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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