Isaac, Kakkattukuzhy M.

Yuan, Fangping

English

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine Collaborative Research: Actively Controllable Microfluidics with Film-Confined Redox-Magnetohydrodynamics -- Video and Data 28 May 2015 A Study of Mixing in a Magnetohydrodynamic (MHD) Microfluidic Cell By Numerical Simulations Fangping Yuan Kakkattukuzhy M. Isaac Missouri University of Science and Technology, isaac@mst.edu Follow this and additional works at: https://scholarsmine.mst.edu/cr-acm  Part of the Aerospace Engineering Commons, and the Fluid Dynamics Commons Recommended Citation Yuan, Fangping and Isaac, Kakkattukuzhy M., "A Study of Mixing in a Magnetohydrodynamic (MHD) Microfluidic Cell By Numerical Simulations" (2015). Collaborative Research: Actively Controllable Microfluidics with Film-Confined Redox-Magnetohydrodynamics -- Video and Data. 4. https://scholarsmine.mst.edu/cr-acm/4 This Presentation is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Collaborative Research: Actively Controllable Microfluidics with Film-Confined Redox-Magnetohydrodynamics -- Video and Data by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. A Study of Mixing in a Magnetohydrodynamic (MHD) Microfluidic Cell By Numerical SimulationsFangping YuanK.M. IsaacMechanical and Aerospace EngineeringMissouri University of Science and Technology1Copyright © 2015 by K. M. Isaac227th ECS MeetingChicago Illinois, May 24-28, 2015Outline• What is MHD and why MHD?• Literature review in MHD microfluidics.• Geometry configuration.• Governing equations, boundary and initial conditions.• Results.• Conclusion.• Future work.• Acknowledgement.2What is MHD?• MHD = Magnetohydrodynamics.• Study the interaction between the electromagnetic force (Lorentz force) and fluid flow.• Can be used for pumping and controlling highly conductive liquid metals and plasma.• Also can be used in weakly conductive electrolyte solution in redox (reduced species-oxidized species) system. ECMHD (electrochemical magnetohydrodynamics)3Why MHD? (1)• Great interest in Lab on a chip (LOAC) devices, which are small in size and can be used in diagnosis of illness, medical treatment, detection of chemicals and synthesis of materials.• Rapid and efficient mixing is an important task among the various LOAC functions.• How to accomplish mixing in micro devices? passive and active methods are being explored.4Why MHD? (2)• Passive method: using specific channel geometry configurations to increase the interface area between fluids.• Active method: introducing driving forces or mechanical components.• Challenges: small size. difficult to manufacture.• Electrostatic force:  requires high electric potential which may introduce significant Joule heating. Bubble generation and electrode erosion are also drawbacks.• Lorentz force, which can overcome these disadvantages, becomes favorable.5Literature Review in MHD microfluidics• Can be used to induce the flow of weakly conductive electrolyte solution in redox MHD-based systems [1]. Experiments along with CFD simulations show that the flow velocity of μm/s or even mm/s is feasible by applying electric potential of ~1V and magnetic field strengths of ~0.5T [2-3].• Can be used as micro-pumps [4-5].6[1] Sen. D, K.M. Isaac, Leventis. N. Investigation of transient redox electrochemical MHD using numerical simulations. Int J heat mass Transf. 2011, 54(25), 5368-5378. [2] Leventis. N, Chan. M, Gao. X, Canalas. M, Zhang. P. Electrochemistry with stationary disk and ring-disk millielectrodes in magnetic fields. J. Phys, Chem B. 1998, 102(18), 3512-3522.[3] Qian. S.; Bau. H.H. Magnetohydrodynamic flow of Redox electrolyte. Physics of Fluids. 2005, 17(6), 067105-067105-12.[4] Lemoff. A.V., Lee, A.P. An Ac magnetohydrodynamic micro-pump. Sensors and Actuators B. 2000, 63(3), 178-185.[5] Jang. J., Lee. S.S. Theoretical and experimental study of MHD (magnetohydrodynamic) micropump. Sensors and Actuators B. 2000, 80(1), 84-89.Literature Review in MHD mixing in microfluidics• A theoretical study in MHD mixing in an annular micro-mixer in which the direction of flow reversed periodically [6].• A simple rectangle MHD minute mixer has been studied by theoretical and experiment tools [7].• Depending on the electrode placements and magnetic field orientation, secondary flows and complex chaotic advection can be generated to enhance the mixing efficiency [8,9].7[6] Gleeson. J.P., Roche. O.M., West. J., Gelb. A. Modelling annular micromixers. SIAM J. APPL. MATH. 2004, 64(4), 1294-1310. [7] Bau. H.H., Zhong. J., Yi. M. A minute magnetohydrodynamic (MHD) mixer. Sensors and Actuators B. 2001, 79(2), 207-215.[8] Rossi. L., Doorly. D., Kustrin. D. Lamination and mixing in three fundamental flow sequences driven by electromagnetic body forces. Physical Review E. 2012, 86(2), 026313-026313-14.[9] Yi. M., Qian. S., Bau. H.H. A magnetohydrodynamic chaotic stirrer. Journal of Fluid Mechanics. 2002, 468, 153-177.Geometry configuration used in this study• A cylindrical cavity with cylindrical rods inside the cavity.• Entire cavity side wall serves as counter electrode.• Inner cylinders serve as working electrode.8Governing equations, boundary and initial conditions (1)• Continuity, momentum and species conservation equations:• Lorentz force:• Current density:90.V 2L.DV p V FDt     ( ) ( ).i i i iC CV D Ct     221mi i i i iiiFJ F z N z D cRT  LF J B B      Governing equations, boundary and initial conditions (2)• Initial species concentration distribution:• Boundary conditions:on the counter electrode.    on the working electrode.where T is the time period.10, 0( , ,0) .1, 0yC x yy  wall 0.V 0 0 sin(2 / )t T  10Mixing quality• Mixing quality which is defined as [10]:• Where,          is the standard deviation of the dimensionless concentration distribution at time t:1122( )( ) 1 .(0)tt  2 ( )t22s( ) ( , , ) ( ) .    t C x y t C t dxdy[10] Qian. S. Bau. H.H. Magnetohydrodynamic stirrer for stationary and moving fluids. Sensors and Actuator B. 2005, 106(2), 859-870.Result (1)Simulation validation12Our numerical simulations of material lines, snapshots taken at t=50s, 110s and 170s Numerical simulation and dye experiment, snapshots taken every 50s. From S. Dufour’spaper [11].[11] Dufour. S., Vinsard. G., Mota. J.P., Saatdjian. E.,Physics of Fluids. 2013, 25(10), 102001-102001-16.Results (2)Concentric cylinder, configuration (a)• In all simulations, 0.1M KCl solution has been chosen as the electrolyte.• The electrical conductivity: σ=1.29 S/m.• Diffusion coefficient D=1.0×10-11 m2/s.• Dynamic viscosity: μ=0.001003 kg/m-s. • Magnetic field B is uniform and perpendicular to the x-y plane.• Applied potential on the counter electrode is zero.• Applied potential on working electrode is set as:130 sin(2 / )t T  Results (3)Concentric cylinder, configuration (a)(a)                                                                  (b)14(a): Time evolution of the electric current and voltage on the working electrode. Concentric cylinder, T=tmax=8s and B=1.75T.(b): Time evolution of maximum velocity magnitude in the whole domain. Concentric cylinder, T=tmax=8s and B=1.75T.Results (4)Concentric cylinder, configuration (a)15Velocity vectors att=3s and 6s. Concentric cylinder T=tmax=8s and B=1.75T.Time evolution of species mass fraction at t=0s, 1s, 2s, 3s, 4s, 5s, 6s and 8s. Concentric cylinder, T=tmax=8s and B=1.75T.0s 1s 2s 3s4s 5s 6s 8s3s 6sConcentric cylinder, T=8s, B=1.75T16Results (5)Concentric cylinder, configuration (a)17(a)                                                               (b)(a): Time evolution of mixing qualities with different time period T.(b): Final mixing quality (solid line with circle symbol) and the maximum velocity magnitude (dashed line with delta symbol) as a function of time period T. Concentric cylinder, tmax=15s and B=1.75T.Results (6)Concentric cylinder, configuration (a)• Time evolution of species mass fraction of T=2s, 4s and 10s. Snapshots are taken every T/2.T=2sT=4sT=10sUnmixed region near the wall18Results (7)Concentric cylinder, configuration (a)• The effect of magnetic field intensity B. Concentric cylinder model, T=8s, t=16s.(a)                                                              (b)• (a): Mixing quality as a function of time t with different magnetic field intensity B.• (b): Final mixing quality and maximum velocity magnitude as a function of magnetic field intensity B. Concentric cylinder, T=8s and tmax=16s. 19Results (8)Configurations (b)-(d)20I II III IVabcSpecies mass fraction contours for (I): eccentric cylinder, (II): two electrodes at 6 and 9 o’clock positions, (III): two electrodes at 3 and 9 o’clock positions with same signs for potential boundary conditions and (IV): two electrodes at 3 and 9 o’clock positions with opposite signs for potential boundary conditions. t=T/4 (a), T/2 (b) and T (c). T=tmax=8s and B=1.75T.T/4T/2TResults (9)Configuration (b)-(d)21Left figure: Stream function at t=2s. (a): eccentric cylinder, (b): two electrodes at 6 and 9 o’clock positions with identical potential boundary conditions, (c): two electrodes at 3 and 9 o’clock positions with identical potential boundary conditions and (d): two electrodes at 3 and 9 o’clock positions with potential boundary conditions with the sign reversed. T=tmax=8s and B=1.75T.Right figure: Mixing quality α as a function of time t. Black lines corresponds to figure a on the left, Green->b, Blue->c and Red->d.a bc dResults (10)Configuration (e)• Four working electrodes model.• Alternative scheme to produce chaotic advection.• Each pair of electrodes (AC and BD) generates a counter-rotating flow and the two pairs alternatively switch on and off.• For the first half period,• For the next half period,22A 0 C 0 B Dsin(2 / ), sin(2 / ), 0 ( / 2)t T t T kT t kT T              A B 0 D 00, sin(2 / ), sin(2 / ) ( / 2 ( 1) )C t T t T kT T t k T               Results (11)Configuration (e), B=1.75T(a)                                                                     (b)23(a): Mixing quality vs. time for different time periods T. Color coding: Red: T=2s, Green: T=4s, Blue: T=6s and Black: T=8s. (b): Maximum velocity magnitude in the computational domain vs. time periods T. tmax = 16s and B=1.75T.T=8s, B=1.75T24Results (12)Configuration (e), B=0.5T(a)                                                                    (b)25(a): Mixing quality vs. time for different time periods T with B=0.5T and tmax=16s. Color coding: Red line: T=2s, green line: T=4s, blue line: T=6s and black line: T=8s. (b): Maximum velocity magnitudes vs. different time periods T.T=2s, B=0.5T26T=4s, B=0.5T27Conclusion• A certain level of mixing can be achieved by the simple use of sinusoidal potential boundary conditions on one pair of electrodes.• The time period has a strong influence on the mixing quality for the concentric cylinder model because of long time period allows the interface to be stretched and folded much more. Obviously, higher magnetic field intensity provides a higher velocity magnitude and therefore enhance mixing.• By introducing more than one flow structure, more complex chaotic fluidic flows can be obtained which strongly enhance mixing even under a small magnetic field intensity.28Future work• Focus on 3D simulations with detailed analysis of chaotic advection including Poincare map, material line/blob stretching experiment, Lyaponov exponent, and other similar analyses.29Acknowledgement• NSF funding, Grant Award Number CBET-1336722.• Assistantship from MAE Department at Missouri University of Science and Technology.30Thank you!• Any Questions?31

A Study of Mixing in a Magnetohydrodynamic (MHD) Microfluidic Cell By Numerical Simulations

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A Study of Mixing in a Magnetohydrodynamic (MHD) Microfluidic Cell By Numerical Simulations

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