Viscoelastic fluid flow past a confined cylinder in microfluidic devices

Vera M. Ribeiroa), Paulo M. Coelhob), Fernando T. Pinhob) and Manuel A. Alvesa)

Faculty of Engineering - University of Porto - Portugal CEFT - a) Dep. of Chemical Eng.; b) Dep. Mechanical Eng.;

XVIth International Congress on Rheology

August, 05 – 10, 2012 • Lisbon, Portugal

Outline

Objectives

Experimental

Rheological characterization

Numerical method

Results

Conclusions

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Set-up Techniques

Objectives

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Benchmark problem in computational rheology(Brown and McKinley,

1994)

Newtonian and viscoelastic flow past

a confined cylinder

Micro-scale increase De

decreases Re

highly elastic effects without inertial effects

Blockage ratio of 50%

Three-dimensional effects in laminar flow past a confined cylinderRibeiro, V.M., Coelho, P.M., Pinho, F.T., Alves, M.A.

Chemical Engineering Science (2012)

Previous work:

Three dimensional effects and stability of viscoelastic fluid flow past a confined cylinder

V.M. Ribeiro, F.T. Pinho, P.M. Coelho and M.A. Alves83rd Annual Meeting of SoR (2011).

Present work:

Macro-scale

Objectives

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Shear-thinningShear-thinningto assess influence of aspect ratio - AR

to assess influence of aspect ratio - AR

NewtonianNewtonian

BogerBoger for BR = 50 %

• Important for validation of 3D numerical codes

Experimental study:

Numerical study:

• To compared with the experimental results (Newtonian and Boger)

BR = 50%

Experimental - Microchannels

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

D = 100 μmH = 200 μm

2.0

1.0

0.5Flow direction

zx

yCoordinate

system

퐴푅 =퐷푒푝ℎ푡(ℎ)

퐷푖푎푚푒푡푒푟(퐷)퐵푅 =퐷푖푎푚푒푡푒푟(퐷)푊푖푑ℎ푡(퐻)

AR h = 200 μm

h = 100 μm

h = 50 μm

Experimental - Techniques

Flow visualizations

Velocity measurements

Streak-line photography

μPIV Micro-particle Image Velocimetry

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Inverted epifluorescence microscope

(DMI 5000M, Leica Microsystems)

Rheological characterization

Fluid PAA(ppm)

Glycerine(%)

Water(%)

NaCl(%)

Newtonian - 40 60 -

Shear-thinning 1000 - 99.9 -

Boger PAA200 200 85 13.98 1.0

Newtonian

η20ºC = 0.00360 Pa.s

Boger Fluid

hp = 0.042 Pa.s

hs = 0.123 Pa·s

λ = 82.2 ms

Oldrody- B model

Shear Rheometer

Extensional Rheometer

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Cone-plate system; D = 75 mm; 1º angle;

(Anton Paar, model Physica MCR 301)

(Haake CaBER 1, Thermo Scientific)

Seeded with 1 µm fluorescent polystyrene tracer particles

(Nile Red, Molecular Probes, Invitrogen, Ex/Em: 520/580 nm)

Numerical method

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

0 u

Mass conservation: Momentum conservation:

Discretization:

Diffusive terms – Central differences

Convective terms – High-resolution scheme – CUBISTA (Alves et al., 2003)

Finite-volume method (Oliveira et al., 1998)

2 h

u uu τ uspt

Constitutive Equation:

T T h

ττ uτ u u τ u u τPt+ + +

0 20 40 60 80 100 120 140 1600

2

4

6

AR = 0.5

AR = 1

L v /

R

Re

AR = 2

Results - Newtonian

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

• Lv decreases with AR

• Lv increases with Re

AR = 2 AR = 1 AR = 0.5

Re = 40

Lv

Results - Newtonian

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

-10 -5 0 5 10 15 20-0.5

0.0

0.5

1.0

1.5

2.0

2.5

u / U

x / R-10 -5 0 5 10 15 20

x / R-10 -5 0 5 10 15 20

x / R

AR = 2 AR = 1 AR = 0.5

Re = 40 Re = 40Re = 40

Re = 10 Re = 10 Re = 10

The development lenghts required increase with Re and AR

The fully-developed velocity is independent of Re and decreases as AR decrease

Due to the geometric

confinement

• Lv increases with Re and decreases with AR

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Boger

Appearance of an elastic instability at a Dec

Symmetric

Asymmetric and stable

De = 1.0

De = 40.0

Unstable

depends on AR

Results - Boger

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

AR = 2 AR = 1 AR = 0.5

Appearance of an elastic instability

at a Dec

Symmetric

Asymmetric and Stable

De = 1.0

De = 50.0

Unstable

Dec ≈ 9.5Dec ≈ 12.0 Dec ≈ 9.5

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results - Boger

De = 4.8De = 19.3 De = 35.2

AR = 1

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Boger

AR = 1 AR = 0.5AR = 2

De = 33.8

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Boger

AR = 2

The development lenghts required increase with De

AR = 1 AR = 0.5

-15 -10 -5 0 5 10 15

x / R-15 -10 -5 0 5 10 15

0.0

0.5

1.0

1.5

2.0

2.5

u / U

x / R

The deceleration is independent of De The fully-developed velocity is independent of De and

descreases as AR decrease

De = 9.6

De = 1.2De = 1.2

De = 9.6

De

The numercial results predicted well the

experimental results

-15 -10 -5 0 5 10 150.0

0.5

1.0

1.5

2.0

2.5

x / R

Elastic effect

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Shear-thinning

Appearance of an elastic instability at a Dec

Symmetric flow

Asymmetric and time-dependent

De = 10.0

De = 1500

Unstable

depends on AR

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Shear-thinning

AR = 2 AR = 1 AR = 0.5

Dec ≈ 200

De = 10.0

Dec ≈ 290

De = 3500

Dec ≈ 220Appearance of an elastic instability

at a Dec

Symmetric

Asymmetric and time-dependent

Unstable

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Shear-thinning

De = 670

AR = 0.5AR = 1AR = 2

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Results – Shear-thinning

AR = 2 AR = 0.5AR = 1

-15 -10 -5 0 5 10 150.0

0.5

1.0

1.5

2.0

u / U

x / R-15 -10 -5 0 5 10 15

0.0

0.5

1.0

1.5

2.0

u / U

x / R

-15 -10 -5 0 5 10 150.0

0.5

1.0

1.5

2.0

u / U

x / R

De = 220

De = 56

The shear-thinning of the fluid leads to a decrease of the

fully-developed velocity

The deceleration occurs further for higher De

The development lenghts required increases with De

Elastic effect

The fully-developed velocity is independent of De and

decreases as AR decrease

DeDe = 220

De = 56

De = 220

De = 56

Conclusions

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Newtonianfluid

Viscoelastic fluids

Recirculation lenght decreases with AR

The deceleration (upstream) and the recovery (dowstream) of the velocity depends on AR and Re

Dec decrease as AR decrease

The development lenghts required for the fully-developed velocity increases with De

The fully-developed velocity:

The shear-thinning behavior of the fluid leads to a decrease of the fully-developed velocity

decreases as AR decrease is independent of De due to the geometric

confinement

due to the elasticity of the fluids

Future Work

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Newtonian and viscoelastic fluid flow in microfluidic devices

Blockage ratio, BR = 50 %

Effect of blockage ratio, BR

50 %

2 1 0.5

Effect of aspect ratio, AR:

25 %

75 %

Acknoledgements

V.M. Ribeiro, P.M. Coelho, F.T. Pinho, M.A. Alves Viscoelastic fluid flow past a confined cylinder in microfluidic devices XVIth ICR - 07 August 2012 • Lisbon, Portugal

Fundação para a Ciência e a Tecnologia (FCT),COMPETE and FEDER for the financial support throughprojects:

• Scholarship SFRH/BD/44737/2008

• Project PTDC/ECM/70744/2006

• PTDC/EME-MFE/114322/2009

CEFT group