The present study focuses on the component transfer from one liquid phase to another liquid phase, commonly known as the extraction process, performed in a microchannel in the presence of spontaneous interfacial convection, driven by either an interfacial tension gradient or an applied external electric field. Marangoni instability occurs as a result of a lateral gradient of interfacial tension existing along the interface of the two fluids. Nonequilibrium phenomena associated with factors such as temperature imbalance, a nonuniform distribution of surface-active components at the interface, evaporation, etc. can lead to the interfacial Marangoni instability. In the present study, first, we have explored temperature gradient driven Marangoni instability, which deforms the interface with significant acceleration and induces local convective mass transfer along with the conventional diffusion mode. Next, we have explored the same phenomenon in the presence of an external electric field, which can also deform the liquid-liquid interface almost instantaneously to a considerable extent. The relative strength of the mass transfer rate for different cases, such as temperature driven instability, in the presence of uniform and nonuniform electric fields has been reported in detail. It has also been observed that, due to the larger mass transfer area, the annular flow offers an enhanced rate of mass transfer compared to the stratified flow. Additionally, this article reports that the nonuniform electric field could influence the process of interfacial instability more strongly compared to the uniform electric field. The effect of the nonuniform electric field with different spatial periodicity on the extraction process has been studied in detail.

1.
T.
Funada
, “
Marangoni instability of thin liquid sheet
,”
J. Phys. Soc. Jpn.
55
,
2191
(
1986
).
2.
S.
Kalliadasis
,
A.
Kiyashko
, and
E.
Demekhin
, “
Marangoni instability of a thin liquid film heated from below by a local heat source
,”
J. Fluid Mech.
475
,
377
(
2003
).
3.
H. P.
Kavehpour
,
B.
Ovryn
, and
G. H.
McKinley
, “
Microscopic and macroscopic structure of the precursor layer in spreading viscous drops
,”
Phys. Rev. Lett.
91
,
196104
(
2003
).
4.
B.
Ray
,
P. D. S.
Reddy
,
D.
Bandyopadhyay
,
S. W.
Joo
,
A.
Sharma
,
S.
Qian
, and
G.
Biswas
, “
Surface instability of a thin electrolyte film undergoing coupled electroosmotic and electrophoretic flows in a microfluidic channel
,”
Electrophoresis
32
,
3257
(
2011
).
5.
R.
Verma
,
A.
Sharma
,
K.
Kargupta
, and
J.
Bhaumik
, “
Electric field induced instability and pattern formation in thin liquid films
,”
Langmuir
21
,
3710
(
2005
).
6.
X.
Lei
,
L.
Wu
,
P.
Deshpande
,
Z.
Yu
,
W.
Wu
,
H.
Ge
, and
S. Y.
Chou
, “
100 nm period gratings produced by lithographically induced self-construction
,”
Nanotechnology
14
,
786
(
2003
).
7.
J.
Oh
,
G.
Manukyan
,
D.
Van den Ende
, and
F.
Mugele
, “
Electric-field–driven instabilities on superhydrophobic surfaces
,”
Europhys. Lett.
93
,
56001
(
2011
).
8.
A.
Pedchenko
and
I.
Grants
, “
Instability of rotating magnetic field driven flow in a counter-rotating cylinder
,”
Phys. Fluids
17
,
104102
(
2005
).
9.
M.
Cowley
and
R. E.
Rosensweig
, “
The interfacial stability of a ferromagnetic fluid
,”
J. Fluid Mech.
30
,
671
(
1967
).
10.
T.
Pfeil
and
H.
Klahr
, “
Mapping the conditions for hydrodynamic instability on steady-state accretion models of protoplanetary disks
,”
Astrophys. J.
871
,
150
(
2019
).
11.
O.
Shklyaev
,
V.
Yashin
,
A.
Balazs
, and
O. E. S.
Team
, “
Chemical and hydrodynamic instabilities produced by enzymatic surface reactions
,” in
APS March Meeting 2019
(
American Physical Society
,
2019
).
12.
Q.
An
and
A. M.
Steinberg
, “
The role of strain rate, local extinction, and hydrodynamic instability on transition between attached and lifted swirl flames
,”
Combust. Flame
199
,
267
(
2019
).
13.
J.-L.
Zhu
,
W.-Y.
Shi
, and
L.
Feng
, “
Bénard-Marangoni instability in sessile droplet evaporating at constant contact angle mode on heated substrate
,”
Int. J. Heat Mass Transfer
134
,
784
(
2019
).
14.
B.
Zhang
,
M.
Shahsavari
,
Z.
Rao
,
S.
Yang
, and
B.
Wang
, “
Contributions of hydrodynamic features of a swirling flow to thermoacoustic instabilities in a lean premixed swirl stabilized combustor
,”
Phys. Fluids
31
,
075106
(
2019
).
15.
A.
Alhushaybari
and
J.
Uddin
, “
Convective and absolute instability of viscoelastic liquid jets in the presence of gravity
,”
Phys. Fluids
31
,
044106
(
2019
).
16.
F. A.
Bhat
and
A.
Samanta
, “
Linear stability analysis of a surfactant-laden shear-imposed falling film
,”
Phys. Fluids
31
,
054103
(
2019
).
17.
G.
Chattopadhyay
,
U.
Ranganathan
, and
S.
Millet
, “
Instabilities in viscosity-stratified two-fluid channel flow over an anisotropic-inhomogeneous porous bottom
,”
Phys. Fluids
31
,
012103
(
2019
).
18.
R.
Alert
,
C.
Blanch-Mercader
, and
J.
Casademunt
, “
Active fingering instability in tissue spreading
,”
Phys. Rev. Lett.
122
,
088104
(
2019
).
19.
S.
Shabahang
,
J.
Kaufman
,
D.
Deng
, and
A.
Abouraddy
, “
Observation of the Plateau-Rayleigh capillary instability in multi-material optical fibers
,”
Appl. Phys. Lett.
99
,
161909
(
2011
).
20.
Q.
Wang
, “
Capillary instability of a viscous liquid thread in a cylindrical tube
,”
Phys. Fluids
25
,
112104
(
2013
).
21.
K.
Chaudhary
and
T.
Maxworthy
, “
The nonlinear capillary instability of a liquid jet. Part 3. Experiments on satellite drop formation and control
,”
J. Fluid Mech.
96
,
287
(
1980
).
22.
K.
Chaudhary
and
T.
Maxworthy
, “
The nonlinear capillary instability of a liquid jet. Part 2. Experiments on jet behaviour before droplet formation
,”
J. Fluid Mech.
96
,
275
(
1980
).
23.
M. K.
Awasthi
, “
Study on Kelvin–Helmholtz instability with heat and mass transfer
,”
J. Fluids Eng.
136
,
121202
(
2014
).
24.
M.
Siegel
, “
A study of singularity formation in the Kelvin–Helmholtz instability with surface tension
,”
SIAM J. Appl. Math.
55
,
865
(
1995
).
25.
W. D.
Smyth
and
J. N.
Moum
, “
Ocean mixing by Kelvin-Helmholtz instability
,”
Oceanography
25
,
140
(
2012
).
26.
M.
Kawaguchi
,
S.
Yamazaki
,
K.
Yonekura
, and
T.
Kato
, “
Viscous fingering instabilities in an oil in water emulsion
,”
Phys. Fluids
16
,
1908
(
2004
).
27.
K.
Ghesmat
and
J.
Azaiez
,
Effect of Medium Dispersivity on the Viscous Fingering Instability in Porous Media
(
IEEE
,
2007
).
28.
A.
Callan-Jones
,
J.-F.
Joanny
, and
J.
Prost
, “
Viscous-fingering-like instability of cell fragments
,”
Phys. Rev. Lett.
100
,
258106
(
2008
).
29.
D.
Bonn
,
H.
Kellay
, and
J.
Meunier
, “
Viscous fingering and related instabilities in complex fluids
,”
Philos. Mag. B
78
,
131
(
1998
).
30.
J. K.
Novev
,
N.
Panchev
, and
R. I.
Slavchov
, “
Evaporating foam films of pure liquid stabilized via the thermal Marangoni effect
,”
Chem. Eng. Sci.
171
,
520
(
2017
).
31.
K.
Semkov
and
N.
Kolev
, “
On the evaluation of the interfacial turbulence (the Marangoni effect) in gas (vapour)—liquid mass transfer: Part I. A method for estimating the interfacial turbulence effect
,”
Chem. Engineering Process.: Process Intensif.
29
,
77
(
1991
).
32.
P. R.
Byron
and
M. J.
Rathbone
, “
Prediction of interfacial transfer kinetics. II. Solute ionization and aqueous phase ionic strength effects in two-phase transfer and rotating diffusion cells
,”
Int. J. Pharm.
29
,
103
(
1986
).
33.
D. G.
Lopes
,
I.
Koutsamanis
,
K.
Becker
,
O.
Scheibelhofer
,
P.
Laggner
,
D.
Haack
,
M.
Stehr
,
A.
Zimmer
, and
S.
Salar-Behzadi
, “
Microphase separation in solid lipid dosage forms as the cause of drug release instability
,”
Int. J. Pharm.
517
,
403
(
2017
).
34.
E.
Skurygin
and
V.
Dil’man
, “
On Marangoni instability during desorption accompanied by evaporation
,”
J. Food Eng.
43
,
125
(
2000
).
35.
E.
Ruckenstein
and
C.
Berbente
, “
The occurrence of interfacial turbulence in the case of diffusion accompanied by chemical reaction
,”
Chem. Eng. Sci.
19
,
329
(
1964
).
36.
T. S.
Sorensen
,
Dynamics and Instability of Fluid Interfaces
, Proceedings of the Meeting, Danmarks Tekniske Hojskole, Lyngby, Denmark, May 1978 (
Springer
,
1979
).
37.
M.
Morozov
and
S.
Michelin
, “
Self-propulsion near the onset of Marangoni instability of deformable active droplets
,”
J. Fluid Mech.
860
,
711
(
2019
).
38.
B.
Sobac
,
P.
Colinet
, and
L.
Pauchard
, “
Influence of Bénard–Marangoni instability on the morphology of drying colloidal films
,”
Soft Matter
15
,
2381
(
2019
).
39.
L.
Stricker
, “
Numerical simulation of artificial microswimmers driven by Marangoni flow
,”
J. Comput. Phys.
347
,
467
(
2017
).
40.
Y. Z.
Sinzato
,
N. J. S.
Dias
, and
F. R.
Cunha
, “
An experimental investigation of the interfacial tension between liquid-liquid mixtures in the presence of surfactants
,”
Exp. Therm. Fluid Sci.
85
,
370
(
2017
).
41.
J.
Fernandes
and
M.
Sharma
, “
Effective interfacial area in agitated liquid–liquid contactors
,”
Chem. Eng. Sci.
22
,
1267
(
1967
).
42.
R.
Verma
and
M.
Sharma
, “
Mass transfer in packed liquid–liquid extraction columns
,”
Chem. Eng. Sci.
30
,
279
(
1975
).
43.
M. N.
Kashid
,
A.
Renken
, and
L.
Kiwi-Minsker
, “
Gas–liquid and liquid–liquid mass transfer in microstructured reactors
,”
Chem. Eng. Sci.
66
,
3876
(
2011
).
44.
E.
Alper
, “
Effective interfacial area in the RTL extractor from rates of extraction with chemical reaction
,”
Chem. Eng. Res. Des.
66
,
147
(
1988
).
45.
T. W.
Phillips
,
J. H.
Bannock
, and
J. C.
deMello
, “
Microscale extraction and phase separation using a porous capillary
,”
Lab Chip
15
,
2960
(
2015
).
46.
P.
Derboven
,
P. H.
Van Steenberge
,
J.
Vandenbergh
,
M. F.
Reyniers
,
T.
Junkers
,
D. R.
D’hooge
, and
G. B.
Marin
, “
Improved livingness and control over branching in RAFT polymerization of acrylates: Could microflow synthesis make the difference?
,”
Macromol. Rapid Commun.
36
,
2149
(
2015
).
47.
P.
Sarkar
,
K.
Singh
,
K.
Shenoy
,
A.
Sinha
,
H.
Rao
, and
S.
Ghosh
, “
Liquid–liquid two-phase flow patterns in a serpentine microchannel
,”
Ind. Eng. Chem. Res.
51
,
5056
(
2012
).
48.
C.-X.
Zhao
and
A. P.
Middelberg
, “
Two-phase microfluidic flows
,”
Chem. Eng. Sci.
66
,
1394
(
2011
).
49.
Y. A.
Olcer
,
M.
Tascon
,
A. E.
Eroglu
, and
E.
Boyaci
, “
Thin film microextraction: Towards faster and more sensitive microextraction
,”
TrAC Trends Anal. Chem.
113
,
93
(
2019
).
50.
A.
Jain
and
K. K.
Verma
,
Single-Drop Microextraction, Liquid Phase Extraction
(
Elsevier
,
2020
).
51.
M.
Kashid
,
I.
Gerlach
,
S.
Goetz
,
J.
Franzke
,
J.
Acker
,
F.
Platte
,
D.
Agar
, and
S.
Turek
, “
Internal circulation within the liquid slugs of a liquid–liquid slug-flow capillary microreactor
,”
Ind. Eng. Chem. Res.
44
,
5003
(
2005
).
52.
M. N.
Kashid
,
A.
Renken
, and
L.
Kiwi-Minsker
, “
Influence of flow regime on mass transfer in different types of microchannels
,”
Ind. Eng. Chem. Res.
50
,
6906
(
2011
).
53.
D. M.
Fries
,
T.
Voitl
, and
P. R.
von Rohr
, “
Liquid extraction of vanillin in rectangular microreactors
,”
Chem. Eng. Technol.
31
,
1182
(
2008
).
54.
A. B.
Vir
,
A.
Fabiyan
,
J.
Picardo
, and
S.
Pushpavanam
, “
Performance comparison of liquid–liquid extraction in parallel microflows
,”
Ind. Eng. Chem. Res.
53
,
8171
(
2014
).
55.
A.
Ghaini
,
M.
Kashid
, and
D.
Agar
, “
Effective interfacial area for mass transfer in the liquid–liquid slug flow capillary microreactors
,”
Chem. Eng. Process.: Process Intensif.
49
,
358
(
2010
).
56.
O.
Tamagawa
and
A.
Muto
, “
Development of cesium ion extraction process using a slug flow microreactor
,”
Chem. Eng. J.
167
,
700
(
2011
).
57.
N.
Naleini
,
M.
Rahimi
, and
R.
Heydari
, “
Oleuropein extraction using microfluidic system
,”
Chem. Eng. Process.: Process Intensif.
92
,
1
(
2015
).
58.
M. G.
Nandagopal
,
R.
Antony
, and
N.
Selvaraju
, “
Comparative study of liquid–liquid extraction in miniaturized channels over other conventional extraction methods
,”
Microsyst. Technol.
22
,
349
(
2016
).
59.
M.
Turkyilmazoglu
,
J.
Cole
, and
J.
Gajjar
, “
Absolute and convective instabilities in the compressible boundary layer on a rotating disk
,”
Theor. Comput. Fluid Dyn.
14
,
21
(
2000
).
60.
J.
Chaudhuri
,
S.
Timung
,
C. B.
Dandamudi
,
T. K.
Mandal
, and
D.
Bandyopadhyay
, “
Discrete electric field mediated droplet splitting in microchannels: Fission, Cascade, and Rayleigh modes
,”
Electrophoresis
38
,
278
(
2017
).
61.
J. A.
Sethian
, “
A fast marching level set method for monotonically advancing fronts
,”
Proc. Natl. Acad. Sci. U. S. A.
93
,
1591
(
1996
).
62.
L. F.
Pease
 III
and
W. B.
Russel
, “
Linear stability analysis of thin leaky dielectric films subjected to electric fields
,”
J. Non-Newtonian Fluid Mech.
102
,
233
(
2002
).
63.
E.
Sultan
,
A.
Boudaoud
, and
M. B.
Amar
, “
Evaporation of a thin film: Diffusion of the vapour and Marangoni instabilities
,”
J. Fluid Mech.
543
,
183
(
2005
).
64.
D. P.
Birnie
 III
, “
A model for drying control cosolvent selection for spin-coating uniformity: The thin film limit
,”
Langmuir
29
,
9072
(
2013
).
65.
R.
Sarma
and
P. K.
Mondal
, “
Marangoni instability in a thin film heated from below: Effect of nonmonotonic dependence of surface tension on temperature
,”
Phys. Rev. E
97
,
043105
(
2018
).
66.
E. A.
Shevchenko
,
S.
Mitra
,
S. A.
Ermakov
,
A. G.
Titov
,
A. A.
Ermakov
, and
P. S. G.
Pattader
, “
Joint mass transfer of two components associated with the spontaneous interfacial convection in the liquid–liquid extraction system
,”
Chem. Eng. Sci.
195
,
301
(
2019
).
67.
M.
Turkyilmazoglu
, “
Convective and absolute instabilities in the incompressible boundary layer on a rotating disk
,”
Hacettepe J. Math. Stat.
35
,
117
(
2006
).
68.
S.
Dutta
,
A.
Ghosh
,
P. S. G.
Pattader
, and
D.
Bandyopadhyay
, “
Electric field mediated von Kármán vortices in stratified microflows: Transition from linear instabilities to coherent mixing
,”
J. Fluid Mech.
865
,
169
(
2019
).
69.
R.
Thaokar
and
V.
Kumaran
, “
Electrohydrodynamic instability of the interface between two fluids confined in a channel
,”
Phys. Fluids
17
,
084104
(
2005
).
70.
A.
Joshi
,
M.
Radhakrishna
, and
N.
Rudraiah
, “
Rayleigh–Taylor instability in dielectric fluids
,”
Phys. Fluids
22
,
064102
(
2010
).
71.
D.
Saville
, “
Electrohydrodynamics: The Taylor-Melcher leaky dielectric model
,”
Annu. Rev. Fluid Mech.
29
,
27
(
1997
).
72.
R.
Craster
and
O.
Matar
, “
Electrically induced pattern formation in thin leaky dielectric films
,”
Phys. Fluids
17
,
032104
(
2005
).
73.
A.
Sharma
,
J.
Chaudhuri
,
V.
Kumar
,
S.
Timung
,
T. K.
Mandal
, and
D.
Bandyopadhyay
, “
Digitization of two-phase flow patterns in a microchannel induced by an external AC field
,”
RSC Adv.
5
,
029545
(
2015
).

Supplementary Material

You do not currently have access to this content.