Mid-Term Review June 16-17 2011 Concentrated suspensions under flow in microfluidic channel and migration effect Florinda SCHEMBRI*, Hugues BODIGUEL, Annie COLIN LOF Laboratory of the Future University of Bordeaux I - Rhodia - CNRS UMR5258 *florinda.schembri@eu.rhodia.com funded by
Motivation Non-Brownian suspensions and migration effect Biomedical Engineering -Fahraeus-Lindqvist effect (1931) Lab-on-a-chip technologies Fournier, R.L., Transport Phenomena in Biomedical Engineering (1999) Industrial processes -paper coating -food processing -cosmetics -paints -separation -filtration -improved encapsulation efficiency Di Carlo, et al. Anal. Chem. 80, 2204 (2008)
Migration Effect in dense suspensions Brief History -1972 Hoffman Hoffman R, Discontinuous and dilatent behavior in concentrated suspensions. I. Observation of flow instability. Trans Soc Rheol 16:155-173. - 1984 Brady & Bossis Bossis G, Brady J, Dynamic simulation of sheared suspensions. I. General method. J Chem Phys 80: 5141-5154 -1987 Leighton & Acrivos -Leighton D, Acrivos A, The shear-induced migration of particles in concentrated suspensions. J Fluid Mech 181:415-439. -1992 Laun & Co Laun HM, Bung R, Hess S, Loose W, Hess O, Hahn K, Hadicke E, Hingmann R, Schmidt F, Lindner P, Rheological and small-angle neutron scattering investigation of shear-induced particle structures of concentrated polymer dispersions submitted to plane Poiseuille and Couette flow. J Rheo 36:743-787 - 2009 Lhuillier Migration of rigid particles in non-brownian viscous suspensions, Physics of Fluids, 21, 023302. - 2010 Boyer Dense suspensions in rotating-rod flows: normal stresses and particle migration, 2009 Lhuillier Modelling particle migration Shear induced migration p 2. ( ) Φ ( Φ) 2 Φ Vi Ui = λ a γ D 9 Stress induced migration Φ ij Φ x j + a 2 B ijkl 2 Ul x x p a IK H ( V U ) 2 2 = λ( Φ) [ Φ( ρ ρ ) g + ( n σ + n Σ )] 9η f p f j k
Aim of the work Theoretical Investigation Φ 0.03 Φ p 2 ( V U ) = Φλ( Φ) i j i 9 = Φ. 2 a γ D 9η f Φ 2 + a B x ijkl p a p ( u u) 2 2 = f ( Φ) Σ ij j 2 Ul x j xk Experimental study Φ = 0.4 0.52 Simplest geometries Di Carlo, et al. APL. 99,4 (2007) Φ 0.63 MICROFLUIDICS P = P input P output Isa, et al. PRL. 98, 198305 (2007)
The microfluidic channels Image slices Image slices Capillary square tube Capillary rectangular tube z y x y 1 Suspension in 2h=100 µm l=100 mm z y x Suspension in y1 w=500 µm 2h=50 µm l=100 mm
The suspension RI and Density Matching suspension 6 µm PMMA hard spheres Thioglycerol Deionized water Thioglycerol was used in a ratio of 4:1 respect to deionized water and fluorescent labelled with rhodamine.
Control Parameters Volume fraction Φ = 0.52 4 π a 3 Φ = A h 3 n Φ = 0.5 Φ = 0.4 Pressure drop P = P input P output
Experimental system Reservoir Pi Square Glass Capillary Po 40X Flow Direction 60 Hz Confocal Piezo Suspensions driven by pressure gradients Time resolved information on the single particle level Microscopic dynamics ---- Bulk flow
Drawbacks of the experiments Initial time of the experiment Pressure >60 mbar Fluid at rest Φ = 0.4 Φ = 0.5 Φ = 0.52 Φ = 0.4 Φ = 0.4 Φ = 0.5
Drawbacks of the experiments 4 x 10-5 Steady state condition 3.5 Peak velocity (m/s) 3 2.5 2 Φ = 0.5 1.5 0 20 40 60 80 100 time (minutes) Start acquisition
Image processing Algorithm computational image analysis Band-pass filter filter in the SF domain 0.5 0.4 Circular Hough Transform Centers Filtering Trajectories Tracking (MSFD) John C. Crocker and Eric R. Weeks fy (cyc/pix) 0.3 0.2 0.1 0-0.1-0.2 Ι -0.3-0.4-0.4-0.2 0 0.2 0.4 fx (cyc/pix) Dynamical information at single particle level Velocity.. Volume fraction Reconstruction of the position of all particles, with sub-pixel accuracy and track individual particle in videos captured at high spatial and temporal resolution in the microfluidic devices.
Tracking particles x Circular Hough Transform y Two-dimensional slice, taken along the vertical axis (z), h=25 µm (half of the channel width) *Particles localization
Particle trajectories Trajectories Tracking We measure individual particle trajectories comprised of more than 50 steps across more than 100 video frames. Flow Direction
Volume fraction calculation Calibration curves Φ AREA (n) DROPLETS OF KNOWN VOLUME FRACTION φ area (n) 0.45 0.4 0.35 0.3 Φ BULK ( z, n) BULK VOLUME FRACTION 0.25 Volume=313 µm 2 x 50 µm 0.2 1000 1200 1400 1600 1800 2000 2200 Particles Number n
Results: square microchannel Number of particles in the bulk of the channel h1 Volume Fraction h4 h6 n 60 50 40 30 20 10 h1 h5 h4 h3 h2 h6 X (µm) 0 Φ INPUT 20 40 60 80 100 x (µm) = 0.5 Z (µm)
Results: square microchannel Z=10 µm X velocity (m/s) 1.6 x 10-4 1.4 1.2 1 0.8 0.6 Y 0.4 0 20 40 60 80 100 width (µm) velocity (m/s) 1.5 1 0.5 0 0 x 10-4 50 X (µm) 100 0 100 200 Y (µm) 300 400
Results: square microchannel Z=50 µm X x 10-4 velocity (m/s) 1.8 1.6 1.4 1.2 2 x 10-4 1 Y 0.8 0 20 40 60 80 100 width (µm) velocity (m/s) 2 1 0 0 X (µm) 50 100 0 200 Y (µm) 400
Results: rectangular microchannel Φ INPUT = 0.4 7 x 10-5 6 velocity (m/s) 5 4 3 2 60 mbar 40 mbar 1 0 10 20 30 40 50 z (µm)
Results: rectangular microchannel Φ INPUT = 0.4 * * Φ( z) 0.5 7 x 10-5 Velocity 0.45 0.4 0.35 6 0.3 velocity (m/s) φ 5 4 3 2 1 0 60 mbar 40 mbar 10 20 30 40 50 z (µm) * 0.25 0.2 0.15 0.1 0 10 20 30 40 50 * X z (µm)
Results: rectangular microchannel Φ ( x, z = 25µm) * * 50 40 Φ( z) φ 30 20 10 VF y mean 0.5 0.45 0.4 0.35 0 0 50 100 150 200 250 300 X (µm) φ 0.3 0.25 0.2 60 50 0.15 0.1 φ 40 30 20 VF y mean * 0 10 20 30 40 50 * X z (µm) 10 0 0 50 100 150 200 250 300 x (µm) Φ INPUT = 0.4
Results: rectangular microchannel Φ INPUT = 0.52 z=13 µm z=18 µm Φ 55 50 45 40 ( x, z = 27µm) Grey value 56 54 52 50 48 46 44 42 40 Z=13 µm Z=18 µm Z=27 µm 38 0 20 40 60 80 100 120 140 Distance X (pixels) z=27 µm φ 35 30 25 20 100 150 x (µm) 200 250
Brief-term perspectives r Φ Phase diagrams: -Pressure -Volume fraction -µchannel spot τ d
Long-term perspectives r Φ Particles vs buffer-fluid velocity Elongational flow Polydisperse emulsions τ d
Thank you for your attention