We theoretically and experimentally study the quasistatic growth of bubbles in a gelatin gel under dissolved-gas supersaturation in order to examine the role of the gel elasticity in the mass-diffusion-driven process. First, we model the diffusion-driven bubble growth with the classical Epstein-Plesset approach for quasistatic bubble growth, accounting for elasticity of the medium surrounding the bubbles. Next, we devise an experimental technique to visualize the bubble growth in an air-supersaturated gel of different gelatin concentrations and to obtain the growth rate of the bubble. We show, from comparisons between the theory and experiments, that the bubble growth is hindered by the gel elasticity.

1.
M.
Robinson
,
A. C.
Fowler
,
A. J.
Alexander
, and
S. B. G.
O’Brien
, “
Waves in Guinness
,”
Phys. Fluids
20
,
067101
(
2008
).
2.
G. Y.
Gor
and
A. E.
Kuchma
, “
Dynamics of gas bubble growth in a supersaturated solution with Sievert’s solubility law
,”
J. Chem. Phys.
131
,
034507
(
2009
).
3.
A. A.
Chernov
,
V. K.
Kedrinsky
, and
A. A.
Pil’nik
, “
Kinetics of gas bubble nucleation and growth in magmatic melt at its rapid decompression
,”
Phys. Fluids
26
,
116602
(
2014
).
4.
P.
Shah
,
G. M.
Champbel
,
S. L.
Mckee
, and
C. D.
Rielly
, “
Proving of bread dough: Modeling the growth of individual bubbles
,”
Food Bioprod. Process.
76
,
73
79
(
1998
).
5.
J. M.
Solano-Altamirano
and
S.
Goldman
, “
The lifetimes of small arterial gas emboli, and their possible connection to inner ear decompression sickness
,”
Math. Biosci.
252
,
27
35
(
2014
).
6.
P. S.
Epstein
and
M. S.
Plesset
, “
On the stability of gas bubbles in liquid-gas solutions
,”
J. Chem. Phys.
18
,
1505
1509
(
1950
).
7.
T.
Yamashita
and
K.
Ando
, “
Aeration of water with oxygen microbubbles and its purging effect
,”
J. Fluid Mech.
825
,
16
28
(
2017
).
8.
C. E.
Brennen
,
Cavitation and Bubble Dynamics
(
Cambridge University Press
,
2013
).
9.
C.
Hua
and
E.
Johnsen
, “
Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium
,”
Phys. Fluids
25
,
083101
(
2013
).
10.
F.
Hamaguchi
and
K.
Ando
, “
Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation
,”
Phys. Fluids
27
,
113103
(
2015
).
11.
R.
Oguri
and
K.
Ando
, “
Cavitation bubble nucleation induced by shock-bubble interaction in a gelatin gel
,”
Phys. Fluids
30
,
051904
(
2018
).
12.
R.
Haberman
,
Applied Partial Differential Equations
(
Pearson
,
2013
).
13.
J. H.
Johnston
and
G. T.
Pread
, “
The surface tension of gelatin solutions
,”
Biochem. J.
19
,
281
289
(
1925
).
14.
E.
Shirota
and
K.
Ando
, “
Estimation of mechanical properties of gelatin using a microbubble under acoustic radiation force
,”
J. Phys.: Conf. Ser.
656
,
012001
(
2015
).
15.
R.
Gaudron
,
M. T.
Warnez
, and
E.
Johnsen
, “
Bubble dynamics in a viscoelastic medium with nonlinear elasticity
,”
J. Fluid Mech.
766
,
54
75
(
2015
).
16.
M. T.
Warnez
and
E.
Johnsen
, “
Numerical modeling of bubble dynamics in viscoelastic media with relaxation
,”
Phys. Fluids
27
,
063103
(
2015
).
17.
C. T.
Wilson
,
T. L.
Hall
,
E.
Johnsen
,
L.
Mancia
,
M.
Rodriguez
,
J. E.
Lundt
,
T.
Colonius
,
D. L.
Henann
,
C.
Franck
,
Z.
Xu
, and
J. R.
Sukovich
, “
A comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media
,”
Phys. Rev. E
99
,
043103
(
2019
).
18.
P.
Movahed
,
W.
Kreider
,
A. D.
Maxwell
,
S. B.
Hutchens
, and
J. B.
Freund
, “
Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based dynamics model
,”
J. Acoust. Soc. Am.
140
,
1374
1386
(
2016
).

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