alfonso m. gañán-calvo , in collaboration with miguel a

Alfonso M. Gañán-Calvo , In collaboration with Miguel A. Herrada, Antonio Ojeda-Monge, g j g

Benjamin Bluth, Pascual Riesco-Chueca

ESI, Dept. Aerospace Engineering and Fluid MechanicsUniversity of Seville, Spain.

IPPT PAN Seminars. Warsaw, January 2008

Focusing fluid

D1D

r

LH

z

Focused fluid

VV


Ganan-Calvo et al. 2007 Nature Phys. 3, 737-742

Gañán-Calvo 1997, W9700034ES

We may wish to control these structures & make them as small as possible


We seek for the geometrical and operational conditionsg pwhere the smallest possible, monodisperse droplets are generated

at a productivity of practical use


aP

gT θφ

j

CT O ll

φ

HD

j

Diθ SθtDt

Parameter ranges in experiments (G-C et al.):


The small yield per orifice has led to the design of multi-orifice devices:

.5 m

m1


3D (axisymmetric) Flow focusing in silicon

Ranges of pressure

FF FB

drop and flow rate:

FF FB

ΔP, bar 0.05 – 30 0.7 – 7.0

Q, uL/min 10 - 5800 10 - 14000

81)(

1Re2

2 llQvQp ρρ ≈≈Δ

>>

2/14/1

8 l Qd ⎟⎟⎞

⎜⎜⎛ ρ

2)( 42

jllgas d

vQpπ

ρ ≈≈Δ

*A. M. Gañán-Calvo. Phys. Rev. Letter, 80, 285, 1998.

/2 l

lj Q

pd ⎟⎟

⎠⎜⎜⎝ Δ

≈πρ

(Bernoulli)( )

4/124/1

2

8⎟⎟⎞

⎜⎜⎛

⎟⎠⎞

⎜⎝⎛=

Qd llo

ρ

Characteristic length

2 ⎟⎟⎠

⎜⎜⎝ Δ

⎟⎠

⎜⎝ p

do π

Based on previous characteristic dimension, four mainparameters inform on the role played by surface tension,

viscosity and geometry (orifice size and tube-orifice distance)

)1(We4/1324/32

OpQll ≥⎟⎟⎞

⎜⎜⎛ Δ

⎟⎟⎞

⎜⎜⎛

=ρπ 4/1234/12R ⎟

⎞⎜⎛ Δ

⎟⎞

⎜⎛ ll pQρ

viscosity and geometry (orifice size and tube orifice distance)

)1(8

We 4 Ol ≥⎟⎟⎠

⎜⎜⎝

⎟⎟⎠

⎜⎜⎝

=σ 42Re ⎟⎟

⎠⎜⎜⎝

⎟⎠⎞

⎜⎝⎛=

l

lll

pQμ

ρπ

4/1 4/1

4

24/1

2

8⎟⎟⎠

⎞⎜⎜⎝

⎛Δ

⎟⎠⎞

⎜⎝⎛=

pDQG llρ

π DHGH /=

Various geometries:

HDHGH /=Role played by

Water 2,60

1

Ethanol

2,20

2,40

1

d50/d

o

1 60

1,80

2,00

GSD

0,1

1,20

1,40

1,60

0,011 10 100 1000 10000

Wel

1,001 10 100 1000 10000

Wel

Flow Focusing

Flow Blurring

R l l d b dRole played by and

l

10Water

2,20

1

Water

Ethanol tFFcFF

1 80

2,00

1

d50/d

o

1,60

1,80

GSD

0,1

1,20

1,40

0,011 10 100 1000 10000

Wel

1,001 10 100 1000 10000

Wel

20We ≈l 20We ≈l

2,2010

1 80

2,00

11.89

1,60

1,80

GSD

1

Water

Ethanold50/d

o

1,20

1,400,1

1,001 10 100

Wel

0,011 10 100

Wel

• Why some liquids (water) exhibit larger sizes than predicted, in some (most) conditions?• Why some conditions exhibit extremely good monodispersity (without external excitation)?• Why some conditions exhibit extremely good monodispersity (without external excitation)?• What exactly sets the minimum flow rate: C/A instability of the jet? Cone-jet flow transition?• Is the dripping mode so bad?

Some recents FF numerical simulations:• Liquid-liquid configuration for the production of microemulsions: Michael M Dupin et al Physical Review E 73 2006Michael M. Dupin et al. Physical Review E,73, 2006.• Microbubbling: M. J. Jensen et al. Physics of Fluids, 18, 2006.

Geometrical configuration is fixed:• R /R = 0 75Q • R1/R = 0.75,• R2/R = 1.75,• R3/R = 3.5, • L/R = 0 75

Qg

• L/R = 0.75.

• H/R = 1

Ql

Characteristic magnitudes:g* R* V=Qg/(π R2)


ratio densities , *l

g=ρρ

α833 33=α

ratio ies viscosit, *l

g

l

=μμ

β

ρWater-air experiments:

55.55833.33

=βα

(gas) Weber ,We*2

g

l

RV=

σρ

μ

(gas) Reynolds ,Re *g

gVR=

μρ

σCase 1

Re = 465.8

Case 2

Re = 931.6

(tube) Reynolds,Re * Rl

ll

g

RU=

μρ We = 8.13 We = 32.55

In these cases, we have studied the effect of changing Q in:

ratio rates Flow ,*g

l

QQQ =

changing Q in:1. Meniscus-jet shape. 2. Minimum flow rate Q* for stable jet.3 Flow structure inside the meniscus3. Flow structure inside the meniscus.


-VOF scheme:

a) Explicit time advanceb) CICSAM reconstruction

*Commercial code used: FLUENT 6.3Co e c a code used U 6 3

Basic mesh: Δz = Δr = 0.02Refined mesh: Δ Δ 0 01Refined mesh: Δz = Δr = 0.01


Case 1

Q=0.004Q

θ

din dout


Case 1 Case 2

Q* (minimum) Q* (minimum)


Case 1 Case 2

Diameters

“Contact angles”


1Re >>

(*) 821)(

1Re

42

22 llllgas d

QvQpπρρ ≈≈Δ

>>

2 jdπ

2/14/1

2

8l

lj Q

pd ⎟⎟

⎠

⎞⎜⎜⎝

⎛Δ

≈πρ

p ⎠⎝

Case 1 Case 2

Q = 0 00004Q = 0.00024 Q = 0.00004Q 0.000

Case 1

Q = 0.00024Q 0.00024

Case 2

Q=0.00004Q

High periodicity near the exit orifice (but not necessarily outside)

water (from syringe pump)(Cole-Palmer 74900 Series) with a 20 ml syringe

jetting dripping

Air (pressure gauge)

370 mm OD, 150 mm ID stainless steel capillary

Aluminium box

Two cameras to verify alignment

Air (pressure gauge)

PMMA window

4 mm stainless steel disk75 μm thick200 μm orifice

Variable distance HPMMA window

μ

5 H=0,200mm Up

4

H=0,200mm DownH=0,150mm UpH=0,150mm DownH=0,100mm Up

Pressure increasing

Jetting

3

Wel

H=0,100mm DownH=0,075mm UpH=0,075mm DownH=0,050mm Up

g

1

2

W , pH=0,050mm DownC/A transition

0

1

jetting dripping

Dripping

20 30 40 50 60 70

Rel

Optimum distance H: H/D~0.5

JETTING

DRIPPING

Case 1 Case 2

Experimental observations

• Co-flowing systems: • S. L. Anna and H. C. Mayer, Phys. Fluids, 18, 121512 (2006).• R. Suryo, O. A. Basaran, Phys. Fluids, 18, 082102 (2006)Experimental observations

of recirculation cells: • Taylor cones: Barrero et al. Phys. Rev. E, 58, 7309-7314 (1998)

Saddle (max. pressure)Saddle (max. pressure)

rQ rQ

Saddle (max. pressure)Q Q

( ) 2/1( )2

2/1

/

/~

lsR

slll

UQUR

δ

ρμδ

=12 Re)/(~)/(~/ −== μ

ρρμδ gllglsgRr QRQUQQQ

)1(~ OSQQQ

rl

lRB

μ−=

RrrllRlr CCRSsQQS Re//)(~ 21 −==⇒− μρ)1(O

QBlρ

Rr CCs Re21 −= Rr CCs Re21

Articles per yearSubject: Flow FocusingSubject: Flow Focusing

(Source: Scopus)300

200

250

100

150

0

50

1998 2000 2002 2004 2006

“Gañán-Calvo [21] pioneered the use of a technique now called flow-focusing where he used a co-flowingaccelerating gas stream to reduce the radius of a liquid jet issuing out of a nozzle.[32] He showed that a nearlymonodisperse spray is produced when the Weber number which characterizes the relative importance of inertial force in themonodisperse spray is produced when the Weber number, which characterizes the relative importance of inertial force in thegas phase to the surface tension force, lies below a critical value.”

Suryo, R. & Basaran O. A. (2006) Phys. Fluids 18, 082102


Most work (experimental) has been devoted toMost work (experimental) has been devoted toliquid-liquid FF in microfluidics

A S L B N S H A (2003) A l Ph L 8 364 ( i d b 199)

(“planar” FF)

or gas in liquid FF (microbubbles) in microfluidics

• Anna, S.L., Bontoux, N., Stone, H.A. (2003), Appl. Phys. Lett. 85, 364 (cited by 199)

…or gas in liquid FF (microbubbles) in microfluidics• Ganan-Calvo, A.M., Gordillo, J.M., (2001), Phys. Rev. Lett. 87, 274501 (cited by 89)

• Garstecki, P., Gitlin, I., Diluzio, W., Whitesides, G.M., Kumacheva, E., Stone, H.A.

(2004), Appl. Phys. Lett. 85, 2649 (cited by 66)


… however, the original liquid-in-gas configuration has been subject of smaller attention:

• Ganan-Calvo, A.M. (1998), Phys. Rev. Lett. 80, 285 (cited by 69)

• Almagro, B., Gañán-Calvo, A.M., Canals, A. (2004), J. Anal. Atom. Spectrom., 19, 1346 (cited by 5)

• Arumuganathar, S., Irvine, S., McEwan, J.R., Jayasinghe, S.N. (2008), J. Appl. Polymer Sci. 107, 1215


alfonso m. gañán-calvo , in collaboration with miguel a

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