Microfluidic Free-Surface Flows: Simulation and ApplicationMicrofluidic Free-Surface Flows: Simulation and Application

J.E Sprittles

Y.D. Shikhmurzaev

Indian Institute of Technology, Mumbai

November 5th 2011

The University

Of Birmingham

Worthington 1876 – First Experiments

Worthington’s Sketches

Millimetre sized drops of milk on smoked glass.

Millimetre Drop Impact

Courtesy of Romain Rioboo

1 2

3 4

Flow Control Using Chemically Patterned Solids

Hydrophobic

Hydrophilic

Inkjet Printing: Impact of Microdrops

100 million printers sold yearly in graphic arts.

Drops ejected have:

Radius ~ 10micronsImpact ~ 10m/s

Surface physics are dominant.

Inkjet printing is now replacing traditional fabrication methods...

Polymer – Organic LED (P-OLED) Displays

Inkjet Printing of P-OLED Displays

Microdrop Impact & Spreading

Why Develop a Model?

11 - Recover Hidden Information- Recover Hidden Information

22 - Map Regimes of Spreading - Map Regimes of Spreading

3 – Experiment3 – ExperimentRioboo et al (2002) Dong et al (2002)

2mm 50 m

Previous Modelling of Drop Spreading

Phenomena

Previous Modelling of Drop Spreading

Phenomena

r

Pasandideh-Fard et al 1996

The Contact Angle

r

t

d( )d f t

d e

• Contact angle is required as a boundary condition Contact angle is required as a boundary condition for the free surface shape.for the free surface shape.

Conventional Approach – Contact Angle

1 3 2cose e e e

R

σ1

σ3 - σ2

Young Equation Young Equation Dynamic Contact Angle FormulaDynamic Contact Angle Formula

)

θd

U

Assumption:Assumption:A unique angle for each speedA unique angle for each speed

edθ = ( )f U

Is the Angle Always a Function of the Speed?(Experiments of Bayer & Megaridis 06)

1mm

60e

Water

10.18ms

10.25ms

)

U

d

-1(ms )U

d 30d d ( )f U

Hydrodynamic Assist to Wetting

Blake & Shikhmurzaev 02

U, cm/s

dθControlled Flow Rate

dθU

d ( )f U

Specific Physics of Wetting:

Interface Formation

Specific Physics of Wetting:

Interface Formation

The Simplest Model of Interface Formation (Shikhmurzaev 93)

uu 0, Re u u P + FSt

t

s1

1

1

1 1s1

1 1s11 1

11|| ||

v 0

n P n n

n P (I nn)=-

(u v ) n

( v )

5(v u )

4

s se

s sses

s

ff

t

t

* 12 || ||2

2 2s2

2 2s22 2

11

2|| || || 2 22

1,2 (0) 1,2

n [ u ( u) ] (I nn) (u U )

(u v ) n

( v )

v (u U ) , v U

s se

s sses

s s

s s

t

In the bulk:

On liquid-solid interfaces:

At contact lines:

On free surfaces:

Interface Formation Model

s s1 1 1 2 2 2

1 3 2

v e v e 0

cos

s s

d

/ 0U L

1

1 1 1 1 1||

u 0

n P n n

n P (I nn)=0

; ; v =u s s se e

ff

t

*|| ||

2 2 2 2

12|| || || 22

n [ u ( u) ] (I nn) (u U )

u U

; ;

v (u U ), v U

s se e

s s

e

Conventional Model

1,2 1,21,2 s1,2 1,2( v )

s sses

t

1,2 s

1,2 1,2 1,2 1,2( v )s

s s se

U

L t

U

Numerical Simulation of Drop Impact and

Spreading Phenomena

Numerical Simulation of Drop Impact and

Spreading Phenomena

Graded Mesh – For Both Models

The Spine Method for Free Surface Flows

The Spine

Nodes fixed on solid.

Nodes define free surface.

Arbitrary Lagrangian-Eulerian Mesh Design

JES & YDS 2011, Int. J. Num. Meth. Fluids ;JES & YDS 2011, Submitted to J. Comp. Phys.

Spines are Bipolar

Free Surface Captured Exactly

Oscillating Drops: Code Validation

For Re=100, f2 = 0.9

JES & YDS 2011, MNF, In Print

Oscillating Drops: Code Validation

a

b

Removal of Spurious Pressure

Removal of Spurious Pressure

Pressure Behaviour for Obtuse Angles

The pressure plot from a typical simulation.

Testing Ground: Flow in a Corner

dθ

U

dθ

In frame moving with contact line.

In frame fixed with solid.

U

Viscous Flow in a Corner

Spurious COMSOL ‘Solution’Spurious COMSOL ‘Solution’

JES & YDS 2011, IJNMF 65; JES & YDS 2011, CMAME 200

Our FEM SolutionOur FEM Solution

Results Results

Microdrop Spreading from Rest(Capillarity Driven Spreading)

Apex

Velocity Scale

Pressure Scale

CapillaryWave

25 m

60e

Microdrop Impact and Spreading

60e

Velocity Scale

Pressure Scale

-15ms

Speed – Angle Relationships:Comparison of IFM with Conventional Model.

0.702cos cos

tanh 4.96cos 1e d

e

U

0.01 100 1

Rest (IFM)

Impact (IFM)

-1(ms )U

Conventional Model.

d

Jiang et al 79

Increase in Contact Line Speed

Jump in Contact Line Speed

Typical Microdrop Experiment (Dong et al 07)

?

?

Early Stages of Spreading

0.5t s1.8t s2.4t s

2.2 m/s 4.4 m/s 12.2 m/s

Recovering Hidden Information

15t s11.7t s

13.4t s10t s

15t s

10t s

Influence of Wettability

130e

-15ms

Surfaces of Variable Wettability

2e1e

1 60e 2 110e

1

1.5

Impact on a Surface of Variable Wettability

4m/s Impact4m/s Impact

5m/s Impact5m/s Impact

-14ms

-15ms

Current/Future Work & Possible Avenues for

Collaboration

Current/Future Work & Possible Avenues for

Collaboration

Current Research: Dynamics at Different Scales

Millimetre Drop

Microdrop

Nanodrop

Current Research:Unexplained Phenomena in Coating Processes

Ca

d

2mmd

4mmd d

θd

Simpkins & Kuck 03

Current Research: Nanofluidics

“While inertial effects may also be important, the influence of the dynamic contact angle should not be ignored.” (Martic et al 02)

Future Research: Pore Scale Dynamics

Wetting Mode

Threshold Mode

Future Research: Additional Physical Effects

Liquid-Liquid Displacement Surfactant Transport

Future Research: Impact on Powders

Marston et al (2010) Aussillous & Quéré (2001)

Mitchinson (2010)

Future Research: Complex Capillary Phenomena

ThanksThanks

Qualitative Test: Pyramidal Drops (mm size drop)

Experiment Renardy et al.

Future Research: Multi-Physics Platform

)

Multiphysics Platform + Multiphysics Platform + Dynamic Wetting PatchDynamic Wetting Patch

Hysteresis of the Dynamic Contact Angle

• Hyteresis:Hyteresis: Receding angleReceding angle

• No hysteresisNo hysteresis -15ms

-15ms

60r e

60e 10 ;r

Small DropsHigh Impact Speed

Analytic Progress: When Does ?

Stokes Region(viscous forces dominate inertial forces)

Length of interface formation process

d ( )f U

Slow Spreading of Large Drops

Comparison With Experiments

0.0001 0.0010 0.0100 0.1000 1.0000

0

30

60

90

120

150

180

d

Ca

0.0001 0.0010 0.0100 0.1000 1.0000

0

30

60

90

120

150

180

d

Ca

Perfect wetting (Hoffman 1975; Ström et al. 1990; Fermigier & Jenffer 1991)

Partial wetting (□: Hoffman 1975;

: Burley & Kennedy 1976; , ,: Ström et al. 1990)

The theory is in good agreement with all experimental The theory is in good agreement with all experimental data published in the literature.data published in the literature.

s/P. 10-103 , 67

0.0 0.1 0.2 0.3

60

90

120

150

180d

Ca

0.0 0.1 0.2 0.3 0.4 0.5

60

90

120

150

180

d

Ca

0.0 0.1 0.2 0.3 0.4

60

90

120

150

180

d

Ca

Here experiments with fluids of differentviscosities (1.5-672 cP) are described with the same set of parameters.It is shown that the mechanism of theInterface formation is diffusive in nature (J. Coll. Interface Sci. 253,196 (2002)). Estimates for parameters of the modelhave been obtained.In particular, for water-glycerol mixtures:

where

Mechanism of relaxation

Numerical Artifacts in the Computation of

Viscous Corner Flow

Numerical Artifacts in the Computation of

Viscous Corner Flow

Pressure Behaviour for Obtuse Angles

The pressure plot from a typical simulation.

Testing Ground: Flow in a Corner

dθ

U

dθ

In frame moving with contact line.

In frame fixed with solid.

U

Obtuse Wedge Angles

Comparison to Asymptotic Solution

• Pressure along two sides of wedgePressure along two sides of wedge

Fixing the Problem

• Remove eigensolution prior to computationRemove eigensolution prior to computation

• Use condition of pressure single-valuedness to Use condition of pressure single-valuedness to determine eigensolution’s contribution.determine eigensolution’s contribution.

ComputedComputedActualActual

Pressure Regularized Successfully