I nverse problems in a microchannel The correlation metho d Tutorial 6 - C hristophe Ravey , C.Pradere I2M Departement TREFLE, CNRS UB1 Esplanade des Arts et Métiers 33405 Talence Cedex, France Research Areas: - Fluids and Flows - Transfers and Porous Media - Energy and Thermal Systems Roscoff, June 13 -18 2011 1
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental work 7. Results 8. Conclusion Roscoff, June 13 -18 2011 2
Objectives of the tutorial session Main goal : presentation of the correlation method -Description of the experimental bench - Microfluidics - IR Thermography -Perform real time treatment - Matlab -See the application of the method to different topics - Flow characterization - Source term detection (chemical reaction or phase change) Roscoff, June 13 -18 2011 3
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 4
Microfluidics Systems Stakes and challenges Chemistry (Lab on a chip) Drug delivery Industrial dispensers Microfluidics MEMS Everyday life (Micro Electro Mechanical Systems) Biological tests Roscoff, June 13 -18 2011 5
Microfluidics Systems Thermal characterization Field of application: chemical reaction (Rhodia) 500 µm Chemical, pharmaceutical, medical industries… Controlling the reaction Challenge Data acquisition Safety Microfluidics chip Thermochemical properties in Thermal analysis tool microfluidics Scale ( ≈ 25 µ m) Thermodynamics and Quantitative measurements kintetics data ( ≈ µW, mK, ms) 500 µm Difficulties : Reactor design Acid/base droplets reaction, film 600 fps Instrumentations, inverse methods Heterogeneous, small sizes, volumes and heat flux… Roscoff, June 13 -18 2011 6
Microfluidics Systems InfraRed Thermography Thermal microscope Instrumentation for measurement of temperature field Multiscale µm-cm Thermal - Energy Data acquisition Microsystem Size reduction Fast acquisition Energy conversion Mass data treatment Inverse methods Electronics (µchip), MEMS, Thermal properties Chemistry (µreactors), Energy control Roscoff, June 13 -18 2011 7
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 8
Experimental setup Microfluidics chip Positive mold PDMS resin pouring + reticulation Unmolding Inlet and outlet drilling Glass slide bounding Glass slide µchannel PDMS resin Roscoff, June 13 -18 2011 9
Experimental setup InfraRed Thermography for microfluidics systems 1D thermal gradient Distorted by microflow K I k=n+Nt k=n+1 k=n J IR temperature fields Flowrate Q = 500 to 1500 µL/h Generator Push Syringe Roscoff, June 13 -18 2011 10
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 11
Modeling of a microfluidics system 3D scheme of used microfluidics chip x y O Glass Thin layer 170 µm Highly conductive λ = 1 W.m -1 .K -1 z Microchannel 200 µm λ = 0.6 W.m -1 .K -1 FLOW PDMS Thick layer 1 cm Insulator λ = 0.1 W.m -1 .K -1 Assumptions: Geometry , thermal properties of layers, flow => 2D model (x,y) for IR measurements Averaged over z direction Roscoff, June 13 -18 2011 12
Modeling of a microfluidics system Heat equation inside the microchannel L x y O l 1 l 2 l 0 z T g e g T f e f Boundary conditions Roscoff, June 13 -18 2011 13
Modeling of a microfluidics system Heat equation inside the glass plate L x y O l 1 l 2 l 0 z T g e g T f e f Boundary conditions Roscoff, June 13 -18 2011 14
Modeling of a microfluidics system Overall heat equation Local thermal equilibrium between the averaged temperatures : Finite differences Roscoff, June 13 -18 2011 15
Modeling of a microfluidics system Overall heat equation T What we measure : Ф Pe Fo What we want : Source term velocity Thermal diffusivity Play with the model create different operating conditions in order to estimate different parameters . Roscoff, June 13 -18 2011 16
Modeling of a microfluidics system “Step by step” approach Without heat source Steady state Calibration of Pe Transient state flow OFF Calibration of Fo Transient state flow ON Calibration of Fo and Pe velocity temperature v Pe* Fo* Fo*+ Pe* 0 time With heat source Steady state Estimation of Pe and Ф Transient state Estimation of Pe, Fo and Ф Roscoff, June 13 -18 2011 17
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 18
The correlation method The correlation coefficient: S Example with steady state, no heat source: Y = A ⋅ X Σ − − Y Y X X ( ).( ) = Correlation between Y and X: S Y X , Σ − − Σ − Y Y X X ( )² ( ) ² Y +1 +0.8 +0.4 0 -0.4 -0.8 -1 X On the same principle, correlation between ∆T and Tx => Look for values of +1, meaning the model is valid Roscoff, June 13 -18 2011 19
The correlation method The spatial correlation coefficient velocity temperature Steady state, no heat source : v Nx Pe* Fo* Fo*+ Pe* 0 time T i,j Tx i,j I I J J Spatial correlation between ∆T and Tx Nx ∆ T i,j I Pe* i,j I if Sx i,j =1 J J Roscoff, June 13 -18 2011 20
The correlation method The temporal correlation coefficient velocity temperature Transient state, no heat source : v Pe* Fo* Fo*+ Pe* K K 0 time Tt i,j k T i,j k I I k=n+Nt k=n+Nt k=n+1 Nt k=n+1 k=n k=n J J Temporal correlation between ∆T and Tt K K if St i,j =1 Fo* i,j k ∆ T i,j k I I k=n+Nt k=n+Nt k=n+1 k=n+1 Nt k=n k=n J J Roscoff, June 13 -18 2011 21
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 22
Experimental work Experiment 1 : Steady state velocity temperature v Pe* Fo* Fo*+ Pe* 0 time (T-T0) T0 T Q = 0 µL/h Q = 500 µL/h _ = Roscoff, June 13 -18 2011 23
Experimental work Experiment 2 : Transient state velocity temperature v Pe* Fo* Fo*+ Pe* 0 time Roscoff, June 13 -18 2011 24
Experimental work Experiment 3 : Phase change The supercooling theory: T°C Liquid Temperature T L Freezing Temperature T F Nucleation Temperature T N Solid Temperature T S time Roscoff, June 13 -18 2011 25
Experimental work MATLAB, temperature fields processing Roscoff, June 13 -18 2011 26
1. Objectives of this tutorial 2. Microfluidics systems 3. Experimental Setup 4. Modeling of a microfluidics system 5. The correlation method 6. Some experimental cases 7. Results 8. Conclusion Roscoff, June 13 -18 2011 27
Results Experiment 1: Steady state -Estimated Peclet number quite stable along the microchannel. -Higher flow rates are not stable : deformation of PDMS walls -Linear evolution consistent with physics Roscoff, June 13 -18 2011 28
Results Experiment 2: Transient state Initial frame Final frame 7700 7500 0.1 0.1 7600 7400 0.2 7500 0.2 7300 7400 0.3 0.3 7200 7300 Distance (cm) Distance (cm) 0.4 0.4 7100 7200 0.5 0.5 7000 7100 0.6 7000 0.6 6900 6900 0.7 0.7 6800 6800 6700 0.8 0.8 6700 6600 0.9 0.9 0.5 1 1.5 2 2.5 3 3.5 4 0.5 1 1.5 2 2.5 3 3.5 4 Distance (cm) Distance (cm) Instant correlation coefficient Averaged estimated Fo mapping 0.8 5 5 14 0.6 10 10 12 0.4 15 15 Pixel in y direction (-) Pixel in y direction (-) 0.2 10 20 20 0 25 8 25 -0.2 30 30 6 -0.4 35 35 4 -0.6 40 40 -0.8 2 45 45 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 Pixel in x direction (-) Pixel in x direction (-) Roscoff, June 13 -18 2011 29
Results Experiment 2: Transient state 10 Inside the channel 9 fitted data outside the channel Averaged apparent Fourier number (-) fitted data 8 7 6 5 4 3 2 1 500 1000 1500 2000 2500 3000 Flow rate (µl/h) -Estimated Fo number not affected by the flow rate. -Difference between inside (water+glass) and outside (PDMS+glass) the microchannel. Roscoff, June 13 -18 2011 30
Results Experiment 3: Phase change T°C Liquid Temperature T L Freezing Temperature T F Nucleation Temperature T N Solid Temperature T S time Roscoff, June 13 -18 2011 31
Results Experiment 3: Phase change High frequency recordings : 484 Hz 4cm Question: How can we localize the heat source ? Roscoff, June 13 -18 2011 32
Results Experiment 3: Phase change Estimation of source term Correlation coefficient Roscoff, June 13 -18 2011 33
Results Experiment 3: Phase change Roscoff, June 13 -18 2011 34
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