Three-dimensional (3D)—steady-developing-laminar-isothermal—and gravity-driven thin liquid film flow adjacent to an inclined plane is examined and the effects of film flow rate, surface tension, and surface inclination angle on the film thickness and film width are presented. The film flow was numerically simulated using the volume of fluid model and experimental verification was conducted by measuring film thickness and width using a laser focus displacement instrument. The steady film flow that is considered in this study does not have a leading contact line, however, it has two steady side contact lines with the substrate surface at the outer edge of its width. Results reveal that the film width decreases and the average film thickness increases as the film flows down the inclined plane. The film thickness and width decrease but its streamwise velocity increases as surface inclination angle (as measured from the horizontal plane) increases. A higher film flow rate is associated with a higher film thickness, a higher film width, and a higher average film velocity. Films with higher surface tension are associated with a smaller width and a higher average thickness. A ripple develops near the side contact line, i.e., the spanwise distribution of the film thickness exhibits peaks at the outer edges of the film width and the height of this ripple increases as the surface tension or the film flow rate increases. The width of the film decreases at a faster rate along the streamwise direction if liquid film has higher surface tension. Measurements of the film thickness and the film width compare favorably with the numerically simulated results.

1.
Oron
,
A.
,
Davis
,
S. H.
, and
Bankoff
,
S. G.
, 1997, “
Long-Scale Evolution of Thin Liquid Films
,”
Rev. Mod. Phys.
0034-6861,
69
, pp.
931
980
.
2.
Gaskell
,
P. H.
,
Jimack
,
P. K.
,
Sellier
,
M.
,
Thompson
,
H. M.
, and
Wilson
,
M. C. T.
, 2004, “
Gravity-Driven Flow of Continuous Thin Liquid Films on Non-Porous Substrates With Topography
,”
J. Fluid Mech.
0022-1120,
509
, pp.
253
280
.
3.
Alekseenko
,
S. V.
, and
Nakoryakov
,
V. E.
, 1995, “
Instability of a Liquid Film Moving Under the Effect of Gravity and Gas Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
38
, pp.
2127
2134
.
4.
Billingham
,
J.
, 2008, “
Gravity-Driven Thin-Film Flow Using a New Contact Line Model
,”
IMA J. Appl. Math.
0272-4960,
73
, pp.
4
36
.
5.
Scholle
,
M.
, and
Askel
,
N.
, 2001, “
An Exact Solution of Visco-Capillary Flow in an Inclined Channel
,”
Z. Angew. Math. Phys.
0044-2275,
52
, pp.
749
769
.
6.
Baxter
,
S. J.
,
Power
,
H.
,
Cliffe
,
K. A.
, and
Hibberd
,
S.
, 2009, “
Three-Dimensional Thin Film Flow Over and Around an Obstacle on an Inclined Plane
,”
Phys. Fluids
0031-9171,
21
, p.
032102
.
7.
Sellier
,
M.
,
Lee
,
Y. C.
,
Thompson
,
H. M.
, and
Gaskell
,
P. H.
, 2009, “
Thin Film Flow on Surfaces Containing Arbitrary Occlusions
,”
Comput. Fluids
0045-7930,
38
, pp.
171
182
.
8.
Luo
,
H.
, and
Pozrikidis
,
C.
, 2007, “
Gravity-Driven Film Flow Down an Inclined Wall With Three-Dimensional Corrugations
,”
Acta Mech.
0001-5970,
188
, pp.
209
225
.
9.
Luo
,
H.
, and
Pozrikidis
,
C.
, 2006, “
Effect of Inertia on Film Flow Over Oblique and Three-Dimensional Corrugations
,”
Phys. Fluids
0031-9171,
18
, pp.
78
107
.
10.
Bontozoglou
,
V.
, and
Serifi
,
K.
, 2008, “
Falling Film Flow Along Steep Two-Dimensional Topography: The Effect of Inertia
,”
Int. J. Multiphase Flow
0301-9322,
34
, pp.
734
747
.
11.
Zhou
,
D. W.
,
Gambaryan-Roisman
,
T.
, and
Stephan
,
P.
, 2009, “
Measurement of Water Falling Film Thickness to Flat Plate Using Confocal Chromatic Sensoring Technique
,”
Exp. Therm. Fluid Sci.
0894-1777,
33
, pp.
273
283
.
12.
Roy
,
R. P.
, and
Jain
,
S.
, 1989, “
A Study of Thin Water Film Flow Down an Inclined Plate Without and With Countercurrent Air Flow
,”
Exp. Fluids
0723-4864,
7
, pp.
318
328
.
13.
Liu
,
J.
,
Schneider
,
J. B.
, and
Gollub
,
J. P.
, 1995, “
Three-Dimensional Instabilities of Film Flows
,”
Phys. Fluids
0031-9171,
7
, pp.
55
67
.
14.
Zhang
,
F.
,
Wu
,
Y. T.
,
Geng
,
J.
, and
Zhang
,
Z. B.
, 2008, “
An Investigation of Falling Liquid Films on a Vertical Heated/Cooled Plate
,”
Int. J. Multiphase Flow
0301-9322,
34
, pp.
13
28
.
15.
Lan
,
H.
,
Friedrich
,
M.
,
Armaly
,
B. F.
, and
Drallmeier
,
J. A.
, 2008, “
Simulation and Measurements of 3-D Shear-Driven Thin Liquid Film Flow in a Duct
,”
Int. J. Heat Fluid Flow
0142-727X,
29
, pp.
449
459
.
16.
Gao
,
D.
,
Morley
,
N. B.
, and
Dhir
,
V.
, 2003, “
Numerical Simulation of Wavy Falling Film Flow Using VOF Method
,”
J. Comput. Phys.
0021-9991,
192
, pp.
624
642
.
17.
Gu
,
F.
,
Liu
,
C. J.
,
Yuan
,
X. G.
, and
Yu
,
G. C.
, 2004, “
CFD Simulation of Liquid Film Flow on Inclined Plates
,”
Chem. Eng. Technol.
0930-7516,
27
, pp.
1099
1104
.
18.
Guerrero
,
H. N.
, and
Naseri-Neshat
,
H.
, 1999, “
Computer Modeling of a Glass Stream Departing From a Pour Spout Knife Edge
,”
Seventh International Symposium on Liquid-Solid Flows Joint SAME-JSME Fluids Engineering Division Summer Meeting
, San Francisco, CA, Jul. 18–23.
19.
FLUENT Inc.
, 2005, FLUENT 6.2 User’s Guide.
20.
Air Products and Chemicals Inc.
, 2004, “
Surfynol 400 Series (420, 440, 465, 485) Surfactants
,” www.airproducts.com/surfynolwww.airproducts.com/surfynol
21.
Takamasa
,
T.
, and
Hazuku
,
T.
, 2000, “
Measuring Interfacial Waves on Film Flowing Down a Vertical Plate Wall in the Entry Region Using Laser Focus Displacement Meters
,”
Int. J. Heat Mass Transfer
0017-9310,
43
, pp.
2807
2819
.
22.
Tbusam
,
S.
,
Ebner
,
J.
, and
Wittig
,
S.
, 2001, “
An Experimental Study of Liquid Film Thickness in Annular Air/Oil Flow in a Vertical Pipe Using a Laser Focus Displacement Meter
,”
International Gas Turbine and Aeroengine Congress and Exhibition
, New Orleans, LA.
23.
Hazuku
,
T.
, and
Fukamachi
,
N.
, 2005, “
Measurement of Liquid Film in Microchannels Using a Laser Focus Displacement Meter
,”
Exp. Fluids
0723-4864,
38
, pp.
780
788
.
24.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
, 2002,
Transport Phenomena
,
2nd
ed.
,
Wiley
,
New York
.
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