We experimentally studied gravity-driven film flow in an inclined corrugated channel. Beyond a critical Reynolds number, three-dimensional patterns appear. We identified two different types of patterns: a synchronous and a checkerboard one. While the synchronous pattern appears at all inclination angles studied, we observed the checkerboard one only at higher inclination angles and Reynolds numbers. The patterns suppress traveling waves and stabilize the steady flow. We characterize the patterns and their generation and provide a flow-regime map.

1.
R. J.
Craster
and
O. K.
Matar
, “
Dynamics and stability of thin liquid films
,”
Rev. Mod. Phys.
81
,
1131
1198
(
2009
).
2.
C.
Heining
,
M.
Sellier
, and
N.
Aksel
, “
The inverse problem in creeping film flows
,”
Acta Mech.
223
,
841
847
(
2012
).
3.
J. P.
Kuehner
,
J. D.
Mitchell
, and
M. R.
Lee
, “
Experimental investigation of gravity-driven film flow inside an inclined corrugated pipe
,”
Phys. Fluids
31
,
122104
(
2019
).
4.
J. P.
Kuehner
,
M. R.
Lee
,
M. M.
Dodson
,
W. R.
Schirmer
,
Á. F.
Vela de la Garza Evia
, and
L. O.
Kutelak
, “
The effect of substrate amplitude and wavelength on gravity-driven film flow inside an inclined corrugated pipe
,”
Phys. Fluids
33
,
112105
(
2021
).
5.
J. P.
Kuehner
, “
Gravity-driven film flow inside an inclined corrugated pipe: An experimental investigation of corrugation shape and tip width
,”
Phys. Fluids
34
,
122113
(
2022
).
6.
M.
Valachogiannis
and
V.
Bontozoglou
, “
Experiments on laminar film flow along a periodic wall
,”
J. Fluid Mech.
457
,
133
156
(
2002
).
7.
J. A.
Rocha
,
J. L.
Bravo
, and
J. R.
Fair
, “
Distillation columns containing structured packings: A comprehensive model for their performance—2: Mass-transfer model
,”
Ind. Eng. Chem. Res.
35
,
1660
1667
(
1996
).
8.
S. V.
Alekseenko
,
V. E.
Nakoryakov
, and
B. G.
Pokusaev
,
Wave Flow of Liquid Films
(
Begell House Inc
.,
New York
,
1994
).
9.
Y.
Guo
,
W.
Hong
, and
J.-U.
Repke
, “
Hydrodynamics of new structured packings: An experimental and micro-scale CFD study
,”
Microgravity Sci. Tech.
30
,
911
924
(
2018
).
10.
Z.
Xu
,
R. K.
Singh
,
J.
Bao
, and
C.
Wang
, “
Direct effect of solvent viscosity on the physical mass transfer for wavy film flow in a packed column
,”
Ind. Eng. Chem. Res.
58
,
17524
17539
(
2019
).
11.
H.-C.
Chang
and
E. A.
Demekhin
,
Complex Wave Dynamics on Thin Films
(
Elsevier Science B.V
,
Amsterdam
,
2002
).
12.
P. H.
Gaskell
,
P. K.
Jimack
,
M.
Sellier
,
H. M.
Thompson
, and
M. C. T.
Wilson
, “
Gravity driven flow of continuous thin liquid films on non-porous substrates with topography
,”
J. Fluid Mech.
509
,
253
280
(
2004
).
13.
S. J.
Baxter
,
H.
Power
,
K. A.
Cliffe
, and
S.
Hibber
, “
Three-dimensional thin film flow over and around an obstacle on an inclined plane
,”
Phys. Fluids
21
,
032102
(
2009
).
14.
S.
Veremieiev
,
H. M.
Thompson
,
Y. C.
Lee
, and
P. H.
Gaskell
, “
Inertial thin film flow on planar surfaces featuring topography
,”
Comput. Fluids
39
,
431
450
(
2015
).
15.
S.
Varchanis
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Steady film flow over a substrate with rectangular trenches forming air inclusions
,”
Phys. Rev. Fluids
2
,
124001
(
2017
).
16.
G. F.
Dietze
, “
Effect of wall corrugations on scalar transfer to a wavy falling liquid film
,”
J. Fluid Mech.
859
,
1098
1128
(
2019
).
17.
Y. Y.
Trifonov
, “
Flow of liquid films over a single element of structured packing. Comparison of microtextures of various types
,”
Thermophys. Aeromech.
26
,
869
878
(
2019
).
18.
H.
Bonart
,
S.
Rajes
,
J.
Jung
, and
J.-U.
Repke
, “
Stability of gravity-driven liquid films overflowing microstructures with sharp corners
,”
Phys. Rev. Fluids
5
,
094001
(
2020
).
19.
S. K.
Pal
,
Y. V. S. S.
Sanyasiraju
, and
R.
Usha
, “
A consistent energy integral model for a film over a substrate featuring topographies
,”
Int. J. Numer. Methods Fluids
93
,
3424
3446
(
2021
).
20.
S. K.
Pal
,
Y. V. S. S.
Sanyasiraju
, and
R.
Usha
, “
Investigation on the performance of meshfree RBF based method for the solution of thin film flows over topographies through depth-averaged Momentum Integral Model
,”
J. Comput. Sci.
63
,
101777
(
2022
).
21.
S.
Kalliadasis
,
C.
Bielarz
, and
G. M.
Homsy
, “
Steady free-surface thin film flows over topography
,”
Phys. Fluids
12
,
1889
1898
(
2000
).
22.
Z.
Cao
,
M.
Vlachogiannis
, and
V.
Bontozoglou
, “
Experimental evidence for a short-wave global mode in film flow along periodic corrugations
,”
J. Fluid Mech.
718
,
304
320
(
2013
).
23.
V.
Bontozoglou
, “
Laminar film flow along a periodic wall
,”
CMES
1
,
133
142
(
2000
).
24.
N. A.
Malamataris
and
V.
Bontozoglou
, “
Computer aided analysis of viscous film flow along an Inclined wavy wall
,”
J. Comput. Phys.
154
,
372
392
(
1999
).
25.
V.
Bontozoglou
and
G.
Papapolymerou
, “
Laminar film flow down a wavy incline
,”
Int. J. Multiphase Flow
23
,
69
79
(
1997
).
26.
V.
Bontozoglou
,
S.
Kalliadasis
, and
A. J.
Karabelas
, “
Inviscid free-surface flow over a periodic wall
,”
J. Fluid Mech.
226
,
189
203
(
1991
).
27.
S.
Veremieiev
and
D. H.
Wacks
, “
Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method
,”
Phys. Fluids
31
,
022101
(
2019
).
28.
A.
Wierschem
,
M.
Scholle
, and
N.
Aksel
, “
Comparison of different theoretical approaches to experiments on film flow down an inclined wavy channel
,”
Exp. Fluids
33
,
429
442
(
2002
).
29.
A.
Wierschem
,
C.
Lepski
, and
N.
Aksel
, “
Effect of long undulated bottoms on thin gravity-driven films
,”
Acta Mech.
179
,
41
66
(
2005
).
30.
S.
Mukhopadhyay
and
A.
Mukhopadhyay
, “
Hydrodynamics and instabilities of falling liquid film over a non-uniformly heated inclined wavy bottom
,”
Phys. Fluids
32
,
074103
(
2020
).
31.
A.
Wierschem
,
M.
Scholle
, and
N.
Aksel
, “
Vortices in film flow over strongly undulated bottom profiles at low Reynolds numbers
,”
Phys. Fluids
15
,
426
435
(
2003
).
32.
N.
Aksel
and
M.
Schörner
, “
Films over topography: From creeping flow to linear stability, theory, and experiments, a review
,”
Acta Mech.
229
,
1453
1482
(
2018
).
33.
M.
Dauth
and
N.
Aksel
, “
Breaking of waves on thin films over topographies
,”
Phys. Fluids
30
,
082113
(
2018
).
34.
A.
Wierschem
and
N.
Aksel
, “
Hydraulic jumps and standing waves in gravity-driven flows of viscous liquids in wavy open channels
,”
Phys. Fluids
16
,
3868
3877
(
2004
).
35.
A.
Wierschem
,
T.
Pollak
,
C.
Heining
, and
N.
Aksel
, “
Suppression of eddies in films over topography
,”
Phys. Fluids
22
,
113603
(
2010
).
36.
V.
Bontozoglou
and
G.
Papapolymerou
, “
Wall-triggered interfacial resonance in laminar gas liquid flow
,”
Int. J. Multiphase Flow
24
,
131
143
(
1998
).
37.
Y.
Guo
,
N.
Liu
,
L.
Cai
, and
W.
Hong
, “
Experimental and numerical investigations of film flow behaviors in resonance section over corrugated plates
,”
J. Zhejiang Univ.-Sci. A
20
,
148
162
(
2019
).
38.
C.
Heining
,
V.
Bontozoglou
,
N.
Aksel
, and
A.
Wierschem
, “
Nonlinear resonance in viscous films on inclined wavy planes
,”
Int. J. Multiphase Flow
35
,
78
90
(
2009
).
39.
D.
Pettas
,
G.
Karapetsas
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Viscoelastic film flows over an inclined substrate with sinusoidal topography—I: Steady state
,”
Phys. Rev. Fluids
4
,
083303
(
2019
).
40.
D.
Pettas
,
G.
Karapetsas
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Viscoelastic film flows over an inclined substrate with sinusoidal topography—II: Linear stability analysis
,”
Phys. Rev. Fluids
4
,
083304
(
2019
).
41.
A.
Sharma
,
P. K.
Ray
, and
D. T.
Papageorgiou
, “
Dynamics of gravity-driven viscoelastic films on wavy walls
,”
Phys. Rev. Fluids
4
,
063305
(
2019
).
42.
S.
Mukhopadhyay
and
A.
Mukhopadhyay
, “
Waves and instabilities of viscoelastic fluid film flowing down an inclined wavy bottom
,”
Phys. Rev. E
102
,
023117
(
2020
).
43.
D.
Pettas
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Steady flow of a viscoelastic film over an inclined plane featuring periodic slits
,”
J. Non-Newtonian Fluid Mech.
278
,
104243
(
2020
).
44.
E. I.
Mogilevskii
, “
Non-Newtonian fluid film flowing down an inclined plane with a periodic topography
,”
Fluid Dyn.
56
,
786
798
(
2021
).
45.
A.
Marousis
,
D.
Pettas
,
G.
Karapetsas
,
Y.
Dimakopoulos
, and
J.
Tsamopoulos
, “
Stability analysis of viscoelastic film flows over an inclined substrate with rectangular trenches
,”
J. Fluid Mech.
915
,
A98
(
2021
).
46.
A.
Åkesjö
,
M.
Gourdon
,
L.
Vamling
,
F.
Innings
, and
S.
Sasic
, “
Modified surfaces to enhance vertical falling film heat transfer—An experimental and numerical study
,”
Int. J. Heat Mass Transfer
131
,
237
251
(
2019
).
47.
S.
Mukhopadhyay
,
N.
Cellier
, and
A.
Mukhopadhyay
, “
Long-wave instabilities of evaporating/condensing viscous film flowing down a wavy inclined wall: Interfacial phase change effect of uniform layers
,”
Phys. Fluids
34
,
042124
(
2022
).
48.
G. R.
Daly
,
P. H.
Gaskell
, and
S.
Veremieiev
, “
Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate
,”
J. Fluid Mech.
930
,
A23
(
2022
).
49.
K.
Argyradi
,
M.
Valachogiannis
, and
V.
Bontozoglou
, “
Experimental study of inclined film flow along periodic corrugations: The effect of wall steepness
,”
Phys. Fluids
18
,
012102
(
2006
).
50.
J.
Liu
,
J. B.
Schneider
, and
J. B.
Gollub
, “
Three-dimensional instabilities of film flows
,”
Phys. Fluids
7
,
55
67
(
1995
).
51.
L.
Kahouadji
,
A.
Batchvarov
,
I. T.
Adebayo
,
Z.
Jenkins
,
S.
Shin
,
J.
Chergui
,
D.
Juric
, and
O. K.
Matar
, “
A numerical investigation of three dimensional falling liquid
,”
Environ. Fluid Mech.
22
,
367
382
(
2022
).
52.
Y. S.
Kachanov
, “
Physical mechanisms of laminar-boundary-layer transition
,”
Annu. Rev. Fluid Mech.
26
,
411
482
(
1994
).
53.
X. Y.
Jiang
,
C. B.
Lee
,
X.
Chen
,
C. R.
Smith
, and
P. F.
Linden
, “
Structure evolution at early stage of boundary-layer transition: Simulation and experiment
,”
J. Fluid Mech.
890
,
A11
(
2020
).
54.
C.-M.
Ho
and
P.
Huerre
, “
Perturbed free shear layers
,”
Annu. Rev. Fluid Mech.
16
,
365
424
(
1984
).
55.
L. S.
Tuckerman
,
M.
Chantry
, and
D.
Barkley
, “
Patterns in wall-bounded shear flows
,”
Annu. Rev. Fluid Mech.
52
,
343
367
(
2020
).
56.
S.
Chen
,
T.
Zhang
,
L.
Lv
,
Y.
Chen
, and
S.
Tang
, “
Simulation of the hydrodynamics and mass transfer in a falling film wavy microchannel
,”
Chin. J. Chem. Eng.
34
,
97
105
(
2021
).
57.
A.
Wierschem
and
H.
Linde
, “
Shadowgraph contrast of internal wave trains during absorption
,” in
Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics
(
Springer-Verlag
,
Berlin, Heidelberg
,
2013
), pp.
363
370
.
58.
W.
Schöpf
,
J. C.
Patterson
, and
A. M.
Brooker
, “
Evaluation of the shadowgraph method for the convective flow in a side-heated cavity
,”
Exp. Fluids
21
,
331
340
(
1996
).
59.
M.
Schörner
,
D.
Reck
, and
N.
Aksel
, “
Does the topography's specific shape matter in general for the stability of film flows?
Phys. Fluids
27
,
042103
(
2015
).
60.
M.
Schörner
,
D.
Reck
, and
N.
Aksel
, “
Stability phenomena for beyond the Nusselt flow Revealed by experimental asymptotics
,”
Phys. Fluids
28
,
022102
(
2016
).
61.
B.
Al-Shamaa
and
A.
Wierschem
, “
Steady three-dimensional free-surface patterns in gravity-driven film flow over a sinusoidal bottom contour
,” in
Experimentelle Strömungsmechanik, Fachtagung, Erlangen, Germany
, edited by
A.
Delgado
,
B.
Gatternig
,
M.
Münsch
,
B.
Ruck
, and
A.
Leder
(
GALA e.V
.,
Karlsruhe
,
2019
), Vol.
27
, p.
36
, https://www.gala-ev.org/images/Beitraege/Beitraege2019/pdf/36.pdf.
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