Frieder Mugele

Physics of Complex Fluids University of Twente

coorganizers:

Jacco Snoeier

Physics of Fluids / UT

Anton Darhuber
Mesoscopic Transport Phenomena / Tu/e
speakers: Jos Bico (ESPCI Paris) Daniel Bonn (UvA) Michiel Kreutzer (TUD) Ralph Lindken (TUD)

program

Monday: 12:00 13:00h registration + lunch 13:00h welcome: Frieder Mugele 13:15h 14:00h Frieder Mugele: Wetting basics (Young-Laplace equation; Young equation; examples) 14:10-15:25h Jacco Snoeijer: Wetting flows: the lubrication approximation 15:25-15:50h coffee break 15:50-16:35h Jacco Snoeijer: Coating flows: the Landau-Levich problem and its solution using asymptotic matching 16:45-17:30h Anton Darhuber: Surface tension, capillary forces and disjoining pressure I Tuesday: 9:00h-9:45h Frieder Mugele: Dewetting 9:5510:40 Anton Darhuber: Surface tension, capillary forces and disjoining pressure II 10:40-11:05h coffee break 11:05h-11:50h Anton Darhuber: Surface tension-gradient-driven flows 12:00h-12:45h Daniel Bonn: Evaporating drops 12:45-14:00h lunch 14:00h-14:45h Daniel Bonn: Drop impact 15:55h-15:40h Jos Bico: Elastocapillarity (I) 15:40-16:05h coffee break 16:05h 16:50h Jos Bico: Elasticity & Capillarity (II) 18:30 -. joint dinner & get together
Wednesday: 9:00h-9:45h Michiel Kreutzer: Two-phase flow in microchannels: the Bretherton problem 9:55h-10:40h Michiel Kreutzer: Drop generation& emulsification in microchannels
10:40h-11:05h coffee break
11:05h-11:50h Michiel Kreutzer: Jet instabilities in microchannels 12:00h-12:45h Ralph Lindken: PiV characterization of capillarity-driven flows

12:45-14:00h lunch

14:00h-15:00h: occasion for excercises 15:00h-17:00h lab tour (Physics of Complex Fluids / Physics of Fluids) Thursday: 9:00h-9:45h Jacco Snoeijer: Contact line dynamics(I) 9:55h-10:40h Jacco Snoeijer: Contact line dynamics (II)
11:05h-11:50h Frieder Mugele: Wetting of heterogeneous surfaces: Wenzel, Cassie-Baxter 12:00h-12:45h: Jacco Snoeijer: Contact angle hysteresis
14:00h-14:45h Jos Bico: Sperhydrophobicity 14:55h-15:40h Anton Darhuber: Thermocapillary flows
15:40h-16:05h coffee break
16:05h-16:50h Anton Darhuber: Surfactant-driven and solutocapillary flows Friday: 9:00h-9:45h Frieder Mugele: Electrowetting: basic principles 9:55h-10:40h Frieder Mugele: Eectrowetting applications.
11:05-12:00h round up highlights / short summaries by students 12:00h closure
principles of wetting and capillarity

p = lv + = lv R R 2 1

capillary (Laplace) equation

sv sl cos Y = lv

Young equation
capillarity-induced instabilities
driving force: minimization of surface energy
time Rayleigh-Plateau instability

drops in microchannels

drop generation drop dynamics

Anna et al. APL 2003

wetting and dewetting flows
coating technology dewetting of paint
e.g. heating Landau-Levich films
fundamental flow properties

lubrication flows

contact line motion
wetting & molecular interactions

nanoscale drop

Y x0 disjoining pressure

vertical scale: 100 nm

capillary forces
capillary bridges exert mechanical forces
wetting of complex surfaces
superhydrophobic surfaces: the Lotus effect

switching wettability

voltage
electrowetting & thermocapillarity

lecture 1:

basics of wetting
wetting & liquid microdroplets

capillary equation

p = pL = 2 lv

cos Y =

sv sl lv
H. Gau et al. Science 1999 14
origin of interfacial energy
width 0: sharp interface model
(will be handled throughout this course)
range of interactions (O(nm))
surface tension is excess energy w.r.t. bulk cohesive energy unhappy molecules at interfaces lv

U coh 2a 2

interfacial tension

liquid A

liquid B
AB: interfacial tension interfacial tensions are always positive

(of immiscible fluids)

interfacial tensions matter at small scales
fraction of molecules close to the surface:

7 A dr 3dr = = V r 3

for r=1 cm for r=1 m
capillarity is crucial for micro- and nanofluidics
mechanical definition of surface tension
definition A: The mechanical work W required to create an additional surface area dA (e.g. by deforming a drop) is given by the surface tension

W = dA

F thermodynamically: = A T , N ,V

dimension and units:

[ ] = energy;

(typically: mJ/m2)

soap film

d e f i n i t i o n

definition B: is a force per unit length acting along the liquid-vapor interface aiming to shrink the interfacial area

force ; length

1N/m = 1J/m2

(typically: mN/m)

connection to definition A work required to move the rod: force per unit length per interface:

W = 2 l x

1 W f = = 2l x
surface tension of selected liquids
material water (25C) water (100C) ethanol decanol hexane decane hexadecane glycerol acetone mercury water/oil surface tension [mJ/m2] 23 28.5 19.4 23.9 27.50
T-coefficient: (-0.07 -0.15) mJ / m2K
consequences: the Laplace pressure
spherical drop R R Pdrop Pext
variation of internal energy:

dVext = dVdrop

U = pdrop dVdrop pext dVext + dA

mechanical equilibrium:

U = ( pext pdrop )dVdrop + dA = 0
p L = pdrop pext dA = dVdrop 2 R

Laplace pressure:

generalization to arbitrary surfaces
upon crossing an interface between two fluids with an interfacial tension s, the pressure increases by

+ p L = 2 = R1 R2

: mean curvature

1 = + R R 2

Young-Laplace law
R1, R2: principal radii of curvature (sphere: R1=R2)
principle radii of curvature

sign convention: air

R1 > 0

R2 < 0

mean curvature:

1 = R + R 2

liquid
( is independent of azimuthal angle )
consequence: liquid surfaces in mechanical equilibrium have a constant mean curvature
(n the absence of other forces)
H. Gau et al. Science 1999
variational derivation of Laplace equation
equilibrium surface profile
minimum of Gibbs free energy (at constant volume)

G = (Fsurf

! p V )= min
pressure: Lagrange multiplier
Fsurf: functional of surface profile A: explicit representation of surface:
Fsurf [ A] = dA z = z ( x, y )
r r r dA =| dA |= s x s y = 1 + ( x z )2 + ( y z )2 xy
Fsurf [ A] = dA = 1 + ( x z ) + ( y z ) dx dy

volume: V = z ( x, y ) dx dy

x r s x = 0 z x x

0 r s y = y z y y

functional minimization

G[ z ( x, y )] = 1 + ( x z ) + ( y z ) p z

} dx dy =! min

f ( z, x z , y z ) Euler-Lagrange equation: f 2xz xz = = S ( x z ) 2 %
d x z xx z S x z ( x z xx z + y z xy z ) / S = S 3 xx z 1 + ( x z ) + ( y z ) x z ( x z xx z + y z xy z ) = 2 dx S S
d f d f f + =0 dx ( x z ) dy ( y z ) z
d f 2 = S 3 xx z 1 + ( y z ) x z y z xy z dx ( x z )

symmetrically:

f = p z
d f 2 = S 3 yy z 1 + ( x z ) x z y z xy z dy ( y z )

Young Laplace equation

2x mean curvature
xx z (1 + ( y z ) ) 2( x z ) ( y z ) ( xy z ) + yy z (1 + ( x z ) ) p = 2 = + = 3/ 2 R R lv (1 + ( x z ) + ( y z ) )
non-linear second order partial differential equation

two-dimensional version:

p = lv

xx z 1 + ( x z )

cylindrical coordinates
surface parameterization: r = r ( , z )
volume: V = dV = dz dr r d =

S = 1 + r + ( z r ) r

dz d r 2
area: A = dA = dz r d S ( r , )

cylindrical symmetry:

r = 0 r = r ( z ) p = 3 zz r rS S
ordinary differential equation

S = 1 + ( z r ) 2

an example
fiber immersed in water (complete wetting; no gravity)

radius R

z=0 r z

1 zz r 3 Sr S

BCs: r : 0 r R: r 0

1 1+ r' r

r' ' 1+ r'
1 d r = r ' dz 1 + r '2 r' =

>0

r 1+ r'

solution:

= const. = R

(r / R )2 1

z >> R
r ( z ) = R cosh( z / R )

exp( z / R )

three phase equilibrium: wetting

= non-wetting

0<< lv

sv complete wetting

partial wetting sl: solid-liquid interfacial energy;
sv (solid-vapor); lv (liquid-vapor)
spreading parameter controls wetting behavior

partial wetting

complete wetting

spreading parameter

1 S = Finit F final = sv ( sl + lv ) A
S > 0 : complete wetting S < 0 : partial wetting
contact angle in partial wetting situation

lv sv sl

dx cos

(horizontal)

force balance

energy minimization

sv = sl + lv cos Y
W = { sl + lv cos Y sv } dx = 0

Young equation cos Y =

v: vapor or second immiscible liquid
connecting wetting behavior & surface properties
> 0 : complete wetting S = sv ( sl + lv ) < 0 : partial wetting high energy surfaces
(metals, ionic crystals, covalent materials)

are usually wetted

Ecoh 500. 5000 mJ m a

low energy surfaces

(polymers, molecular crystals)
are usually partially wetted

k BT 10. 50 mJ m a

How to relate wetting behavior to microscopic interaction energies ?

Gedankenexperiment

W = U final U init
= 2 Av 0 = VAA () VAA (d 0 ) 2 Av = VAA (d 0 ) W = Av + Bv AB

= V AB (d 0 )

(2 Bv = VBB (d 0 ) )

(I) (II)

= VAB () V AB (d 0 )

Gedankenexperiment (II)

2 Av = VAA (d 0 ) 2 Bv = VBB (d 0 ) Av + Bv AB = VAB (d 0 )
A: solid; B: liquid (III)-(II) (I) (II) (III)
sv ( lv + sl ) = S = Vll (d 0 ) Vsl (d 0 )

binding energies: <0

Vll > Vsl Vsl > Vll
van der Waals interaction:

S <0 S >0

partial wetting complete wetting

Vsl s l

Vll l2

S l ( s l )

complete wetting if solid more polarisable than liquid

wetting and gravity

hydrostatic pressure

( p + g (h0 z )) dA

h0 - z

lv dA

now =(z)

lv = p + g (h0 z )

non-dimensionalization
dimensionless variables: z = R ~ z

1 ~ x R

lv ~ p R
2 ~ ~ ~ = ~ + g R (h ~ ) = ~ + Bo ( h ~ ) p z p z lv
Bo: Bond number equivalently: capillary length

Bo << 1

gravity negligible

c = g / lv

R << c gravity negligible

water in air: 2.7mm

gravity is usually negligible in microfluidics

summary

equilibrium shape of wetting structures is determined by minimum of surface energy variation of free energy functional results in sv sl cos Y = p = lv + = lv R R lv
capillary (Laplace) equation Young equation
occurrence of complete vs. partial wetting is determined by relative strength of adhesive vs. cohesive forces gravity is negligible on length scales << capillary length

DIMENSIONS OIL BOILERS INTREPID TR SERIES

E B A C

25" 1458" 4"
A.S.M.E. Relief valve Combination gauge Supply Tankless heater Service switch High/Lo limit or combination control for P or PT boiler Observation Port Burner Drain cock and alternate tapping Combustion Chamber Primary control Burner

3178"

Observation port

334"

Left EndWATER BOILER FrontWATER BOILER

Dimensions (inches)

5A 6 5B Tapping Location 7
WATER BOILER 112" supply 4" air vent or expansion tank 3 4" water relief valve 1 2" tankless inlet 1 2" tankless outlet 1 4" pressure temp. gauge 1 2" hi limit, hi/lo or comb. control 112" return & 34" drain cock 112" alternate return

Boiler Model No.

14 (Rear)

Front view WATER

1 1A 4 5A 5B 10 11A 11B 14 15

Boiler Length A

Front to Flue B

Flue Dia. C

TR-20 TR-30H TR-30
Return Circulator Flange D 114

Overall Length E

TR-40H TR-40 TR-50H TR-50 TR-60 TR-70
SLANT/FIN CORPORATION, Greenvale, NY 11548 Phone: (516) 484-2600
FAX: (516) 484-5921 In Canada: Slant/Fin LTD/LTEE, Mississauga, Ontario

www.slantfin.com

Slant/Fin Corp. 2007
Pressure cut-out control POP safety valve
E B A C A.S.M.E. POP Safety valve

4"

Tankless limit control Siphon

Gauge glass

112"
Water line Observation port skimmer tapping

LWCO Primary control

Burner

25 2"

Combustion Chamber

312"

Left EndSTEAM BOILER FrontSTEAM BOILER

134"

9 11A 11B 12 10

Tapping Location

STEAM BOILER 3" supply 2" supply tapping (rear section of L-50, L-60 & L-70 models only) Second 14" siphon, pressure gauge & pressure cut-out 3 4" steam safety valve 1 4" siphon, pressure gauge & pressure cut-out 3 4" low water cut-off, alternate 112" skimmer tapping 1 2" low limit for tankless 1 2" tankless inlet 1 2" tankless outlet 1 2" steam gauge glass & 67 LWCO 112" return & 34" drain cock 112" condensate return 3 4" zone tapping

1 1A 2

Dimensions (inches) Boiler Model No. Boiler Length A Front to Flue B Flue Dia. C Overall Length E

5A 5B 10 11A 11B 14 15

TR-30 TR-40H TR-40 TR-50H TR-50 TR-60 TR-70

Front view STEAM

Top view (Front section)

Flue collector

DIMENSIONS OIL BOILERS INTREPID TRDV SERIES

DIRECT VENT

E B A C Dia. 4" SUPPLY A.S.M.E. Relief Valve 25" 1458" D Supply Combination Gauge Tankless Heater
High/Lo Limit or combination control for P or PT boiler
Burner 312" 334"

COMBUSTION CHAMBER

LEFT END
Dimensions (inches) Boiler Length A 1478" 1478" 1478" Front to Flue B 10116" 10116" 10116" Flue Dia. C 6" 6" 6" Circulator Flange D 114" 114" 114" Overall Length E 2758" 2758" 2758" Boiler Sect 3
Boiler Model TRDV-30-0.85 TRDV-30-1.00 TRDV-30-1.10
DIMENSIONS OIL BOILERS XL-2000

18 7/1/4

SUPPLY CIRCULATOR FLANGE

"E"

A.S.M.E. RELIEF VALVE TO POWER
VENT/EXPANSION TANK TAPPING DIA.

SUPPLY

COMBINATION GAUGE

OBSERVATION PORT COVER

ELECTRICAL CONDUIT COMBINATION CONTROL OBSERVATION PORT COVER
POWER CONECTION JUNCTION BOX

30 3/8

HINGED BURNER MOUNTING DOOR

1 1/2 RETURN

PRIMARY CONTROL RELAY

COMBUSTION AREA

OIL BURNER HINGED BURNER MOUNTING DOOR

3 1/3/4

FRONT VIEW

LEFT END VIEW

TOP VIEW
3/4" RELIEF VALVE TAPPING

DIMENSIONS

BOILER MODEL NO. BOILER LENGTH A FRONT FLUE CIRCULATOR TO COLLAR SUPPLY FLUE DIA. FLANGE D B C NPT APPROX. OVERALL LENGTH E

1 1/2 SUPPLY TAPPING

1 1/2 RETURN TAPPING
1/2" AIR VENT OR EXPANSION TANK TAPPING
XL-20 XL-30H XL-30 XL-40H XL-40 XL-50
81116" 1236" 12316" 151116" 151116" 19316"
4916" 6516" 6516" 8116" 8116" 91316"
6" 6" 6" 7" 7" 8"

1" 114"

25 "\ 2878"
1/4 NPT PRESSURE & TEMPERATURE TAPPING
114" 114" 114" 112"

2878" 3238"

3/4" RELIEF 3238" VALVE TAPPING 1 1/2 RETURN TAPPING 1 1/2 SUPPLY 3578" TAPPING
FRONT VIEW 1/2 NPT CONTROL TAPPING
1 1/2 ALTERNATE REAR RETURN

3/4 REAR DRAIN

DIMENSIONS OIL BOILERS EUTECTIC EC-10

Left End

1 1-1/4 threaded supply

2 Tapping 1/4"

3 Relief valve 3/4"

4 Flue outlet D

5 1-1/4 threaded return tapping

6 1/2" drain outlet

DIMENSIONS OIL BOILERS EUTECTIC EC-20
1 1-1/4 threaded supply tapping

3 Refief valve 3/4"

6 1/2" draining outlet