Complex flows in microfluidic geometries

Transcription

1 Complex flows in microfluidic geometries 10 mm 10mm Casanellas, AL et al, Soft Matter, 2016 Anke Lindner, PMMH-ESPCI, Paris, Peyresq, May 29 th June 2 nd 2017

2 Blood flow Motivation Lava flow 10mm Paper fabrication Food processing 1m 1mm Often difficult to characterize: fluid and flow are complex Often small Reynolds numbers (small size, high viscosity) Microfluidic model systems

3 Some examples.. elastic flow instabilities 100 microns Laminar flow increasing flow rate Secondary flow Unstable time dependent flow solution of PEO 4Mio

4 Some examples.. deformation of semiflexible polymers Flow L = 4. 9μm γ = 2. 77s 1 Jeffery orbit Rigid fiber Stage L = 6. 8μm γ = 2. 61s 1 Fiber buckling flexible fiber L = 26. 6μm γ = 1. 76s 1 U bending very flexible fiber L = 33. 5μm γ = 1. 46s 1 S bending very flexible fiber Yanan Liu, PMMH-ESPCI, 2017

5 Some examples.. viscosity of active suspensions

6 Outline 1. Rheology and complex fluids 2. Transport dynamics of complex particles 3. Suspension rheology

7 Some comments on microfluidics Square channels Typical dimensions: 100mmx100mm Small scale Low Reynolds number Very good flow control by the geometry High shear rates (high viscoelasticity) Transparent: easy flow visualization or particle tracking Small volumes required

8 Microchannel fabrication

9 Outline 1. Rheology and complex fluids 2. Transport dynamics of complex particles 3. Suspension rheology

10 Some examples of Newtonian fluids Newtonian fluids water alcohol acetone oil honey h=1mpa.s h~1mpa.s h~0.3 mpa.s h=1 Pas h=10 Pa.s Newtonian fluids are scarce.. but very wide spread!

11 Examples of non-newtonian fluids Biology blood (red blood cells aggregate and the orient with flow, shear thinning) saliva (polymers), long and stable filaments Food mayonnaise (emulsion, oil in lemon juice or vinegar), yield stress fluid chocolate mousse, yield stress fluid beer foam, dry or humid yoghurt (xanthane, polymers) shear thinning

12 Examples of non-newtonian fluids Cosmetics tooth paste (polymers and particles), yield stress fluid hair gel(polymers), yield stress fluid creams (emulsions), yield stress fluid shampoo (polymers), normal stresses Geology lava mud (non-brownian suspensions), particles in water clay (Brownian suspensions, particles in water), very dense suspensions

13 Building materials cement Examples of non-newtonian fluids

14 Examples of non-newtonian fluid flow Resistance to elongation: tubeless siphon and droplet detachment

15 Examples of non-newtonian fluid flow «Rod climbing» - normal stresses «Die Swell» normal stresses

16 «shear thinning» Examples of non-newtonian fluid flow

17 Classical rheometers shear measurements

18 Geometries Cone - Plate Couette Plate - Plate

19 Shear thinning fluid Xanthan (rigid polymer) Viscosity plateau Power law fluid 1/l

20 How to measure normal stress differences? Cone and plate rheometer Fz Shear viscosity Now: measure normal force on plate Fz N 1 = 2 F z a 2 p Keep in mind: shear rate is a constant!

21 Example: solution of flexible polymer Shear viscosity Normal stress difference N1 c PEO solutions, c= ppm Viscosity is constant N 1 is quadratic in g, N 2 negligible p Oldroyd-B type model

22 Comment on simple shear flow Combination between rotation and elongation!

23 Experimental observations: DNA molecules Teixeira, Macromulecules, 2005

24 Normal stress differences for flexible polymers without shear under shear stretched and slightly rotated into direction of streamlines Normal stress differences Only non zero diagonal element: S xx >0 tension in direction of stream lines Other elements are zero: S yy =S zz =0. N 1 (g) = S xx - S yy >0. N 2 (g) = S yy - S zz =0

25 Droplet detachment water solution of flexible polymer Flexible polymers strongly stabilize the filament Competition between surface tension and elongational viscosity determines the thinning dynamics Can be used to determine elongational viscosity films slowed down

26 Droplet detachment water PEO solution tp time of pinch off

27 CaBER rheometer

28 CaBER rheometer Filament created by pulling two plates apart Minimal diameter measured as a function of time using a laser

29 Molecular origine

30 Coil-stretch transition Predicted by de Gennes to take place at Experimental observations Schroeder et al, Science, 2003

31 Turbulent drag reduction used by New York fireman..

32 Molecular models: «bead and dumbbell» Molecular model Two bead connected by a spring Transported by the flow Evaluate polymer contribution to stress tensor Obtain constitutive equation

33 Molecular models: Oldroyd B Oldroyd-B or «2nd order fluid» model hookian springs single relaxation time t With n concentration (number of molecules/volume) Viscosity First normal stress difference Elongational viscosity small departure from Newtonian behavior small extension rates not realistic for elongational viscosities

34 Microfluidic rheometers Characteristics of microfluidic rheometers Perfect control of flow geometry Small Reynolds number (due to small size) Small volumes required Transparent, particles (polymers) can be visualized directly in flow Channel flows Types of rheometers Relying on measurement of flow rate and pressure drop Indirect determination of non- Newtonian property

35 Measuring shear viscosities Darcy s law Q 2 h 12 h d h p x Most rheometers rely on a simultaneous measure of the flow rate and the pressure drop Can be corrected for square channel geometry Measuring flow velocities Flow profiles Average local flow velocities (thermal flow rate sensors) Koser et al. Lab on a Chip, 2013 Berthet et al. Lab on a Chip, 2010

36 Local pressure measurements- example Pressure measurements Principe Calibration Orth et al, Lab on Chip, 2011

37 Measuring shear viscosities Shear thinning fluids «Transient viscosities» Correct Darcy s law for shear thinning Direct measure of local flow profile Klessinger, Microfluidic Nanofluidic, 2013

38 Elongational viscosity OSCER (Optimized Shape Cross Slot Extensional rheometer) Flow field Birefringence measurements Haward et al, PRL, 2012

39 Elongational viscosity Measure of pressure difference (or birefringence) for a given flow rate. Haward et al, PRL, 2012

40 Cross-slot elongational viscosity Filament thinning Elongational viscosity from the thinning dynamics Here thinning imposed by the flow of the Newtonian fluid. Arratia, New J. Physics, 2009

41 Comparative rheometer for shear viscosities Y-channel Q η 1 d 1 Q η 2 d 2 Principle For a given pressure gradient the flow rate is proportional to the viscosity Q h d h i i p x The more viscous fluid occupies more space h1 h 2 d d 1 2 Simple approximation valid in the limit of Hele- Shaw flow and small viscosity difference. P. Guillot et al., Langmuir (2006).

42 Normal stress differences - Elastic flow instabilities (low Re) Laminar flow nontrivial coherent flow turbulent flow Newtonian fluids Re Laminar flow nontrivial coherent flow turbulent flow Visco-elastic fluids Wi Re inertia viscosity U W h Wi normal stresses shear stress N1 h g A. Morozov, et al., Physics Reports, 2007

43 Elastic flow instabilities experimental observations in solutions of flexible polymers Taylor Couette flow Plate plate set-up Microfluidic Channel Larson, Shaqfeh & Muller, 1990 Groisman & Steinberg, 2000 Groisman and Steinberg, Elastic instability observed for: Curved streamlines Normal stress differences

44 Elastic flow instabilities Pakdel-McKinley criterium Unified instability criterium L N1 hg 0,5 M crit ; L U P. Pakdel, G.H. McKinley, Phys. Rev. Lett. (1996) l Definitions U typical velocity l polymer relaxation time typical radius of curvature of streamlines Hoop stress

45 Example: instability onset in a serpentine microchannel Experiments Use of microfluidic systems: Easy to change geometry High shear rates (and Wi) at low Re (small size) Well known solution of flexible polymer: PEO, M W = 2x10 6, 2x varying percentage of Glycerol dilute regime Numerical simulations Same geometry 3D simulations W=H=100µm R=50µm µm UCM model to describe rheology N 2 1 2h plg h h p N1 Wi l g hg

46 Experimental observations Laminar flow increasing flow rate Unstable time dependent flow solution of PEO 4Mio

47 Instability onset Critical shear rate Critical Weissenberg number Shear rate (1/s) % Glycerol 40% Glycerol 50% Glycerol 60% Glycerol Weissenberg number % Glycerol 50% Glycerol 40% Glycerol 60% Glycerol 0% Glycerol (W=60microns) Radius (microns) R/W Solution with c=125ppm 2x10 6 MW PEO and varying percentages of Glycerol Zimm relaxation time l=0,36ms in water, varies with solvent viscosity Rodd et al, JNNFM, 143 (2007) Using Zimm relaxation time and average shear rate: g U W

48 Dependence of instability onset on radius of curvature Pakdel-McKinley criterium Critical Weissenberg number U l N1 hg 0,5 M crit Wi crit /W For channel flow Flow profile is parabolic Shear rate is not constant Radius of curvature varies R>>W, (y) R i R/W 0 Use local values, maximize, combine the two limits a

49 Critical Wi as a function of the radius of curvature Good agreement between experiments, simple theory and numerical simulations. Zilz, AL et al. Geometric scaling of purely-elastic flow instabilities, J. Fluid. Mech, 2012

50 Calibrate the serpentine rheometer Classical rheology Serpentine channel Relaxation time from viscosity and first normal stress difference Critical shear rate l N1 / h p g. 2. g c C / l 1 R W Note: one has to correct for the solvent viscosity! PEO, Mw=2x10 6, 400ppm

51 a (ms) Serpentine channel Calibration Calibrate with classical rheology measurements PEO 2 Mio l (ms) Rheometer fits proportional to h s Calibration factor C= l/c Classical rheology 400pp Serpentine 125ppm Serpentine 400ppm h s (mpas) Serpentine rheometer can now be used to access relaxation times Zilz, AL et al, Serpentine channels: micro rheometers for fluid relaxation times, Lab on Chip, 2013

52 Relaxation time measurements As a function of concentration For different molecular weights 2.0 PEO, Mw=2Mio, solvent viscosity 4,9mPas 5 lambda (ms) lambda (ms) serpentine PEO 2Mio PEO 4Mio-1 PEO 4Mio concentration (ppm) lambda (ms) classical rheometer Very good resolution even at small concentration.

53 Outline 1. Rheology and complex fluids 2. Transport dynamics of complex particles 3. Suspension rheology

54 Motivation Biofluids Separation and clogging Red blood cell under flow, Stefano Guido, Naples Biofilm in microchannel Rusconi et al, J R Soc Interface, 2011 Properties of complex suspensions Clogging of a microfilter PhD, Gbedo, 2011, Toulouse Locomotion at small Reynolds-numbers Lost circulation problems in oil wells Schlumberger Normal stresses in fiber suspensions Becker & Shelley, PRL, (2001) Bacteria: E. Coli Artificial swimmers Dreyfus et al., Nature, 2005

55 Transport dynamics of complex particles Rigid particles with complex shape Spheres Fibers Helices Microswimmers Microfabrication Flexible particles

56 Single translating sphere All illustrations from: Guazzelli, Morris, An introduction to suspension dynamics, Cambridge University Press

57 Flow field point force Guazzelli, Morris, An introduction to suspension dynamics, Cambridge University P

58 Guazzelli, Morris, An introduction to suspension dynamics, Cambridge University P Single sphere freely transported in shear flow Rotation and straining

59 Flow induced by a point stresslet - dipole Guazzelli, Morris, An introduction to suspension dynamics, Cambridge University P

60 Flow around a sphere in a shear flow Guazzelli, Morris, An introduction to suspension dynamics, Cambridge University P

61 Force and Stresslet Sedimenting sphere Freely transported sphere in shear Stokes drag Stresslet

62 Sedimenting fiber Horizontal fiber Vertical fiber Inclined fiber v 1 v 2? Falls two times quicker!

63 Sedimenting fiber Horizontal fiber Vertical fiber Inclined fiber v 1 v 2 Falls two times quicker! Fiber drifts due to anisotropic friction coefficient!

64 Elongated objects in shear flows Fiber dynamics in simple shear? Jeffery orbits! Center of mass is transported with the fluid velocity along the stream lines Fiber rotates with given dynamics and period around its axis. Jeffery, 1922

65 Jeffery orbits Solutions for an ellipsoid in simple shear in 2D (only motion in x-y-plane) Dynamics of angle f: b a f=acrtan{r tan (t/t)} with period T=2 p (r+1/r)/g r=a/b (=L/(2R)) f vs time/t for more and more elongated particles r= r= r= For more elongated particles the particle spends more time aligned with the flow direction! Period increases with increasing elongation.

66 More complex orbits in 3D! aligned with z-axis in x-y plane Guazzelli & Morris, A Physical Introduction to Suspension Dynamics, Cambridge 2012

67 Normal stress differences dilute rigid fiber suspensions Line tension of a rigid fiber in shear flow Fiber perturbs the flow by its presence, but in average (over one Jeffery orbit) the contribution to the normal stresses is zero. No experiments.

68 Shear induced migration. Can isolated particles migrate across streamlines? Spherical particles do not drift in simple shear or Poiseuille flows (reversibility of Stokes flows). Axis-symmetric particles follow the stream lines, but perform complex Jeffery orbits. What happens for non axis-symmetric particles? Curved fibers (non-chiral objects) Spirals (chiral objects) Deformable objects Importance for particle separation devices? Fiber drift together with wall interaction can lead to stable equilibrium positions function of particle properties.

69 Spirals drift in vorticity direction! Jeffery orbit aligns helix with stream linesdirection of drift In the reference frame of the helix upper part and lower part see flows of opposite directions Due to the anisotropy in drag, both segments lead to a drift velocity in the z direction Spirals drift in vorticity direction, as a function of chirality! Only works when spirals are preferentially aligned with flow! Marcos, PRL, 2009

70 Spirals drift in vorticity direction! Can be used to separate particles of different chirality in microfluidic devices! Marcos, PRL, 2009

71 E-coli bacteria in shear flows Combination between shape and activity leads to rheotaxis E-coli bacteria swim towards a given direction in simple shear flows (opposite to simple helices).. Marcos et al., PNAS, 2011

72 Transport dynamics of complex particles Rigid particles with complex shape Spheres Fibers Helices Microswimmers Microfabrication and 3D tracking Flexible particles

73 Microfabrication of polymeric fibers Projection photo-lithographie Photo sensitive fluid of PEGDA with photo-initiator: crosslinks under UV exposure Projecting a fiber 2D shape into channel P. Doyle group, MIT Control of size, concentration, orientation: Control of fiber confinement by the channel height:

74 Mechanical properties In situ beam bending experiment Deflection as a function of flow speed Balancing viscous and elastic forces allows to determine the Youngs modulus

75 Deformation of the beam The viscous flow exerts a force per length on the fiber (due to pressure gradient and viscous friction): Euler Bernoulli equation for a slender beam : leads to leads to The Young s modulus E can be measured from the deflection! Strong dependence on channel and fiber geometry!

76 Mechanical properties Young s modulus vs exposure time Young s modulus varies strongly with exposure time Duprat, AL et al, Lab on Chip, 2016

77 Micro-helix fabrication - I Flow coating nano-ribbons Flexible Spontaneaous ribbons when helix released formation ON TOP when OF relased IN water t Long, flexible ribbons CdSe Quantum Dots 10 μm Al Crosby, UMass, Amherst Kim et al, Advanced Materials, 2010 Pham et al, Advanced Materials, 2013 Fluorescent Lee et al, Advanced PMMA Materials, µm

78 Spontaneous helix formation Ribbon cross section Helix Ribbon dimensions determine the radius R of the helix

79 Mechanical characterization PDMS 1 cm Glas s 50 μm View from side Pham et al, PRE 2015

80 Stretching of helices under flow Pham et al, 2015

81 Stretching of helices under flow Helix extension (linear) Pham, AL, et al, PRE, 2015

82 3D printed using Nanoscribe Micro-helix fabrication - II Francesca Tesser, Justine Laurent PMMH-ESPCI

83 Lagrangian tracking of swimming E.coli 3D automatic tracker T.Darnige, AL, et al. Review of Scientific Instrument, 2017

84 Lagrangian tracking of swimming E.coli Obtain 3D trajectories in the bulk at surfaces with /without flow varying environmental conditions N.Figueroa-Morales (2017) T.Darnige, AL, et al. Review of Scientific Instrument, 2017

85 Flow geometry Fiber transport in confined geometries Hele-Shaw cell Plug flow in the channel width Poiseuille flow in the channel height H Fiber geometry Top view W lateral confinement Cross-section transverse confinement

86 Single fiber transport Experimental observations Transport velocities Fiber is faster in perpendicular than in parallel direction! Berthet, AL, et al, PoF, 2014, Nagel, AL, et al, under revision, JFM, 2017

87 Consequences of transport anisotropy Anisotropic transport velocity leads to fiber drift of inclined fibers

88 Consequences of transport anisotropy Anisotropic transport velocity leads to fiber drift of inclined fibers Sedimenting fiber drifts due to anisotropic friction coefficient g Transported and sedimenting fibers drift in opposite directions!

89 Wall effects: oscillations

90 Wall effects: oscillations

91 More complex shaped fibers Rotation and drift are observed. Stable orientations reached are function of fiber shape and confinement.

92 Transport dynamics of complex particles Rigid particles with complex shape Spheres Fibers Helices Microswimmers Microfabrication and 3D tracking Flexible particles

93 Fluid-structure interactions Elastic objects can be deformed by viscous flows. Deformation can change transport properties. Here: study mainly deformation and transport of slender objects (fibers).

94 Buckling instability Elastic elongated objects show a buckling instability under compression It is energetically more favorable to bend than to compress the object above a threshold in deformation (force). For comparison: bulk objects are compressed without instability!!!

95 Buckling of elastic fibers in viscous flows Competition between viscous forces.. F v ~ h L 2 g and elastic forces F el ~ E/L 2 with E the bending modulus for elastic filaments E=Y*I Y=Youngs modulus, I=moment of inertia I pr 4 /4 for semi-flexible polymers E=kT lp lp=persitance length Control parameter elasto-visous number ~ h g L h ~ c B. 4 Strong dependence on fiber length (aspect ratio)!

96 Flexible fibers in shear flows Actin filament - a semi flexible polymer Characterization Flow geometry L c = 17μm L c = 15μm L c = 14μm Flow W=200μm Z=200μm H=500~800μm W/2 η = 1mPa s η = 7mPa s η = 28mPa s Motorized Stage Objective 63X y z Typical length: 5 mm 20 mm Width: 6 nm Persistence length lp: 17 mm B l p kt Top view z~200μm see also Harasim PRL 2013 and Kantsler, PRL, 2012

97 Experimental observations Flow L = 4. 9μm γ = 2. 77s 1 Jeffery orbit Rigid fiber Stage L = 6. 8μm γ = 2. 61s 1 Fiber buckling flexible fiber L = 26. 6μm γ = 1. 76s 1 U bending very flexible fiber L = 33. 5μm γ = 1. 46s 1 S bending very flexible fiber Yanan Liu, PMMH

98 Characteristic of typical dynamics Jeffery orbit C shape buckling L ee /L E φ/π End to end distance over length Bending energy Angle between L ee and u x over π

99 Characteristic of typical dynamics U shape bending S shape bending

100 Evolution of typical dynamics ζ= 8πη γl4 /c B

101 Evolution of typical dynamics comparison to simulations Simulations: Chakrabarti B. & Saintillan D. (non-linear slender body + Brownian fluctuations)

102 Evolution of typical dynamics comparison to simulations U and S Transition? Role of Brownian fluctuations? Buckling transition Becker et al, PRL, (2001)

103 Fiber in shear flow - simulations Jeffery orbit and buckling instability Buckling threshold h * 152,6 Becker & Shelley, PRL, (2001)

104 Stretch coil transition leads to normal stress differences.

105 First Normal Stress difference over one period First normal stress difference Shear stress Tornberg et al, J. Comp. Phys, 2004

106 Flexible fiber: confined geometry Fiber transported in plug flow Slight deformation of the fiber (inverse C shape). Jean Cappello, PMMH

107 Flexible fiber: confined geometry Fiber transported in plug flow Slight deformation of the fiber (inverse C shape).

108 Why do they deform? Total viscous drag balances gravity -> sedimentation speed But.. Spheres on the outside lack neighbors, so they feel more friction! Viscous force not uniform (higher order terms in 1/ln(L/R)) - > deformation!

109 Why do they deform? Li et al, JFM, 2013

110 Predicted fiber shape in good agreement with experimental observations! Fiber is a local pressure distribution sensor! with F. Gallaire, EPFL, Lausanne Flexible fiber: C-shape Force per length on the fiber Resulting fiber shape (using Euler elastica)

111 Fiber buckling in sedimentation Numerical simulations (Saintillan, UCSD and Spanoglie, Wisconsin) Buckling threshold can be determined Filament is under compression in the bottom part and under extension in the upper part! Li et al, JFM, 2013

112 Why do they deform? Total viscous drag balances gravity -> sedimentation speed, but. Spheres on the outside lack neighbors, so they feel more friction. Viscous force not uniform (higher order terms in 1/ln(L/R)) Filament is under compression in the bottom part and under extension in the upper part -> buckling instability can occur!

113 Flexible fiber: buckling Confined fiber in plug flow Jean Cappello, PMMH-ESPCI, 2017

114 Flexible fiber: buckling Confined fiber in plug flow Jean Cappello, PMMH-ESPCI, 2017

115 Outline 1. Rheology and complex fluids 2. Transport dynamics of complex particles 3. Suspension rheology

116 Active suspensions E-coli bacteria

117 Swimming at low Reynolds number Low Reynolds number Far field description velocity field No net force No net torque Sign of dipole depends on swimming strategie Shun Pak and Lauga, Theoretical models in low Reynolds-number locomotion, 2014

118 Microswimmers Pusher Puller E.Coli Clamydomonas reinhardtii Drescher et al, PNAS, 2011 Drescher et al. PRL (2010)

119 Effective shear viscosity of a suspension of microswimmers Particles elongated active orientation under shear force dipole Predictions of the effective viscosity

120 Mean orientation of elongated particles in shear flow Jeffery orbit Mean orientation including noise under shear Increasing shear rate Elongated objects rotate under shear Spend most of the time aligned with shear rate Noise for bacteria: rotary diffusion tumbling D.Saintillan, Exp. Mech. (2010) Very little direct measurements for bacteria up to now.

121 Consequence of disturbance field Anisotropic orientation and force dipole Pushers n Viscosity decrease for pusher like bacteria Theoretical models rely on description of distribution of orientation of individual bacteria. Hatwalne et al, PRL, 2004

122 Bacterial suspension Q Adapt a microfluidic rheometer measurement region η 1 d 1 h=100mm w=600mm Suspending fluid Q Q 1 12 η 2 3 h d h i i p x 2 1 Advantages of the measurement technique: Very good resolution on the viscosity Reasonable to impose small shear rates Small volumes needed In-situ visualization P.Guillot et al., Langmuir (2006) h1 h 2 d 2 g m d d 1 2 6Q h d

123 Compare motile to non-motile bacteria Viscosity measurements Relative viscosity : h r f=0.8% Non-Motile Bacteria Motile Bacteria Shear rate : g (Hz) f=0.8% Non-Newtonian viscosity of active suspensions revealed : non-monotonic behavio Maximum at shear rate of 20s -1 (comparable to V/L~ 10 s -1 ) Gachelin et al, Non-Newtonian viscosity of E-coli suspensions, Phys. Rev. Lett. 2013

124 Compare motile to non-motile bacteria Viscosity measurements Theoretical predictions f=0.8% Saintillan and Shelley, CRAS, 2013 Non-Newtonian viscosity of active suspensions revealed : non-monotonic behavio Maximum at shear rate of 20s -1 (comparable to V/L~ 10 s -1 ) Gachelin et al, Non-Newtonian viscosity of E-coli suspensions, Phys. Rev. Lett. 2013