We discuss a simple experiment investigating the shrinkage of surface soap bubbles sitting on a thin solid plate with a circular orifice located under the apex of the bubble. We identify three different shrinking regimes, the occurrence of which depends on a combination of key parameters that include the ratio between initial bubble and orifice sizes and physicochemical properties of the fluid system. For low-viscosity liquids and/or large ratios, a bubble remains quasi-hemispherical as shrinking proceeds. In contrast, for liquids with sufficiently large viscosities and/or small geometric ratios, a bubble seeks the shape of a spherical cap while the air inside it escapes through the orifice. In this case, shrinking proceeds with a bubble foot that either recedes over time or does not move for the largest viscosities and/or smallest ratios. We use basic physical arguments to rationalize the three identified regimes and to explain the shrinking dynamics. Specifically, this model which captures observations and measurements is based on Bernoulli's principle for the air flow, volume conservation, and a friction law that accounts for viscous dissipation at the moving bubble foot.

1.
E.
Torricelli
,
Opera Geometrica, De Sphaera et Solidis Sphaeralibus; De Motu Gravium; De Dimensione Parabolae
(
Amadoro Massa & Lorenzo de Landis
,
Florence
,
1644
).
2.
J.
Ferrand
,
L.
Favreau
,
S.
Joubaud
, and
E.
Freyssingeas
, “
Wetting effect on Torricelli's law
,”
Phys. Rev. Lett.
117
,
248002-1
5
(
2016
).
3.
D. P.
Jackson
and
S.
Sleyman
, “
Analysis of a deflating soap bubble
,”
Am. J. Phys.
78
,
990
994
(
2010
).
4.
J.
Plateau
,
Statique Exp érimentale et Théorique Des Liquides Soumis Aux Seules Forces Moléculaires
(
Gauthier-Villars
,
Paris
,
1873
).
5.
H.
Bouasse
,
Capillarité-Phénomènes Superficiels
(
Librairie Delagrave
,
Paris
,
1924
).
6.
P. G.
de Gennes
,
F.
Brochard-Wyart
, and
D.
Quéré
,
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
(
Springer
,
New York
,
2004
).
7.
L.
Salkin
,
A.
Schmit
,
P.
Panizza
, and
L.
Courbin
, “
Generating soap bubbles by blowing on soap films
,”
Phys. Rev. Lett.
116
,
077801-1
5
(
2016
).
8.
P.
Panizza
and
L.
Courbin
, “
Bubble blowing by the numbers
,”
Phys. Today
69
(
7
),
78
79
(
2016
).
9.
B.
Dollet
,
P.
Marmottant
, and
V.
Garbin
, “
Bubble dynamics in soft and biological matter
,”
Annu. Rev. Fluid Mech.
55
,
331
355
(
2019
).
10.
J.
Wu
, “
Evidence of sea spray produced by bursting bubbles
,”
Science
212
,
324
326
(
1981
).
11.
A. H.
Woodcock
,
C. F.
Kientzler
,
A. B.
Arons
, and
D. C.
Blanchard
, “
Giant condensation nuclei from bursting bubbles
,”
Nature
172
,
1144
1145
(
1953
).
12.
F.
MacIntyre
, “
Flow patterns in breaking bubbles
,”
Nature
77
,
5211
5228
(
1972
).
13.
J. C.
Bird
,
R.
de Ruiter
,
L.
Courbin
, and
H. A.
Stone
, “
Daughter bubble cascades produced by folding of ruptured thin films
,”
Nature
465
,
759
762
(
2010
).
14.
H.
Lhuissier
and
E.
Villermaux
, “
Bursting bubble aerosols
,”
J. Fluid Mech.
696
,
5
44
(
2012
).
15.
L.
Champougny
,
M.
Roché
,
W.
Drenckhan
, and
E.
Rio
, “
Life and death of not so ‘bare' bubbles
,”
Soft Matter
12
,
5276
5284
(
2016
).
16.
J.
Miguet
,
M.
Pasquet
,
F.
Rouyer
,
Y.
Fang
, and
E.
Rio
, “
Stability of big surface bubbles: Impact of evaporation and bubble size
,”
Soft Matter
16
,
1082
1090
(
2020
).
17.
S.
Poulain
and
L.
Bourouiba
, “
Disease transmission via drops and bubbles
,”
Phys. Today
72
(
5
),
70
71
(
2019
).
18.
F.
Seychelles
,
Y.
Amarouchene
,
M.
Bessafi
, and
H.
Kellay
, “
Thermal convection and emergence of isolated vortices in soap bubbles
,”
Phys. Rev. Lett.
100
,
144501-1
4
(
2008
).
19.
T.
Meuel
,
Y. L.
Xiong
,
P.
Fischer
,
C. H.
Bruneau
,
M.
Bessafi
, and
H.
Kellay
, “
Intensity of vortices: From soap bubbles to hurricanes
,”
Sci. Rep.
3
,
3455-1
7
(
2013
).
20.
L.
Salkin
,
A.
Schmit
,
R.
David
,
A.
Delvert
,
E.
Gicquel
,
P.
Panizza
, and
L.
Courbin
, “
Interfacial bubbles formed by plunging thin liquid films in a pool
,”
Phys. Rev. Fluids
2
,
063604-1
10
(
2017
).
21.
See <https://physlets.org/tracker/> for a free image processing program.
22.
See <https://imagej.nih.gov/ij/> for a free image processing program.
23.
See supplemental material at https://doi.org/10.1119/10.0002348 for an annotated script of the image processing software written with matlab and three movies (Movies S1, S2, and S3) that illustrate the three regimes seen experimentally. They can also be found here, i.e., <https://drive.google.com/drive/folders/1W5m3jq9D-gB9Cnm3HUl8GViCTtuuFT31?usp=sharing>. We provide a description of these movies in  Appendix A.
24.
S.
Arscott
, “
Wetting of soap bubbles on hydrophilic, hydrophobic, and superhydrophobic surfaces
,”
Appl. Phys. Lett.
102
,
254103-1
4
(
2013
).
25.
L.
Salkin
,
A.
Schmit
,
P.
Panizza
, and
L.
Courbin
, “
Influence of boundary conditions on the existence and stability of minimal surfaces of revolution made of soap films
,”
Am. J. Phys.
82
(
9
),
839
847
(
2014
).
26.

In the case of a spherical drop of radius R, the well-known expression of the Laplace pressure is 2γ/R. For bubbles, the factor 2 in the overpressure 2×2γ/Rc that appears in the Bernoulli's relation is due to the presence of two liquid-gas interfaces as illustrated in Fig. 4.

27.
B.
Dollet
and
I.
Cantat
, “
Deformation of soap films pushed through tubes at high velocity
,”
J. Fluid Mech.
652
,
529
539
(
2010
).
28.
I.
Cantat
, “
Liquid meniscus friction on a wet plate: Bubbles, lamellae and foams
,”
Phys. Fluids
25
,
031303-1
21
(
2013
).
29.
I.
Cantat
, private communication (March 28, 2019).

Supplementary Material

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