Alfonso M. Gañán-Calvo ,

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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 Mechanics University of Seville, Spain.

IPPT PAN Seminars. Warsaw, January 2008

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Focusing fluid

D₁ D

r

L H

z

Focused fluid

V V

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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

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We seek for the geometrical and operational conditionsg p

where the smallest possible, monodisperse droplets are generated at a productivity of practical use

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Pa

g

T φ θ

j

T C O l

l

φ

H

D

j

D

_i

θ θ

_t _S

D

_t

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

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

.5 mm1

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3D (axisymmetric) Flow focusing in silicon

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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

8 ) 1

(

1 Re

2

2 l

Q

l

v Q

p ≈ ρ ≈ ρ

Δ

>>

2 / 1 4 /

8

_l 1

Q d ⎟⎟ ⎞

⎜⎜ ⎛ ρ ) 2

(

₂ ₄

j l

l

gas

v d

Q

p ≈ ρ ≈ π Δ

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

/

2 l

l

j

Q

d ≈ ⎜⎜ ⎝ Δ p ⎟⎟ ⎠ π

ρ

(Bernoulli)

( )

4 / 2 1 4

/ 1 2

8 ⎟⎟ ⎞

⎜⎜ ⎛

⎟ ⎠

⎜ ⎞

⎝

= ⎛

Q

d_o

ρ

^l ^l

Characteristic length

2

⎟⎟

⎜⎜ ⎠

⎟ ⎝ Δ

⎜ ⎠

⎝

p

d_o

π

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Based on previous characteristic dimension, four main parameters inform on the role played by surface tension, viscosity and geometry (orifice size and tube-orifice distance)

) 1 ( We

4 / 3 1 4 2

/ 2 3

p O Q_l

l

⎟⎟ ⎞ ≥

⎜⎜ ⎛ Δ

⎟⎟ ⎞

⎜⎜ ⎛

= π ρ ₂

¹^/⁴ ³ ² ¹^/⁴

R ⎟ ⎞

⎜ ⎛ Δ

⎟ ⎞

⎜ ⎛ ρ

_l Q_l p viscosity and geometry (orifice size and tube orifice distance)

) 1 8 (

We

_l

⎟⎟ ⎜⎜ ⎝

₄

⎟⎟ ⎠ ≥

O

⎜⎜ ⎠

= ⎝

σ ^Re ⁼ ^⎜ _⎝ ^⎛

²

^⎟ _⎠ ^⎞ ^⎜⎜ _⎝

⁴

^⎟⎟ _⎠

l l l l

p Q

μ ρ π

4 / 1 4/ 1

4 4 2

/ 1 2

8 ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛

⎟ Δ

⎠

⎜ ⎞

⎝

= ⎛

p D G

ρ

^lQ^l

π

^G^H

⁼

^H

^/

^D

Various geometries:

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H

D H G_H

= /

Role played by

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Water 2,60

1

Ethanol

2,20 2,40

1

d50/do

1 60 1,80 2,00

GSD

0,1

1,20 1,40 1,60

0,01

1 10 100 1000 10000

We^l

1,00

1 10 100 1000 10000

We^l Flow Focusing

Flow Blurring

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R l l d b d

Role played by and

l

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10 Water 2,20

1

Water

Ethanol tFF

cFF

1 80 2,00 1

d50/do

1,60 1,80

GSD

0,1

1,20 1,40

0,01

1 10 100 1000 10000

We^l

1,00

1 10 100 1000 10000

We^l

20 We

_l

≈ 20

We

_l

≈

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10 2,20

1 80 2,00 1

1.89

1,60 1,80

GSD

1

Water Ethanol

d50/do

1,20 0,1 1,40

1,00

1 10 100

We^l

0,01

1 10 100

We^l

• Why some liquids (water) exhibit larger sizes than predicted, in some (most) conditions?

• 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?

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Some recents FF numerical simulations:

• Liquid-liquid configuration for the production of microemulsions:

Michael M Dupin et al Physical Review E 73 2006 Michael M. Dupin et al. Physical Review E,73, 2006.

• Microbubbling: M. J. Jensen et al. Physics of Fluids, 18, 2006.

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Geometrical configuration is fixed:

• R /R = 0 75

Q • R₁/R = 0.75,

• R₂/R = 1.75,

• R₃/R = 3.5,

• L/R = 0 75 Q_g

• L/R = 0.75.

• H/R = 1 Q_l

Characteristic magnitudes:g

* R

* V=Q

_g

/( π R

²⁾

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ratio densities

,

*

l

=

g

ρ α ρ

833 33 α =

ratio ies

viscosit ,

*

l g l

= μ β μ

ρ

Water-air experiments:

55.55 833.33 β =

α

(gas) Weber

, We

*

2 g l

R

= V

σ ρ μ

(gas) Reynolds

, Re

*

g

VR

= μ

ρ σ

Case 1 Re = 465.8

Case 2 Re = 931.6

(tube) Reynolds

, Re

*

_R

l l l g

R

= U μ

ρ

^{We = 8.13} ^{We = 32.55}

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

ratio rates

Flow

,

*

g l

Q Q = Q

changing Q in:

1. Meniscus-jet shape.

2. Minimum flow rate Q* for stable jet.

3 Flow structure inside the meniscus 3. Flow structure inside the meniscus.

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-VOF scheme:

a) Explicit time advance b) CICSAM reconstruction

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

Basic mesh: Δ_z = Δ_r = 0.02 Refined mesh: Δ Δ 0 01 Refined mesh: Δ_z = Δ_r = 0.01

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Case 1 Q=0.004 Q

θ

d_in d_out

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Case 1 Case 2

Q* (minimum) Q* (minimum)

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Case 1 Case 2

Diameters

“Contact angles”

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1 Re >>

(*) 8

2 ) 1 (

1 Re

4 2

2

2 l l

l l

gas

d

v Q Q

p π

ρ ≈ ρ

≈ Δ

>>

2 π d

_j

2 / 1 4 / 1 2

8

l l

j

Q

d p ⎟⎟

⎠

⎜⎜ ⎞

⎝

⎛

≈ Δ π

ρ p ⎠

⎝

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Case 1 Case 2

Q = 0 00004

Q = 0.00024 Q = 0.00004

Q 0.000

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Case 1

Q = 0.00024 Q 0.00024

Case 2 Q=0.00004 Q

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

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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 disk 75μm thick

200 μm orifice Variable distance H

PMMA window

μ

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5 H=0,200mm Up

4

H=0,200mm Down H=0,150mm Up H=0,150mm Down H=0,100mm Up Pressure increasing

Jetting

3

Wel

H=0,100mm Down H=0,075mm Up H=0,075mm Down H=0,050mm Up

g

1

W 2 ^, ^p

H=0,050mm Down C/A transition

0 1

jetting dripping

Dripping

20 30 40 50 60 70

Re^l

Optimum distance H: H/D~0.5

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JETTING

DRIPPING

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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)

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

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Qr Q_r

Saddle (max. pressure)

Q Q

( )

¹^/²

( )

2

2 / 1

/ /

~

l s R

s l l

l

U Q

U R

δ ρ μ

δ

=

1

2 ) ~ /( ) Re

/(

~

/ = ⁻

= _R _g _s δ_l _g μ_l ρ_l _g _μ^ρ

r Q Q U Q R Q

Q

) 1 ( S ~ O

Q Q

Q

r l

l R

B

μ

−

=

R r

r l

l R

l

r Q Q s S R C C

S ~ ρ ( − )/μ ⇒ = / = ₁ − ₂ Re )

1 ( Q_B O

ρl

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R

r

C C

s

_r

= C

₁

− C

₂

Re

_R

s

₁ ₂

Re

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Articles per year

Subject: Flow Focusing Subject: 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-flowing accelerating gas stream to reduce the radius of a liquid jet issuing out of a nozzle.[32] He showed that a nearly

monodisperse spray is produced when the Weber number which characterizes the relative importance of inertial force in the monodisperse spray is produced when the Weber number, which characterizes the relative importance of inertial force in the gas phase to the surface tension force, lies below a critical value.”

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

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Most work (experimental) has been devoted to Most work (experimental) has been devoted to

liquid-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)

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… 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

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Alfonso M. Gañán-Calvo ,