Microfluidic rheometry on a chip

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Microfluidic rheometry on a chip

• C. J. Pipe, N. J. Kim and G. H. McKinley
• Hatsopoulos Microfluids Laboratory, MIT

Supported by NSF DMS-0406590 and NASA NNC04GA41G
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Why microfluidic rheometry?
Hong et al. (2006)

• Biology / lab-on-a-chip
• Automation of biological processing
• Insight into physiological flows
• Industry
• Liquid crystal displays, ink jet printer heads
• lubrication flows, heat management
• Convenience..!
• Small sample volumes, O(nl)
• Length scales O(µm) ? large deformation rates
  with low inertia

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Important to understand the behaviour of complex
liquids at small length scales.
Squires Quake (2005) Rev. Mod. Phys.
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Bulk micro-rheometry

• Micro-rheometry at least one length scale
  O(1 µm)
• Sliding plate µ-rheometer Dhinojwala Granick
  (1997) J. Chem. Phys.
• Clasen McKinley (2004) JNNFM
• Particulate probes Solomon Lu (2001) Curr.
  Opin. Colloid Interf.
• µ-CABER Kojic et al. (2006) J. Exp. Biology
• Microfluidic devices
• Crossed slot flow Hudson et al. (2004) App.
  Phys. Lett.
• Abrupt contractions Rodd et al. (2005, 2007)
  JNNFM
• µ-PIV profiles Degré et al. (2006) Appl. Phys.
  Lett.
• Interface rheometer Guillot et al. (2006)
  Langmuir
• Wall pressure at T-junction Zimmerman et al.
  (2006)
• Microfluid Nanofluid
• Hyperbolic contractions (Newtonian) Oliveira et
  al. (2007)
• Exp. Fluids

Hudson et al. (2004)
Rodd et al. (2005)
Guillot et al. (2006)
Zimmerman et al. (2006)
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Soft lithography and microfluidics
Fabrication of master (mould)

• Micro-fabrication permits flow devices with
  features O(1 µm).
• Soft lithography
• Simple
• Quick
• Requires spin-coater, hot plate, oven, UV lamp,
  microscope
• PDMS optically clear chemically and thermally
  stable modifiable surface properties not
  hydroscopic deformable mechanically homogeneous.

SU8
Silicon
Pouring of PDMS over master
PDMS
Cure and release PDMS bond to substrate
Glass substrate
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RheoSense VROC sensors

• Capacitive pressure sensor - less sensitive to
  temperature and packaging than piezoresistive
  sensors
• Area of sensor less than 1 mm x 1 mm
• Etched silicon 7 µm thickness
• Air gap of 5 µm between electrodes
• Bottom electrode deposited on Pyrex
• wafer
• Full scale O(50 kPa), 0.2 resolution
• Deflection of upper surface is 1 µm
• at upper design limit.

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Overview
Viscosity Straight channels
Extensional properties Contraction flows
Pipe, Majmudar McKinley High Shear Rate
Viscometry (Submitted)
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Microfluidic slit viscometer

• Measurement of the pressure difference
• for flow through a known geometry allows
• the viscosity to be calculated.
• Stokes capillary viscometer
• Ubbelohde (1933) J. Inst. Petrol. Tech.
• Baird Lodge (1974) RRC Uni. Wis.
• Laun (1983) Rheo. Acta

Pressure sensors (800x800 µm2)
Baek Magda (2003) J. Rheol.
Q
L
d
www.RheoSense.com
?P
W
Glass microchannel on gold-coated silicon base
2-D Weissenberg Rabinowitsch correction to find
wall shear rate for fluid with shear- dependent
viscosity (Macosko, Rheology, 1994)
Apparent shear rate for a Newtonian fluid,
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VSS Pressure Measurements
55 Glycerol - 45 Water solution ? 7 mPa s
Pressure vs. time plot, 3 flow rates
Q 0.3 ml/min
Q 0.2 ml/min
Q 0.3 ml/min, t 10-30 s
Q 0.1 ml/min
?P
Measure ?P(Q) ? want

• Measurements
• are steady
• dP/dx is constant
• ?P Q

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Newtonian liquids
N1-3 mineral oils, sold as calibration
fluids Parallel plates data using plate
separations of 50 µm and analyzed following
method of Connelly and Greener (1985).

• Newtonian fluids
• measure viscosity over two decades of shear rate
• shear rate range depends on viscosity of fluid
  (stress controlled device)
• High viscosity ? low shear rates.
• Low viscosity ? high shear rates O(105 s-1)

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Slightly shear-thinning liquid
Dilute polymer solution 55 Glycerol, 44.9
Water, 0.1 PEO (Mw 2x106 gmol) ?Z 0.002 s
CaBER ? 0.04 s
Microchannel captures shear-thinning behaviour up
to 5000 s-1
Nahme number (viscous heating vs. thermal
conduction)
Na lt 0.01 for water
Re lt 0.01 for N1-3 Re lt 100 for water (Onset of
turbulent flow at Re 2000) Channel entry
length 50dh Fully developed flow at 5dh for
water
Reynolds number
Entrance length
Shah and London (1978)
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Shear-thinning liquid
Water-Xanthan gum (0.3 wt)
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2-D WeissenbergRabinowitsch correction

• VROC accurately captures rate dependent
• viscosity up to rates O(30000 s-1)
• Shear-thinning behaviour extends effective
• range of VROC

? 1 (Constant viscosity, 1)
1
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Shear-banding micellar solution
Cetylpyridinium chloride / sodium salicylate 100
/ 50 mM (3.2 / 0.76 wt) in 100 mM NaCl solution
(0.56 wt) Berret et al. J. Phys. II France
(1994)
?0 14.4 Pas, ? 0.63 s
T22.5ºC
1
1/6
1

• Able to investigate
• response of micellar
• solution far beyond the
• shear stress plateau region

Pipe, Majmudar McKinley High Shear Rate
Viscometry (Submitted)
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Viscosity Straight channels
Extensional properties Contraction flows
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Planar hyperbolic contractions
Strong extensional deformation occurs in
converging flows
Free Convergence - sink flow

• Confined Convergence

Cogswell (1978) JNNFM
Can we control the extension rate?
Approximately constant extension rate generated
in flow through an axisymmetric hyperbolic
contraction (i.e. confined convergence). James,
AIChE J. (1991)
Hele-Shaw
PDMS channel
Planar hyperbolic contraction
SEM image wu 500 µm wt 25 µm ? 3 -
y
w(x)
x
z
d
1 mm
U (x,y,z)
wc width at contraction
wu width upstream
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Quantifying extensional effects
The pressure drop across a contraction can be
decomposed into components due to shear and
extensional deformation. Cogswell (1972) Polymer
Eng. Sci.
?Ptotal ?Pext ?Pshear
Measured
? const, Re lt 1 ?Pshear Q (Darcy pressure
drop) Compare with lubrication approx. for ?P
due to viscous flow through a slowly varying
contraction. Lauga et al. (2004) Phys. Fluids
Pressure drop due to extensional flow
Can estimate extensional stress for dilute
polymer solutions using Oldroyd-B model
Kinematics in extension
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Experimental set-up
Differential pressure transducer (Honeywell F.S.
35kPa200kPa)

• Micro-channels are mounted on an
• inverted microscope
• Flow seeded with latex spheres
• d 1.1 µm (c 0.02 wt)

Syringe pump Q ml/hr (Harvard PHD)

• Video camera ? Particle streaklines
• ?PIV system ? Velocity field
• Pressure transducer ? Pressure drop

Test Fluids Newtonian 55 Glycerol, 44.9 Water,
0.1 SDS Dilute polymer solution 55 Glycerol,
44.9 Water, 0.1 PEO (Mw 2x106 gmol)
Rodd et al. (2005) JNNFM
201
0.0002, 0.5
3
y
0.005, 35
w(x)
x
z
0.03, 100
d 50 µm
U (x,y,z)
wc 50 µm
wu 1000 µm
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Newtonian flow
Fluid 55 Glycerol, 44.9 Water, 0.1 SDS
Streamwise velocity for L 400µm Q 2.5 ml/hr
µ-PIV measurements
? 3
u m/s
L
Re 0.5
y µm
x µm
Streamwise velocity calculated from slowly
varying channel approximation
u m/s
y µm
Symbols measured ?P Lines ?P calculated from
slowly varying channel approximation
x µm
Excellent agreement for pressures and velocities
between experiments and theory
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Centre-line velocity (Newtonian)
Fluid 55 Glycerol, 44.9 Water, 0.1 SDS
uCL(x)
CL velocity profiles collapse well for a wide
range of flow rates and geometries.
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Viscoelastic flow regimes
Fluid 55 Glycerol, 44.9 Water, 0.1 PEO
Steady hyperbolic streamlines Q lt 0.7 ml/hr
? 3
Q 0.1 ml/hr Re 0.001
Q 0.5 ml/hr Re 0.003
Q 0.3 ml/hr Re 0.003
L 400 µm
Diverging flow at inlet Q 0.7 ml/hr
Unsteady 3-D flow at large extension rates
HeleShaw approximation fails Elastic stresses
important and streamwise pressure drop is
not dominated by shearing in thin dimension. ?
Streamlines no longer follow potential flow
solution
Q 2.0 ml/hr Re 0.02
Q 0.9 ml/hr Re 0.009
100
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Pressure drop
Glass channel with flush pressure sensors with
Rheosense
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Conclusions
RheoSense.com
Q

• Hyperbolic contractions
• Can impose extension rates
• O(1000 s-1)
• Newtonian kinematics and
• stresses well described by theory
• Large extensional stresses lead
• to break-down of Hele-Shaw flow
• Measure an apparent extensional
• viscosity

Microfluidic slit viscometer Accurately measure
shear rate dependent viscosity for a wide range
of shear-thinning fluids.
Acknowledgements Prof. Gareth McKinley
RheoSense, Dr. S.-G. Baek MIT
Trushant Majmudar, Trevor Ng Nahn-Ju Kim
(SNU/MIT) Supported by NSF DMS-0406590
and NASA NNC04GA41G
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Future work
Combine microfluidic slit viscometer with
hyperbolic contraction
Glass hyperbolic channel with flush pressure
sensors
Photo from RheoSense
P
?P
x
Monitor shear and extensional rheology
simultaneously
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EVROC Glycerol
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EVROC PEO Solution
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EVROC Aqueous xanthan gum
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?P for a viscoelastic liquid
Fluid 55 Glycerol, 44.9 Water, 0.1 PEO
Pressure drop increases when streamlines
depart from potential flow solution
? 3
L
Non-hyperbolic streamlines
Pressure drop due to extension becomes large for
De 0.5