julien landel...aps-dfd, 18-20 november 2018 julien landel university of manchester françois j....
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![Page 1: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/1.jpg)
Discussion of the impact of surfactant on the drag-
reduction potential of superhydrophobic surfaces
APS-DFD, 18-20 November 2018
Julien Landel University of Manchester
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François J. Peaudecerf
Fernando Temprano-Coleto
Frederic Gibou
Supported by
Paolo Luzzatto-Fegiz
Julien Landel, U. Manchester UK
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Superhydrophobic surfaces (SHSs)
hydrophobic surface chemistry + micro/nano patterning
500 micronsPicture by M. Reyssat
Quéré, Annu. Rev. Mater. Res. (2008)
plastron
Barthlott & Neinhuis, Planta (1997) Columbine (Aquilegia vulgaris)Lotus
Photograph by Michael Apel
Julien Landel, U. Manchester UK
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Drag reduction with SHSs
slip velocity
Wikimedia Commons
J. Philip, Z. Angew. Math. Phys. (1972)
E. Lauga and H. Stone, JFM (2003)
air-water interface ~ no shear
Julien Landel, U. Manchester UK
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Other applications of SHSs
emptying ketchup bottles
cooling heat transfer (e.g. cpu) self-cleaning windows
reduce pressure gradient in microfluidics
Julien Landel, U. Manchester UK
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Drag reduction with SHSs
• In experiments: mixed results
• Park, Sun and Kim, JFM (2014), long gratings, up to 75%
• Gruncell (2014), meshes/amorphous, negligible DR
• McHale et al., Soft Matter (2011) • Kim and Hidrovo, PoF (2012), • Bolognesi et al.. PoF (2014), • Schäffel et al., PRL (2016)
Hypothesis: surfactants might deteriorate performance
Julien Landel, U. Manchester UK
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Drag reduction with SHSs
Hypothesis: surfactants might deteriorate performance
surface tension�water
Julien Landel, U. Manchester UK
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Drag reduction with SHSs
Hypothesis: surfactants might deteriorate performance
surfactants (bulk)
surfactants (adsorbed at interface)
surface concentration
surface tension
�
�(�) < �water
Julien Landel, U. Manchester UK
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Drag reduction with SHSs
Hypothesis: surfactants might deteriorate performance
-> Marangoni forces resisting flow
�start < �end
�start > �end
reduced free-slip
Difficult to test experimentally:
In Schäffel et al. (2016), adding surfactant has an effect of the order of experimental uncertainty
Julien Landel, U. Manchester UK
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Analogy with air bubbles rising in water
Clean bubble
airwater
UniformMarangoni force Stagnant cap Remobilisation
• Bond & Newton, Phil. Mag. (1928) • Frumkin & Levich, Zhur. Fiz. Khim. (1947) • Palaparthi et al., JFM (2006)
Julien Landel, U. Manchester UK
clean does not occur and the remobilsation reduces very slightly as well as the plastron would likely fail
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Studies revealing the impact of surfactant on SHS
10�6 10�4 10�2 100
Concentration c0 (mM)
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
h⌧i/
⌧ P
Free slip
No slip
Peaudecerf, Landel, Goldstein & Luzzatto-Fegiz, PNAS (2017)
Equivalent SDS concentration in fog
Increasing surfactant concentration reduces slip
101 102 103 104
Grating length g (µm)
0.0
0.2
0.4
0.6
0.8
1.0
h⌧i/
⌧ P
contaminated
clean
Increasing gap length increases slip
Julien Landel, U. Manchester UK
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Studies revealing the impact of surfactant on SHSSong, Song, Hu, Du, Du, Choi, Rothstein, PRF (2018)
• Marangoni stresses significantly reduce slip on SHS and increase drag
• Presence of return flow in rectangular gratingsConvex surface Concave surface
• Large slip for circular grating
Lee, Choi & Kim, PRL (2008)Julien Landel, U. Manchester UK
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Bulk
• Navier-Stokes for incompressible fluid
Steady model, periodic domain
r · u = 0Rer · (uu) = �rp+r2u
r · (uc) = 1
Per2c
@(uI �)
@x=
1
Pes
@2�
@x2+ S(cI , �)
S(cI , �) = BihkcI(1� �)� eA��
i
�k
Pe
@c
@z
����I
= �S(cI , �)
@u
@z
����I
= �Ma
✓1
1� �+A�
◆@�
@x• Marangoni stress:
• Interfacial flux:
• Modified Frumkin kinetics flux:
Top wall: air water interface
• Surfactant advection diffusion:
l/2
x
y
1
g
u
Julien Landel, U. Manchester UK
• Surfactant advection diffusion
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Bulk
• Navier-Stokes for incompressible fluid
r · u = 0Rer · (uu) = �rp+r2u
r · (uc) = 1
Per2c
@(uI �)
@x=
1
Pes
@2�
@x2+ S(cI , �)
S(cI , �) = BihkcI(1� �)� eA��
i
�k
Pe
@c
@z
����I
= �S(cI , �)
@u
@z
����I
= �Ma
✓1
1� �+A�
◆@�
@x• Marangoni stress:
• Interfacial flux:
• Modified Frumkin kinetics flux:
Top wall: air water interface
• Surfactant advection diffusion:
l/2
x
y
1
g
u
Julien Landel, U. Manchester UK
• Surfactant advection diffusion
gU
D
gU
Ds
RT�m
µU
gd
�ma
gd
Uc0a
d
Steady model, periodic domain
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Bulk
• Navier-Stokes for incompressible fluid
r · u = 0Rer · (uu) = �rp+r2u
r · (uc) = 1
Per2c
@(uI �)
@x=
1
Pes
@2�
@x2+ S(cI , �)
S(cI , �) = BihkcI(1� �)� eA��
i
�k
Pe
@c
@z
����I
= �S(cI , �)
@u
@z
����I
= �Ma
✓1
1� �+A�
◆@�
@x• Marangoni stress:
• Interfacial flux:
• Modified Frumkin kinetics flux:
Top wall: air water interface
• Surfactant advection diffusion:
l/2
x
y
1
g
u
Julien Landel, U. Manchester UK
• Surfactant advection diffusion
gU
D
gU
Ds
RT�m
µU
gd
�ma
gd
Uc0a
d
aspect ratio
gas fraction
Steady model, periodic domain
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Numerical simulations137 finite-element Comsol simulations
Julien Landel, U. Manchester UK
4⇥ 10�4 Re 105
10�7 k 102
10�6 Pe 106
2 Pes 2⇥ 107
1.25⇥ 10�5 Bi 2⇥ 2.5
3 Ma 1012
2⇥ 10�3 � 2⇥ 102
Parameter variations:
0 20 40 60 80 100 120 140Simu #
10-10
10-5
100
105
1010DKkPesPe
Diffusive flux to surface Surface convection
Adsorption flux Surface convection
4⇥ 10�6 D =�(1 + k)
Pe1/2 7⇥ 102
10�5 K = Bi(1 + k) 50
2 extra parameters:
Palaparthi et al., JFM (2006)
Uniform Stagnant cap
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Uniform regime vs stagnant cap regime
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5x
10-5
100
γM
a
uniform
stagnant cap
transition
Palaparthi et al., JFM (2006)
Julien Landel, U. Manchester UK
Stagnant cap regime:K 5⇥ 10�4
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D 5⇥ 10�2<latexit sha1_base64="Z2L8jDbJBggcFCju41lRFa/gD/g=">AAACCXicbVDLSsNAFJ34rPUVdelmsAhuLElRdFnUhcsK9gFNLJPpTTt08nBmIpSQrRt/xY0LRdz6B+78GydtFtp64MLhnHu59x4v5kwqy/o2FhaXlldWS2vl9Y3NrW1zZ7clo0RQaNKIR6LjEQmchdBUTHHoxAJI4HFoe6PL3G8/gJAsCm/VOAY3IIOQ+YwSpaWeiZ2AqCElPL3KHA73+BQ7igUgsW3dpce1rGdWrKo1AZ4ndkEqqECjZ345/YgmAYSKciJl17Zi5aZEKEY5ZGUnkRATOiID6GoaEr3MTSefZPhQK33sR0JXqPBE/T2RkkDKceDpzvxuOevl4n9eN1H+uZuyME4UhHS6yE84VhHOY8F9JoAqPtaEUMH0rZgOiSBU6fDKOgR79uV50qpVbatq35xU6hdFHCW0jw7QEbLRGaqja9RATUTRI3pGr+jNeDJejHfjY9q6YBQze+gPjM8f4YCZJA==</latexit><latexit sha1_base64="Z2L8jDbJBggcFCju41lRFa/gD/g=">AAACCXicbVDLSsNAFJ34rPUVdelmsAhuLElRdFnUhcsK9gFNLJPpTTt08nBmIpSQrRt/xY0LRdz6B+78GydtFtp64MLhnHu59x4v5kwqy/o2FhaXlldWS2vl9Y3NrW1zZ7clo0RQaNKIR6LjEQmchdBUTHHoxAJI4HFoe6PL3G8/gJAsCm/VOAY3IIOQ+YwSpaWeiZ2AqCElPL3KHA73+BQ7igUgsW3dpce1rGdWrKo1AZ4ndkEqqECjZ345/YgmAYSKciJl17Zi5aZEKEY5ZGUnkRATOiID6GoaEr3MTSefZPhQK33sR0JXqPBE/T2RkkDKceDpzvxuOevl4n9eN1H+uZuyME4UhHS6yE84VhHOY8F9JoAqPtaEUMH0rZgOiSBU6fDKOgR79uV50qpVbatq35xU6hdFHCW0jw7QEbLRGaqja9RATUTRI3pGr+jNeDJejHfjY9q6YBQze+gPjM8f4YCZJA==</latexit><latexit sha1_base64="Z2L8jDbJBggcFCju41lRFa/gD/g=">AAACCXicbVDLSsNAFJ34rPUVdelmsAhuLElRdFnUhcsK9gFNLJPpTTt08nBmIpSQrRt/xY0LRdz6B+78GydtFtp64MLhnHu59x4v5kwqy/o2FhaXlldWS2vl9Y3NrW1zZ7clo0RQaNKIR6LjEQmchdBUTHHoxAJI4HFoe6PL3G8/gJAsCm/VOAY3IIOQ+YwSpaWeiZ2AqCElPL3KHA73+BQ7igUgsW3dpce1rGdWrKo1AZ4ndkEqqECjZ345/YgmAYSKciJl17Zi5aZEKEY5ZGUnkRATOiID6GoaEr3MTSefZPhQK33sR0JXqPBE/T2RkkDKceDpzvxuOevl4n9eN1H+uZuyME4UhHS6yE84VhHOY8F9JoAqPtaEUMH0rZgOiSBU6fDKOgR79uV50qpVbatq35xU6hdFHCW0jw7QEbLRGaqja9RATUTRI3pGr+jNeDJejHfjY9q6YBQze+gPjM8f4YCZJA==</latexit><latexit sha1_base64="Z2L8jDbJBggcFCju41lRFa/gD/g=">AAACCXicbVDLSsNAFJ34rPUVdelmsAhuLElRdFnUhcsK9gFNLJPpTTt08nBmIpSQrRt/xY0LRdz6B+78GydtFtp64MLhnHu59x4v5kwqy/o2FhaXlldWS2vl9Y3NrW1zZ7clo0RQaNKIR6LjEQmchdBUTHHoxAJI4HFoe6PL3G8/gJAsCm/VOAY3IIOQ+YwSpaWeiZ2AqCElPL3KHA73+BQ7igUgsW3dpce1rGdWrKo1AZ4ndkEqqECjZ345/YgmAYSKciJl17Zi5aZEKEY5ZGUnkRATOiID6GoaEr3MTSefZPhQK33sR0JXqPBE/T2RkkDKceDpzvxuOevl4n9eN1H+uZuyME4UhHS6yE84VhHOY8F9JoAqPtaEUMH0rZgOiSBU6fDKOgR79uV50qpVbatq35xU6hdFHCW0jw7QEbLRGaqja9RATUTRI3pGr+jNeDJejHfjY9q6YBQze+gPjM8f4YCZJA==</latexit>
Pes � 4⇥ 105<latexit sha1_base64="WAmECsaWfBXGPS6M4bM0/LOZDQo=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARXJVEKrosunFZwT6giWEyvWmHTiZxZiKUUDf+ihsXirj1L9z5N04fC209cOFwzr3ce0+Ycqa043xbhaXlldW14nppY3Nre8fe3WuqJJMUGjThiWyHRAFnAhqaaQ7tVAKJQw6tcHA19lsPIBVLxK0epuDHpCdYxCjRRgrsgzoEyuvBPa5iT7MYFHadu/xsFNhlp+JMgBeJOyNlNEM9sL+8bkKzGISmnCjVcZ1U+zmRmlEOo5KXKUgJHZAedAwVxOzy88kHI3xslC6OEmlKaDxRf0/kJFZqGIemMya6r+a9sfif18l0dOHnTKSZBkGni6KMY53gcRy4yyRQzYeGECqZuRXTPpGEahNayYTgzr+8SJqnFdepuDfVcu1yFkcRHaIjdIJcdI5q6BrVUQNR9Iie0St6s56sF+vd+pi2FqzZzD76A+vzB6kZlbk=</latexit><latexit sha1_base64="WAmECsaWfBXGPS6M4bM0/LOZDQo=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARXJVEKrosunFZwT6giWEyvWmHTiZxZiKUUDf+ihsXirj1L9z5N04fC209cOFwzr3ce0+Ycqa043xbhaXlldW14nppY3Nre8fe3WuqJJMUGjThiWyHRAFnAhqaaQ7tVAKJQw6tcHA19lsPIBVLxK0epuDHpCdYxCjRRgrsgzoEyuvBPa5iT7MYFHadu/xsFNhlp+JMgBeJOyNlNEM9sL+8bkKzGISmnCjVcZ1U+zmRmlEOo5KXKUgJHZAedAwVxOzy88kHI3xslC6OEmlKaDxRf0/kJFZqGIemMya6r+a9sfif18l0dOHnTKSZBkGni6KMY53gcRy4yyRQzYeGECqZuRXTPpGEahNayYTgzr+8SJqnFdepuDfVcu1yFkcRHaIjdIJcdI5q6BrVUQNR9Iie0St6s56sF+vd+pi2FqzZzD76A+vzB6kZlbk=</latexit><latexit sha1_base64="WAmECsaWfBXGPS6M4bM0/LOZDQo=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARXJVEKrosunFZwT6giWEyvWmHTiZxZiKUUDf+ihsXirj1L9z5N04fC209cOFwzr3ce0+Ycqa043xbhaXlldW14nppY3Nre8fe3WuqJJMUGjThiWyHRAFnAhqaaQ7tVAKJQw6tcHA19lsPIBVLxK0epuDHpCdYxCjRRgrsgzoEyuvBPa5iT7MYFHadu/xsFNhlp+JMgBeJOyNlNEM9sL+8bkKzGISmnCjVcZ1U+zmRmlEOo5KXKUgJHZAedAwVxOzy88kHI3xslC6OEmlKaDxRf0/kJFZqGIemMya6r+a9sfif18l0dOHnTKSZBkGni6KMY53gcRy4yyRQzYeGECqZuRXTPpGEahNayYTgzr+8SJqnFdepuDfVcu1yFkcRHaIjdIJcdI5q6BrVUQNR9Iie0St6s56sF+vd+pi2FqzZzD76A+vzB6kZlbk=</latexit><latexit sha1_base64="WAmECsaWfBXGPS6M4bM0/LOZDQo=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARXJVEKrosunFZwT6giWEyvWmHTiZxZiKUUDf+ihsXirj1L9z5N04fC209cOFwzr3ce0+Ycqa043xbhaXlldW14nppY3Nre8fe3WuqJJMUGjThiWyHRAFnAhqaaQ7tVAKJQw6tcHA19lsPIBVLxK0epuDHpCdYxCjRRgrsgzoEyuvBPa5iT7MYFHadu/xsFNhlp+JMgBeJOyNlNEM9sL+8bkKzGISmnCjVcZ1U+zmRmlEOo5KXKUgJHZAedAwVxOzy88kHI3xslC6OEmlKaDxRf0/kJFZqGIemMya6r+a9sfif18l0dOHnTKSZBkGni6KMY53gcRy4yyRQzYeGECqZuRXTPpGEahNayYTgzr+8SJqnFdepuDfVcu1yFkcRHaIjdIJcdI5q6BrVUQNR9Iie0St6s56sF+vd+pi2FqzZzD76A+vzB6kZlbk=</latexit>
![Page 18: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/18.jpg)
Modelling the uniform regime: velocity field
Bulk
• Navier-Stokes for incompressible fluid
Assumptions
Expansion solution of the surfactant-free Stokes problem,coefficients computed numerically (Lauga & Stone JFM, 2003)
Solution
l/2
x
y
1
g
u
Julien Landel, U. Manchester UK
• Stokes flow:
• Uniform Marangoni shear at interface:
![Page 19: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/19.jpg)
Modelling the uniform regime: surfactant Marangoni shear
Full transport problem coupled with the Stokes flow solution and the surfactant kinetics
l/2
x
y
1
g
u
Julien Landel, U. Manchester UK
Assumptions
� ⌧ 1• small surfactant concentration:
• linearisation of transport equations
Solution
�Ma ⇡ �2F(g, s)k⇤
g
2F(g, s)k⇤
g+
1
Pes+
1
2
✓1
2g+
1
2
◆2 Bi
1 + BiPe�g �
!�1
from Stokes flow Note: k⇤ = kMaMarangoni weighted normalised bulk concentration
![Page 20: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/20.jpg)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1|γMa|
10-5
100
105
|λtheory−λda
ta|/|λ
data| With Surfactant
No surfactant
Slip length in uniform regime
Julien Landel, U. Manchester UK
Free slip interface
No slip interface
10% error
�Ma ⇡ �2F(g, s)k⇤
g
2F(g, s)k⇤
g+
1
Pes+
1
2
✓1
2g+
1
2
◆2 Bi
1 + BiPe�g �
!�1
![Page 21: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/21.jpg)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1|γMa|
10-5
100
105
|λtheory−λda
ta|/|λ
data| With Surfactant
No surfactant
Slip length in uniform regime
Julien Landel, U. Manchester UK
Free slip interface
No slip interface
10% error
�Ma ⇡ �2F(g, s)k⇤
g
2F(g, s)k⇤
g+
1
Pes+
1
2
✓1
2g+
1
2
◆2 Bi
1 + BiPe�g �
!�1
![Page 22: Julien Landel...APS-DFD, 18-20 November 2018 Julien Landel University of Manchester François J. Peaudecerf Fernando Temprano-Coleto Frederic Gibou Supported by Paolo Luzzatto-Fegiz](https://reader036.vdocuments.us/reader036/viewer/2022070821/5f2388e5a3fa6e043066f05c/html5/thumbnails/22.jpg)
Conclusion
Julien Landel, U. Manchester UK
•Surfactants can reduce significantly slip and drag reduction for SHS
•In 2D, 2 regimes observed: •uniform •stagnant cap
•How to reduce surfactant Marangoni effects: • increase grating length •(reduce surfactant concentration?) •no stagnation point: e.g. circular lanes •3D geometries: pillars, rough surfaces?
scaling model