the nucleation theory k.-m. valant*, b. prunet-foch*, m. adler *, p. lehuédé**...

The nucleation theory

K.-M. Valant*, B. Prunet-Foch*, M. Adler*, P. Lehuédé***LPMDI **Saint-Gobain Recherche

Motivation: gushing bottlesNormal bottle

t = 2.88 s

Gushing bottle

t = 3.8 s

Bubbles

foam

1) Intempestive foaming occurring during filling ofcarbonated beverages (water, beer, champagne…)

2) unwanted foaming may occur after bottle opening

Sparkling wine

• hydroalcoholic solution

• pH ~ 3.2

• CO2 supersaturation = 6 atm

• foaming liquid

Bottle neck ~ 6 cm3

timescale = 10 sec

The critical radius Rc of gas bubble nucleation in supersaturated solution

0

0.001

0.002

0.003

0.004

0.005

0.006

0 2 3 4 5 6 8

CO2 Molar fraction

Partial pressureCO2

(bars)

Initial state(equilibrium state)

After a certain time(equilibrium)

Just after a rapid decompressionsupersursaturation (non-equilibrium state)

XeqCO2

= H PCO2 (Henry’s law)

= Pi / Pf – 1

> 0Supersaturation:

PiPf

Water in bottle

= 0, PL = 7 atm

= 0.061 N/m (after Lubetkin, 1995)

Rc = 52.3 µm

CO2 Supersaturated water

= 6, PL = 1 atm

= 0.071 N/m

Rc = 0.24 µm

Sparkling wine

= 6, PL = 1 atm

= 0.045 N/m

Rc = 0.15 µm

( )ηLsat

C PPR

+= 2

Psat = 0.023 atm η ~ 1

Homogeneous Nucleation Energy

W Hnuc

107 R (m)

W H (10-14 J)

Rc

CaseH2O/CO2

1 2 3

R > Rc = bubble growth

R < Rc = bubble dissolution

0

1

2

3

0.51

1.5

-2

-1

0

1

2

3

0

1

2

3

0.51

1.5

C

0 < C < 1

C = 1

C > 1

C = 0 C < 0

C()

Homogeneous nucleation()

Hydrophobic surface ()

hydrophilic surface()

Nucleation on a flat surface()Nucleation energy WC

nuc in a conical cavity: 

C : form factor

depending on and

WCnuc = WH

nuc C

Whnuc : Homogeneous

nucleation energy

= contact angle

= conical cavity angle

R

Heterogeneous Nucleation Energy

(case of a conical cavity)

pre-existing gas cavities

Type IIISemi-classical

Type IVNon-classical

R < Rc R Rc

(Rc = critical radius)

Type IClassical homogeneous

Nucleation in the bulk ~ 103 (beverages: ~ 6)

Type IIClassical heterogeneous

Heteronucleation at the interface liquid/glass

The types of gas bubble nucleation

The known types of nucleation(After Jones et Al., 1999)

The chemically aided heteronucleation (This work)

• at the surface of a calcium carbonate crystal• pre-existing gas cavities (?)

CaCO3

CrystalAcidified liquid

Type V heteronucleation

CaCO3 + 2H+ ⇄ Ca2+ + CO2dis + H2O

Dissolution of CaCO3 with HClWhat can generate bubbles on glass surface?

• in air-filled cavities (small, deep, hydrophobic) • on hydrophobic coatings on the glass

But these sites of nucleation are still too rare in bottles to explain the gushing phenomenon

Physical heteronucleation (type III & IV) can occur on the glass surface:

The beverages themselves can be at the origin of a gushing phenomenon (particles in the liquid) In this work, we are focusing on GLASS SURFACE ONLY

3

1 2

4

High speed camera 1kHz frame grabbing

Capillary

Temperaturecontrolled bath

Stroboscopiclight

CO2 Supersaturatedwater

Height

Wine

Beer

Perrier

25°C

Polynomial fit : V(h) = h 2 + h + V0

V0 being negligible in our case

Example: at 25 °CPerrier: V(h) = 4.1 x 10-5 h2 + 2.4 x10-3 hWine: V(h) = 1.1 x 10-5 h2

+ 1.2 x10-3 hBeer: V(h) = 2.5 x 10-6 h2 + 1.9 x10-3 h several nucleations per siteAggravating factor

Volume of CO2 in the bottleneck generated by type V nucleations as a function of the crystal density

density (crystals/cm2)

Bubble radius at the detachment

(mm)

CO2 generated in the bottle neck

(cm3)

0,2 0,22

1 0,3 0,31

0,4 0,44

0,2 1,1

5 0,3 1,6

0,4 2,2

0,2 2,2

10 0,3 3,1

0,4 4,4

Case of the wine at 25°C

Unusual crystallization

on glass bottles

CaCO3

• Insoluble in water

• Soluble in acidic liquids

Na2CO3

Soluble in water

Ageing of glass

100µm

Heteronucleation occurs on CaCO3

crystals in wine

(pH 3)

Type V nucleation and the gushing phenomenon

Density of sites: d

( )HVdRV 2bb ∂=

∫ −=tsH

0bms zz)(HVRd2V dπ

( )∫ −⎥⎦

⎤⎢⎣

⎡ −⎟⎠⎞

⎜⎝⎛ −+=

H

H ts

tbtts

ts

zz)(HVzHH

RRRd2V dπ

Vtotal = Vb + Vms + Vts

Fond

Borddroit

Bordconique

H ts

H

R t

b

z

bottom

middlesection

topsection

H

Hms

R

R

z

H

0

h0 h0 + 2,5 cm h0 + 5 cm h0 + 10 cm h0 + 18 cm

2mm

Bubbles rising…Experiment

Foam Volume > Bottle Neck Volume

close to critical volume

for gushing (~ 6 cm3)

Chemical contribution to the nucleation

increases

decreases

decreases

decreases

2 bubbles growing in non supersaturated acidic liquid

More nucleation sites with CaCO3 in acidific

supersaturated beverages

Nucleationif Rc < Rhole

4mm 12mm

4mm

2 0.9 0.65µm

0.8 0.5 0.71

0.5 0.8 10.7

0.9 2 50.6

Rhole

Rbubble

Rmin =

Rhole

Dissolution Local Supersaturation Local Critical Radius Rc nucleation

Chemically Aided Nucleation of Bubblesin Sparkling Baverages

Chemically Aided Nucleation of Bubblesin Sparkling Baverages