Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502 Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci. International Science Congress Association 83 Numerical Simulation of Time-Dependent Electro-osmotic Micro-Mixer for Laboratory-On-a-Chip Applications Charmin Asghar, Fazlalipour Hossein, Hadji Aghayie and Vafaie Reza Department of Electrical Engineering, Ahar branch, Islamic Azad University, Ahar, IRAN Available online at: www.isca.in,www.isca.me Received 10th January 2014, revised 23rd April 2014, accepted 27th May 2014Abstract Design of Laboratory-On-a-Chip (LOC) devices and components such as micro-pump, micro-mixer, micro-separator, and micro-needle are main challenges in chemical and biological micro-engineering process. Due to low Reynolds number in micro-channel we need to perturb the fluid by time-dependent secondary lateral force. In this paper we design a novel miniaturized micro-channel with embedded electrodes in both micro-chamber and micro-channel. Efficient electro-osmotic flows are generated near the electrodes by exciting the electrodes properly. We studied the interaction between the fluids behavior, electric field and convection-diffusion equation in the proposed model. Velocity field and concentration analysis revealed a high performance mixing efficiency (above 96%) for a 130µm long mixer. The exciting parameters such as frequency and voltage effect are discussed to optimize the proposed micro-mixer. Keywords: Laboratory-On-a-Chip, Low Reynolds number, Chaotic regime, Micro-mixer, electro-osmotic force. IntroductionMicro process engineering is the science of various physics and applications1-4. In last decades, advances in micro-process engineering have been applied in biological testing and chemical laboratory applications. Laboratory-On-a-Chip (LOC) devices integrate the micro-mixers, micro-pumps, micro-valves, micro-separators, micro-reactors and detectors in a chip and done the whole process with small fluid and sample volume, in short time and low cost. In most processes we need to mix two or multiple fluids (for example: blood solution with particles or biomarkers immersed in a buffer solution) and the mixing efficiency, mixing time and controlling the time is very important. Perform the mixing operation in a micro-channel resulting to low Reynolds number flow (equation-1): Re(1) Where, Re is the dimension less Reynolds number, is the fluid density, U is the average flow velocity, d is the hydraulic diameter of the channel and µ is the dynamic viscosity of the liquid. Without external force, the main transport phenomenon in micro-channel is the molecular diffusion, so the mixing performance is poor. Broadly speaking, micro-mixers can be categorized to passive and active types. The passive micro-mixer perturbs the fluid streamlines by complicated channel geometry, such as serial lamination micro-mixer, enhance the mixing process by obstacles. Contrary to the passive mixers, the active mixers achieving a mixing process by using external force to improve the mixing effect, including ultrasonic perturbation, electro-kinetic instability mixer and so on. The chaotic regime is more efficient to generate significant increase in the fluids interfacial contact area and overcome the viscous resistance of the fluid flow. Recently the chaotic mechanism is used to mix low Reynolds number liquids, associated with stretching, folding and breaking process. AC electro-osmotic force shows the potential for application in LOC devices. If a tangential electric field is applied to an electrolyte solution, the charges in the electrical double layer between the electrolyte and the surface experience a significant force. As a result, these double layer charges move, pulling the fluid along the micro-channel, and generating a flow, called electro-osmotic effect10. A ring electro-kinetic chaotic micromixer with integrated electrodes was designed by Chen, H. and et al11. This study investigates mixing process in a novel miniaturized micro-chamber and micro-channel. The paper is organized as follows: First, the methods and design of the micro-mixer will be described in Section 2. Second, the micro-mixer design, theory, and the initial/boundary conditions of the proposed micro-mixer will be described in Section 3. Third, a set of simulations will perform to investigate a chaotic regime and corresponding mixing performance in Section 4. The both geometrical and excitation parameters are going to be investigated in this section. Finally, conclusion and comparison with same works will be presented in Section 5. Material and Methods In this work, we use the both chamber and channel for high throughput mixing process. Actually, two fluid at nano-liter scale inter the micro-channel (from inlets A and B), we use a miniaturized micro-chamber for premixing process (LChamber) and then the high performance mixing will be occurred in the micro-channel (LMix). Curvatures ‘r’ at the corners of the model Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 84 enhances generation of electro-osmotic flow (the Coanda effect). The design and the value of geometrical parameters are visualized in figure-1 and the dimensions were assigned in accordance with table-1. Four electrodes are embedded in the chamber and some electrodes are embedded in the long micro-channel (the size and positions of the electrodes are shown in figure-1). We design an AC electro-osmotic micro-pump for Lab-On-a-Chip applications12. So, it assumes the pumping process occurred by AC electro-osmotic pump and we perturb the initial pumped fluid by time-dependent electro-osmotic force. Table-1 Geometrical parameters of the micro-mixerSymbol Description Value m) W Chamber Width of the chamber 40 W Channel Width of the channel 20 L elec Length of the electrodes 8 interface Length between the electrodes in the channel 14 d Length between the electrodes in the chamber 3 L i Length of the channel before the chamber 15 Lo Length of the channel after the last electrode 31 r Curvature radius of the chamber 5 Electro-osmotic Theory and Initial/Boundary Conditions: As discussed earlier, the initial mixing performance relies on molecular diffusion and is poor, but we can improve it by electro-osmotic force. In order to solve the mixing process we need to solve the Navier-Stokes equation (equation-2) and continuity equation (equation-3)13. (2) .0(3) Where, is the fluid density, is the bulk electroosmotic flow velocity, is the pressure in the microchannel, is the fluid viscosity, is the net electric charge density, and is the local electric field strength. The interaction between electrical double layer (EDL) and excess ions represents the electrical driving force which can be expressed as14: -Ñ (4) Where, is the applied electric potential. The charges in the EDL will experience an efficient force by applying a tangential electric field. As a result, the charges move, pulling the fluid along and generating a secondary flow called as electro-osmotic flow. The electroosmotic velocity (osmoticelectro) is approximated by Helmholts-Smoluchowski equation (equation-5). This approximation is valid only for thin double layer (typically 10 nm)14: Figure-1 Schematic view of geometrical parameters of the miniaturized micro-mixer (including micro-chamber, micro-channel, micro-electrodes, inlets and outlet) Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 85 osmoticelectro (5) Where is the dielectric permittivity in a vacuum,is the relative dielectric permittivity of the solution,is the electro-osmotic zeta potential, is the fluid dynamic viscosity and is the electric field. Another equation required for solving mixing process is Convection-Diffusion equation (equation-6), which solve the concentration field of the solutions. The effect of electroosmotic flow is considered as slip wall boundary condition for fluid motion equation. phoreticelectroosmoticelectro (6) Where is the concentration of species (Species concentration of the fluids A and B are described by 1 and 0 mol.m-3, respectively), is the diffusion coefficient of the fluid A and B, osmoticelectro is the electroosmotic velocity of the solutions, and phoreticelectro is the electrophoretic velocity of the solutions. phoreticelectro is negligible in comparison with osmoticelectro15. Material properties of the proposed micro-mixer were assigned in accordance with table-2. Initial and boundary conditions of the micro-mixer are visualized in figure-2. As shown in figure-2, the electrodes are located in the side walls and excited by time-dependent voltages)),),)and). The phase difference between and is 180 degrees (there is similar relation between the)()(and). As discussed earlier, the current simulation model considers the laminar flow due to the small characteristic length scale. It mixes two species in to the micro channel. It assumes the variation in the fluid concentration does not alter the viscosity and density properties of two fluids16. The mean velocity of the initial fluid is (driven by AC electro osmotic17. The pressures at the inlet and outlet of the micro-channel were specified as zero () and also pressure gradient at the micro-channel walls set to be zero, considering no flux across the walls (). Table-2 Fluid material properties, excitation and related diffusion parameters of the mixing process11Symbol Description Value Density of fluid 1×10 3 [kg.m - 3 ] µ Viscosity of fluid 1×10 - 3 [N.s.m - 2 ]  Vacuum permittivity 8.854×10 - 12 [F.m - 1 ]  Dielectric constant 80.2 U 0 Mean input velocity 0.1 [mm.s - 1 ] Zeta Potential for Si or Glass channels -80 [mVolt] Amplitude of electric potential (t) and ((t) = 1 (t)) 150 [mVolt] Amplitude of electric potential (t) and ((t) = 4 (t)) 100 [mVolt] ƒ Excitation frequency 4 [Hz] D Diffusion coefficient 1×10 - 11 [m 2 .s - 1 ] Figure-2 Boundary conditions; fluids A and B are taken into the channel with different concentration and the micro-electrodes are placed in the side walls of the micro-chamber and micro-channel to mix them. The inlets, outlet and black boundary lines are electrical insulation. The side walls, except the surface of the electrodes (shown with the black lines) have slip velocity condition corresponding with U= -E/µ Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 86 As shown in figure-2, the electrodes in the side walls are excited by applying (t) and insulation conditions were applied at other boundary conditions. We can solve the transverse electric potential by Laplace equation () and subject to the boundary conditions shown in Figure-2. The potential effect determines by slip boundary conditions, so, we apply and at the micro-channel walls, and at the inlet and outlet of the micro-channel. The electrodes are excited and all the three, incompressible Navier-Stokes equation, Convection-Diffusion of species equation and electric field are solved with finite element method18,19. Results and Discussion A set of numerical simulations were performed to evaluate the proposed high throughput micro-mixer. Secondary flow streamlines are generated in different times by applying efficient electric potential to the electrodes. Velocity field streamlines and electric potential during a period of the sinusoidal wave are illustrated in figure-3. Resulting, time-varying flow patterns will generate by interaction between the primary steady flow and oscillatory external electric field20. When the electrodes are excited, different flow patterns are generated by interacting between the initially pumped fluid and secondary oscillating electric field. These secondary flow streamlines cause chaotic regime in the micro-channel and resulting high performance mixing process. We generate flow patterns in the micro-chamber stronger than that of in the micro-channel. So called, the electro-osmotic flows are time-dependent with the frequency of ƒ. Resulting, we can see rotation effects near the electrodes. Actually, we stretch, fold and break the two fluids up (solute and solvent) sufficiently in the micro-chamber by applying sinusoidal wave))and, which increase the interfacial area between the fluids21. Pre-mixed fluid in the micro-chamber, will be thoroughly mixed by applying a set of sinusoidal waves ()()(and) in the micro-channel. Figure-4 illustrates the species concentration distribution caused by electro-osmotic flow. Figure-3 Electric potential surface plot and Fluid velocity streamlines in a period of time (t = 0.25sec) Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 87 Figure-4 Species concentration distribution, two fluids are taken into the channel with different concentration C = 1 and 0 [mol/m3]. The generated ac electro-osmotic flows cause repeatedly stretching and folding actions, resulting a high performance mixing process (C is about 0.5 [mol/m3] at the outlet) As discussed earlier, when the electrodes are not excited, the mixing process is based on molecular diffusion (figure-4(a)). But, when the electrodes are excited, chaotic perturbation associated with stretching, folding and breaking the fluids up will occur repeatedly. Concentration profiles at the outlet of the mixer are shown for various times (t = 0, 0.25, 0.6875 and 1 second) as a function of channel width in Figure-5. As shown in the figure, without the electro-osmotic flow the concentration profile has smooth profile. Mixing Quality: For a certain application, different mixers quality can be compared by mixing time, mixing efficiency, energy consumption, size of the mixer and some others. In order to estimate mixing process, obviously, the mixing efficiency Q at any cross-section of the channel can be quantified by the equation-1322. %.1001[dAdA (13) Where, C is the species concentration across the width of the channel, C is the species concentration in the completely mixed state (=0.5), and C is species concentration in the perfectly unmixed condition (=0 or 1). Fiqure-6 visualize mixing quality for miniaturized micro-mixer. Mixing efficiency of the proposed mixer is over 96 % in a one second. Therefore, it is very efficient for Lab-On-a-Chip applications. Optimization Parameters: The most important parameters for enhance the mixer yield, are frequency and voltage of the applied sinusoidal wave. We can control the electro-osmotic flow intensity by frequency and voltage of the excitation. As shown in Figure-7 by increasing the frequency, electro-osmotic flow intensity decreases because it has not sufficient time to overcome the primary flow. Frequency range of 3[Hz] to 8[Hz] is effective for mixing process. Using high voltage amplitudes cause intensive electro-osmotic flow. But on the other hand, high voltage amplitude leads to high electric field and resulting, damage the fluid or samples. Broadly speaking, the frequency effect is more significant than amplitude. Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 88 Figure-5 Concentration C versus channel width WChannel at the outlet of the mixer; the concentration profile is shown for different times, (as shown in figure legend). It should be noted that t = 0 sec is corresponds to lack of excitation Figure-6 Mixing quality; the micro-mixer efficiency over the channel width in different times as shown in the figure legend (a). Concentration plot (b) Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 89 Figure-7 Frequency and voltage amplitude effect on mixing efficiency; this profile are plotted for two different cases of voltages, as shown in legendConclusion In this paper a novel miniaturized micro-mixer was designed and investigated numerically. We drive ac electro-osmotic flow by interaction between the initial pumped fluid and time-dependent electric field which applied to the electrodes embedded in the side walls of the channel. These flows generate intensive perturbation effects associated with stretching, folding and breaking the fluid up actions. Numerical results revealed high mixing process with efficiency of over 96% for a 130µm long channel. Since the high electric field will damage the medium fluid and cells, we use below the 0.15 Volt for voltage excitation amplitude. The frequency variation revealed the proposed mixer works efficiently at low frequencies. The mixer is compared with same type of the other mixers in accordance with table-3. Acknowledgement The authors would like to thank Ahar Branch, Islamic Azad University for the financial support of this research. References 1.Alam A. Eman, Initiation of Pharmaceutical Factories depending on more Application of Biotechnology on some Medicinal Plants Review Article, 1(ISC-2011), Res. J. Recent Sci., 398-404 (2012)2.Mussarat Y., Muhammad S. and Sajjad Mohsin., Survey Paper on Diagnosis of Breast Cancer Using Image Processing Techniques, Res. J. Recent Sci., 2(10), 88-98 (2013)3.Raeisi Fard H., Nikkhah Bahrami M. and Yousefi-Koma A., Nonlinear Analysis and Mechanical Characterization of a Micro-Switch under Piezoelectric Actuation, Res. J. Recent Sci., 2(11), 35-41 (2013)4.Chauhan Rajsinh B. and Thundil Karuppa Raj R., Numerical Investigation of External Flow around the Ahmed Reference Body Using Computational Fluid Dynamics, Res. J. Recent Sci., 1(9), 1-5 (2012)Table-3 Comparison Table Reference Mixing Type Channel width Using chamberVelociy [mm/s]Frequency [Hz]Mixing Efficiency 23 Passive-parallel 85 [µm] Without chamber 0.7 - Not reported 24 Chaotic-patterned wall 200 [µm] Without chamber 0.01-0.09 - 90 % 25 Dielectrophoretic 50 [µm] Without chamber 0.5 1 Not Reported 11 AC-Electroosmotic 10 [µm]With Circular chamber0.1 8 75 % This paper Electro-osmotic 20 [µm] With chamber 0.1 4 96 % Research Journal of Recent Sciences _____________________________________________________________ ISSN 2277-2502Vol. 4(2), 83-90, February (2015) Res.J.Recent Sci International Science Congress Association 90 5.Squires T.M. and Quake S.R., Microfluidics: Fluid physics at the nanoliter scale, Reviews of modern physics, 77, 977 (2005)6.He B., Burke B.J., Zhang X., Zhang R. and Regnier F.E., A picoliter-volume mixer for microfluidic analytical systems, Anal. Chem., 73, 1942-1947 (2001)7.Wang H., Iovenitti P., Harvey E. and Masood S., Optimizing layout of obstacles for enhanced mixing in microchannels, Smart materials and structures, 11, 662 (2002)8.Yang Z., Matsumoto S., Goto H., Matsumoto M. and Maeda R., Ultrasonic micromixer for microfluidic systems, Sensors and Actuators A: Physic., 93, 266-272 (2001)9.Oddy M., Santiago J. and Mikkelsen J., Electrokinetic instability micromixing, Anal. Chem., 73, 5822-5832, (2001)10.Morgan H. and Green N.G., AC electrokinetics: Colloids and nanoparticles. Research Study Press LTD, Baldock, Hertfordshire, England, (2003)11.Chen H., Zhang Y., Mezic I., Meinhart C. and Petzold L., Numerical simulation of an electroosmotic micromixer, Proceedings of International Mechanical Engineering Congress and Exposition, November 15-21, Washington D. C, USA, (2003)12.Mehdipour M., Vafaie R.H., Pourmand A., Poorreza E. and Ghavifekr H.B., A novel four phase AC electroosmotic micropump for lab-on-a-chip applications, in Proceedings of the 8th International Symposium on Mechatronics and its Applications (ISMA12, 2012), Sharjah, UAE, 10-12 April, (2012)13.Chang C. and Yang R.J., Computational analysis of electrokinetically driven flow mixing in microchannels with patterned blocks, Journal of Micromechanics and Microengineering, 14, 550 (2004)14.Probstein R.F., Physicochemical hydrodynamics, 833 : Wiley Online Library, (1994)15.Wu Z. and Micromixing D. Li, using induced-charge electrokinetic flow, Electrochimica Acta, 53, 5827-5835, (2008)16.Chen J. K. and Yang R. J., Electroosmotic flow mixing in zigzag microchannels, Electrophoresis., 28, 975-983, (2007)17.Ajdari A., Pumping liquids using asymmetric electrode arrays, Physical Review E, 61, 45-48 (2000)18.Kumar K. and Aggarwal M.L., A Finite Element Approach for Analysis of a Multi Leaf Spring using CAE Tools Res. J. Recent Sci., 1(2), 92-96, (2012)19.Thundil Karuppa, Raj R. and Ramsai R., Numerical study of fluid flow and effect of inlet pipe angle In catalytic converter using CFD, Res. J. Recent Sci., 1(7), 39-44 (2012)20.Vafaie R. H., Mehdipoor M., Pourmand A. and Badri H., An Electroosmotically-driven Micromixer modified for high Miniaturized Microchannels using Surface Micromachining, Biotechnology and Bioprocess Engineering, 18, 594-605, April (2013)21.Ottino J.M., The kinematics of mixing: stretching, chaos, and transport, Cambridge Univ Pr, , (1989)22.Erickson D. and Li D., Influence of surface heterogeneity on electrokinetically driven microfluidic mixing, Langmuir, 18, 1883-1892 (2002)23.Koch M., Witt H., Evans A. and Brunnschweiler A., Improved characterization technique for micromixers, Journal of Micromechanics and Microengineering 9, 156, (1999)24.Biddiss E., Erickson D. and Li D., Heterogeneous surface charge enhanced micromixing for electrokinetic flows, Analytical chemistry, 76, 3208-3213 (2004)25.Deval J., Tabeling P. and Ho C.M., A dielectrophoretic chaotic mixer Proc. MEMS’02, 15th IEEE Int. Workshop Micro Electromechanical System (Las Vegas, Nevada), 36–9, (2002)