Chemical reactions can induce Marangoni flows by changing the surface tension of a solution open to the air, either by changing the composition and/or by modifying the temperature. We consider the case of a simple A + B → C reaction front propagating in a thin horizontal system open to air. The effect of the three chemical species on the surface tension of the aqueous solution is quantified by three solutal Marangoni numbers, while the effect of temperature changes is determined by the thermal Marangoni number. By integrating numerically the incompressible Navier–Stokes equations coupled to reaction-diffusion-convection equations for the chemical concentrations and temperature taking into account the Lewis number (ratio between heat and mass diffusivities), we emphasize the importance of thermal changes occurring due to the heat of reaction on the dynamics of chemically induced Marangoni convection. Based on the reaction-diffusion profiles of concentrations and temperature, asymptotic analytical solutions for the surface tension profiles are obtained and classified as a function of the Marangoni numbers and the Lewis number. This new classification allows for the prediction of the convective patterns in thermo-solutal Marangoni flows. The analytical predictions are further confirmed by numerical results and additional extrema in surface tension profiles induced by the thermal effects are found to affect the nonlinear dynamics.

1.
L.
Gálfi
and
Z.
Rácz
,
Phys. Rev. A
38
,
3151
(
1988
).
2.
Z.
Koza
,
J. Stat. Phys.
85
,
179
(
1996
).
3.
M.
Sinder
and
J.
Pelleg
,
Phys. Rev. E
62
,
3340
3348
(
2000
).
4.
Z.
Jiang
and
C.
Ebner
,
Phys. Rev. A
42
,
7483
7486
(
1990
).
5.
S.
Cornell
,
Z.
Koza
, and
M.
Droz
,
Phys. Rev. E
52
,
3500
(
1995
).
6.
S.
Cornell
,
M.
Droz
, and
B.
Chopard
,
Phys. Rev. A
44
,
4826
4832
(
1991
).
7.
Z.
Koza
and
H.
Taitelbaum
,
Phys. Rev. E
54
,
R1040
R1043
(
1996
).
8.
H.
Larralde
,
M.
Araujo
,
S.
Havlin
, and
H. E.
Stanley
,
Phys. Rev. A
46
,
855
859
(
1992
).
9.
B.
Chopard
and
M.
Droz
,
Europhys. Lett.
15
,
459
(
1991
).
10.
H.
Taitelbaum
,
Y.-E. L.
Koo
,
S.
Havlin
,
R.
Kopelman
, and
G. H.
Weiss
,
Phys. Rev. A
46
,
2151
2154
(
1992
).
11.
Y. E.
Koo
,
L.
Li
, and
R.
Kopelman
,
Mol. Cryst. Liq. Cryst. Incorporating Nonlinear Opt.
183
,
187
192
(
1990
).
12.
Y. E. L.
Koo
and
R.
Kopelman
,
J. Stat. Phys.
65
,
893
(
1991
).
13.
A.
Yen
,
Y.-E. L.
Koo
, and
R.
Kopelman
,
Phys. Rev. E
54
,
2447
2450
(
1996
).
14.
R.
Tiani
,
A.
De Wit
, and
L.
Rongy
,
Adv. Colloid Interface Sci.
255
,
76
83
(
2018
).
15.
L.
Rongy
and
A.
De Wit
,
J. Chem. Phys.
124
,
164705
(
2006
).
16.
L.
Rongy
,
N.
Goyal
,
E.
Meiburg
, and
A.
De Wit
,
J. Chem. Phys.
127
,
114710
(
2007
).
17.
L.
Rongy
,
P. M. J.
Trevelyan
, and
A.
De Wit
,
Phys. Rev. Lett.
101
,
084503
(
2008
).
18.
L.
Rongy
,
P.
Assemat
, and
A.
De Wit
,
Chaos
22
,
037106
(
2012
).
19.
L.
Rongy
,
P. M. J.
Trevelyan
, and
A.
De Wit
,
Chem. Eng. Sci.
65
,
2382
2391
(
2010
).
20.
P. M. J.
Trevelyan
,
C.
Almarcha
, and
A.
De Wit
,
J. Fluid Mech.
670
,
38
65
(
2011
).
21.
P. M. J.
Trevelyan
,
C.
Almarcha
, and
A.
De Wit
,
Phys. Rev. E
91
,
023001
(
2015
).
22.
R.
Tiani
and
L.
Rongy
,
J. Chem. Phys.
145
,
124701
(
2016
).
23.
A.
De Wit
and
G. M.
Homsy
,
Phys. Fluids
11
,
949
951
(
1999
).
24.
Y.
Nagatsu
,
Y.
Kondo
,
Y.
Kato
, and
Y.
Tada
,
J. Fluid Mech.
625
,
97
124
(
2009
).
25.
F.
Haudin
and
A.
De Wit
,
Phys. Fluids
27
,
113101
(
2015
).
26.
P.
Shukla
and
A.
De Wit
,
Phys. Rev. E
93
,
023103
(
2016
).
27.
D. A.
Vasquez
,
J. M.
Littley
,
J. W.
Wilder
, and
B. F.
Edwards
,
Phys. Rev. E
50
,
280
284
(
1994
).
28.
H.
Wilke
,
Physica D
86
,
508
513
(
1995
).
29.
T.
Plesser
,
H.
Wilke
, and
K. H.
Winters
,
Chem. Phys. Lett.
200
,
158
162
(
1992
).
30.
E.
Pópity-Tóth
,
D.
Horváth
, and
A.
Tóth
,
J. Chem. Phys.
135
,
074506
(
2011
).
31.
N.
Jarrige
,
I.
Bou Malham
,
J.
Martin
,
N.
Rakotomalala
,
D.
Salin
, and
L.
Talon
,
Phys. Rev. E
81
,
066311
(
2010
).
32.
G.
Schuszter
,
T.
Tóth
,
D.
Horváth
, and
A.
Tóth
,
Phys. Rev. E
79
,
016216
(
2009
).
33.
A.
Keresztessy
,
I. P.
Nagy
,
G.
Bazsa
, and
J. A.
Pojman
,
J. Phys. Chem.
99
,
5379
5384
(
1995
).
34.
J.
D’Hernoncourt
,
A.
Zebib
, and
A.
De Wit
,
Chaos
17
,
013109
(
2007
).
35.
K.
Matthiessen
,
H.
Wilke
, and
S. C.
Müller
,
Phys. Rev. E
53
,
6056
6060
(
1996
).
36.
D.
Horváth
,
T.
Bánsági
, and
A.
Tóth
,
J. Chem. Phys.
117
,
4399
4402
(
2002
).
37.
I. B.
Malham
,
N.
Jarrige
,
J.
Martin
,
N.
Rakotomalala
,
L.
Talon
, and
D.
Salin
,
J. Chem. Phys.
133
,
244505
(
2010
).
38.
M.
Böckmann
and
S. C.
Müller
,
Phys. Rev. Lett.
85
,
2506
2509
(
2000
).
39.
G.
Schuszter
,
G.
Pótári
,
D.
Horváth
, and
A.
Toth
,
Chaos
25
,
064501
(
2015
).
40.
S. H.
Park
,
S.
Parus
,
R.
Kopelman
, and
H.
Taitelbaum
,
Phys. Rev. E
64
,
055102
(
2001
).
41.
K.
Eckert
,
L.
Rongy
, and
A. D.
Wit
,
Phys. Chem. Chem. Phys.
14
,
7337
7345
(
2012
).
42.
D.
Horváth
,
M. A.
Budroni
,
P.
Bába
,
L.
Rongy
,
A.
De Wit
,
K.
Eckert
,
M. J. B.
Hauser
, and
A.
Tóth
,
Phys. Chem. Chem. Phys.
16
,
26279
26287
(
2014
).
43.
O.
Miholics
,
T.
Rica
,
D.
Horváth
, and
A.
Toth
,
J. Chem. Phys.
135
,
204501
(
2011
).
44.
R.
Tiani
and
L.
Rongy
,
Philos. Trans. R. Soc. A
381
,
20220080
(
2023
).
45.
R.
Tiani
and
L.
Rongy
,
Front. Phys.
10
,
860419
(
2022
).
46.
M. A.
Budroni
,
V.
Upadhyay
, and
L.
Rongy
,
Phys. Rev. Lett.
122
,
244502
(
2019
).
47.
M. A.
Budroni
,
A.
Polo
,
V.
Upadhyay
,
A.
Bigaj
, and
L.
Rongy
,
J. Chem. Phys.
154
,
114501
(
2021
).
48.
M. A.
Budroni
,
F.
Rossi
, and
L.
Rongy
,
ChemSystemsChem
4
,
e202100023
(
2021
).
49.
A.
Bigaj
,
M. A.
Budroni
,
D. M.
Escala
, and
L.
Rongy
,
Phys. Chem. Chem. Phys.
25
,
11707
11716
(
2023
).
50.
A. A.
Nepomnyashchy
,
M. G.
Velarde
, and
P.
Colinet
,
Interfacial Phenomena and Convection
(
Taylor & Francis
,
2001
).
51.
P.
Bába
,
L.
Rongy
,
A.
De Wit
,
M.
Hauser
,
A.
Tóth
, and
D.
Horváth
,
Phys. Rev. Lett.
121
,
024501
(
2018
).
52.
P.
Bába
,
A.
Tóth
, and
D.
Horváth
,
Langmuir
35
,
406
412
(
2019
).

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