even with a planar array in a channel with significant height, the mixing can be enhanced by just switching two of the electrode arrays from their default pumping mode exci-
The method of configurable geometric asymmetry is applied to the problem of combined pumping and mixing using AC electroosmosis. A number of excitation modes are present here that can be realised on a single device. This demonstrates the flexibility of the method. Furthermore, novel excitation modes are tested and evaluated in comparison to pure pumping and other excitation modes previously proposed in the literature. It is found that it is possible to design modes with very good mixing performance, but there is always a trade off in pumping performance and the desired efficiency index can be used to select the mode to be utilised for a given application. Furthermore, a three-dimensional device is tested and it was found that with even simple switching of two electrodes, significant mixing can be achieved. References [1] A. Ramos, H. Morgan, N.G. Green, A. Castellanos, J. Phys. D 31 (1998) 2338– 2353. [2] A. Ramos, H. Morgan, N.G. Green, A. Castellanos, J. Colloid Interface Sci. 217 (1999) 420–422. [3] A. Ajdari, Phys. Rev. E 61 (2000) R45–R48. [4] A.B.D. Brown, C.G. Smith, A.R. Rennie, Phys. Rev. E 63 (2001) 016305. [5] M. Sigurdson, D. Wang, C. Meinhart, Lab Chip 5 (2005) 1366–1373. [6] W.Y. Ng, S. Goh, Y.C. Lam, C. Yang, I. Rodriguez, Lab Chip 9 (2009) 802–809. [7] M.S. Yoon, B.J. Kim, H.J. Sung, Int. J. Heat Fluid Flow 29 (2008) 269–280. [8] B.J. Kim, S.Y. Yoon, H.J. Sung, C.G. Smith, J. Appl. Phys. 102 (2007) 074513. [9] Y. Huang, X.W.J. Yang, F. Beckerand, P. Gascoyne, J. Hematother. Stem Cell Res. 8 (1999) 481–490. [10] N. Loucaides, A. Ramos, G.E. Georghiou, Microfluid. Nanofluid. 3 (2007) 709– 714. [11] P. Garcia-Sanchez, A. Ramos, N. Green, H. Morgan, IEEE Trans. Dielectr. Electr. Insul. 13 (2006) 670–677. [12] N.G. Green, A. Ramos, A. Gonzalez, H. Morgan, A. Castellanos, Phys. Rev. E 66 (2002) 026305–026311. [13] D. Li, Electrokinetics in Microfluidics, Academic Press, 2004.