Mean and maximal drop size during

emulsification in turbulent flow -

effect of emulsification conditions

Nina Vankova, Slavka Tcholakova,

Vasko Vulchev, Nikolai D. Denkov, Ivan B. Ivanov

Laboratory of Chemical Physics & Engineering,

Faculty of Chemistry, Sofia University,Sofia, Bulgaria

Studied factors

• Geometry of the processing element: One vs two slits

Planar vs cylindrical

• Flow rate

Re = 8450, Re = 13270

• Viscosity of the dispersed phase

From 3 to 500 mPa.s

• Interfacial tension

From 5.5 to 14 mN/m

Aim: To clarify the effect of several factorson the mean and maximal drop size in emulsions,

prepared with narrow-gap homogenizer

Materials

Aqueous phase:

1 wt % Brij 58 + 150 mM NaCl

1 wt % SDS + 10 mM NaCl

0.5 wt % Na Caseinate + 150 mM NaCl + 0.01 wt % NaN3

Oil phase:

Hexadecane: D = 3 mPa.s; OW = 7. 0 mN/m

Soybean oil (SBO): D = 50 mPa.s; OW = 5.5 to 14.0 mN/m

Silicone oil: D = 50 to 500 mPa.s; OW = 10.3 mN/m

Emulsification method

Cylindrical

Two slits with 1 mm length

Used processing elementsExperimental set-up

Cylindrical

One slit with1 mm length

Planar

One slit with1 mm length

Results: Flow rate vs applied pressure

At same Q p(2 slits) 2p(1slit) At same p Q(planar) ~ 1.4 Q(Cyl-1slit)

Pressure, p x 105, Pa

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4

Flo

w r

ate

Q,

L/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Cyl - 1 slit Cyl - 2 slitsPlanar

0 5271 .Q k p

k1

Planar 4.498

Cylindrical – 1 slit 3.293

Cylindrical – 2 slits 2.307

Effect of homogenizer construction on mean drop size

d32, m Re

D,

mPa.s

OW,

mN/m Planar Cyl - 1 Cyl - 2

5.5 5.8 5.5 5.0

7.4 7.2 6.6 6.0 13270

14.0 10.3 9.7 8.0

8450

50

7.4 12.8 12.0 10.0

3 7.0 3.6 3.3 3.0 13270

95 10.3 11.3 9.7 8.9

d32 for 2-slits is ~ 12 % smaller than that for 1-slit

d32 for planar is ~ 8 % larger than that for cylindrical

Mean: + 8 % - 12 %

% vs Cyl-1

Planar Cyl – 2

+ 5 - 9

+ 9 - 10

+ 6 - 18

+ 7 - 17

+ 9 - 9

+ 16* - 8

The polydispersity depends mainly on oil viscosity

Higher viscosity more polydisperse emulsions

Effect of the same factorson drop polydispersity

dV95, m dv95/d32 Re

D,

mPa.s

OW,

mN/m Cyl - 1 Planar Cyl - 1 Cyl - 2 Mean

5.5 11.2 2.12 2.03 2.02

7.4 13.9 2.08 2.10 1.93 13270

14.0 21.5 2.01 2.22 2.00

8450

50

7.4 23.9 2.03 1.99 2.12

2.1 0.08

3 7.0 5.4 1.67 1.63 1.53 1.6 0.08 13270

95 10.3 20.7 2.13 2.13 1.96 2.1 0.08

Maximal drop size during emulsificationin the inertial regime of turbulent flow

Davies, 1985

3 5 3 51 3 1 31 2 3 5 2 5

2

1 2

4

4

D

OW C

dd C

CC

Pressure fluctuations

Capillary pressure

Viscous stress inside breaking drop

2 321 1 2TP ( d ) C u C C d

4CP d

1 31 22DDC du

d d

3 51 3 1 3 3 5 2 5

1 2OW D Cd A A d

3 5 1 2

1 1 2 2 24 4 1.9; 0.35A CC A C1 20 7 2;C . C Batchelor, 1956

Mean drop size during emulsificationin the inertial regime of turbulent flow

Calabrese et al., 1986

1 22 3 5 3 1 3 1 3

5 3

1 21C C D

OW D OW

d dA A

3 3 2 3 2 3~ ( ) ~6 6TE d P d d d

2~ OWE d

2 323~ ~

6 6CD

DISS Dd

ddE d

Mean turbulent energy

Surface energy

Energy dissipated inside breaking drop

Literature data for the constants A1 and A2

Athors Homogenizer Viscosity range Interfacial tension

A1 A2

Hinze, 1955

Coaxial cylinders low 0.725

for dMAX

0.138 for dMAX Sprow,

1967 Impellers 0.51 mPa.s 41.8 mN/m

0.0524 for d32

Narsimhan et al., 1979

Impellers low 0.053 for d32

Davies, 1985

Clearance valve Colloidal mills Liquid whistles

Turbine impellers

3.5 to 200 mPa.s 30 mN/m 1 ( 0.354)

0.054 for d32

4.08 – 4.42 for d32

Calabrese et al., 1986

Impellers 5 to 500 mPa.s 1 to 45 mN/m 0.09

for dmax

3 51 3 1 3 3 5 2 5

1 2OW D Cd A A d

2 3 5 3 1 3 1 35 3

1 21C D

OW OW

d dA A

Analisys of our data with -mean(cylindrical gap)

A1 = 1.13; A2 = 0.195; r2 = 0.80 A1 = 0.601; A2 = 0.198; r2 = 0.87

D(dV95OW

0 2 4 6 8 10 12 14 16 18

(2/

5 C

d

V95

O

W

0

1

2

3

4

5

6

HexadecaneSBOSilicone oil

SDSBrij 58

NaCaseinate

Data for dV95

D(d32OW

0 2 4 6 8 10 12 14

(2/

5 C

d

32

OW

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

HexadecaneSBOSilicone oil

SDSBrij 58

NaCaseinate

Data for d32

Time, sec

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

- 0,

mN

/m

-10

-8

-6

-4

-2

0

0.02 wt % NaCas

0.0015 wt % SDS

Dynamic interfacial tension of Na caseinate

Na caseinate adsorbs much slower than low-molecular mass surfactants

2 3 5 3 1 3 1 35 3

1 21C D

OW OW

d dA A

D(dV95OW

0 2 4 6 8 10 12 14 16 18

(2/

5 C

d

V95

O

W

0

1

2

3

4

5

6

HexadecaneSBOSilicone oil

SDSBrij 58

NaCaseinate

Data for dV95

D(d32OW

0 2 4 6 8 10 12 14(

2/5

C

d

32

OW

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

HexadecaneSBOSilicone oil

SDSBrij 58

NaCaseinate

Data for d32

A1 = 0.944; A2 = 0.280; r2 = 0.935 A1 = 0.510; A2 = 0.285; r2 = 0.957

Fit of our data with -mean and corrected

Check of the values of A1 and A2

with additional experimental data 2 3 5 3 1 3 1 3

5 3

1 21C D

OW OW

d dA A

A1 = 0.944; A2 = 0.280 A1 = 0.510; A2 = 0.285

D(dv95OW

0 20 40 60 80 100 120 140

(2/

5 C

d

V95

OW

0

10

20

30

40

HexadecaneSBOSilicone oil

SDSBrij 58

NaCaseinate

D(d32OW

0 20 40 60 80 100

(2/

5 C

d

32

OW

0

2

4

6

8

HexadecaneSBOSilicone oilx vs Col 39

SDSBrij 58

NaCaseinate

Data for dV95 Data for d32

dmax, exp (m)

0 10 20 30 40 50

dm

ax,

theo

r (

m)

0

10

20

30

40

50 A1 = 0.944

A2 = 0.280

rel error = 8 %

Correlation plotpredicted and measured dmax

Comparison of our constants A1 and A2

with literature values

Viscosity range Interfacial tension

A1 A2

Hinze, 1955

Coaxial cylinders low 0.725

Sprow, 1967

Impellers 0.51 mPa.s 41.8 mN/m 0.138

Davies, 1985

Clearance valve Colloidal mills Liquid whistles

Turbine impellers

3.5 to 200 mPa.s 30 mN/m 1 ( 0.354)

Calabrese et al., 1986

Impellers 5 to 500 mPa.s 1 to 45 mN/m 0.09 4.08 – 4.42

Current study

Narrow-gap homogenizer

3 to 500 mPa.s 5 to 30 mN/m 0.944 0.28

3 51 3 1 3 3 5 2 5

1 2OW D Cd A A d

For impellers: 3 2'C N L C’ is a function of the position in the vessel (0.9 to 70)

Planar homogenizereffect of on the values of A1 and A2

D(dV95OW

0 5 10 15 20

(2/

5 C

d

V95

OW

0

2

4

6

8

10

12

HexadecaneSilicone oilSBO

SDSBrij 58

NaCaseinate

Mean

D(dV95OW

0 5 10 15 20 25 30

(2/

5 C

d

V95

OW

0

2

4

6

8

10

12

14

16

18

20

22

HexadecaneSilicone oilSBO

SDSBrij 58

NaCaseinate

Maximal

10-5, J/kg.s A1 A2

3.45 1.08 0.36

10.44 1.69 0.25

Conclusions

Experiment:

• The effects of oil viscosity, interfacial tension and construction of the processing element on drop size are clarified.

• The polydispersity of the obtained emulsions increases with oil viscosity.

Interpretation:

• The data for dV95 are reasonably well described by Davies’ equation, which

accounts for the viscous dissipation inside the drops.

• The values of A1 and A2 are determined from the experimental data (but depend

significantly on the presumed value of ).

• It is worth to specify better A1 and A2 - relative contributions of capillary pressure

and viscous dissipation in drop breakup (collaboration with Graz and Warsaw).

To finalize these studies

Cylindrical homogenizer:

• Deeper analysis of the effect of - graph (V), if available.

• More convincing data for the kinetics of adsorption (Na caseinate)

• Comparison of the constants with those available in the literature.

• Preparation of a paper (Sofia+Graz).

Planar homogenizer:

• More emulsification experiments at various conditions.

• Graph (V), if available, for detailed analysis.

• Paper ?

Comparison of planar and cylindrical homogenizers (hydrodynamic flow, )?

On behalf of the Bulgarian team:

Thank you for the kind attitude

and fruitful co-operation!