boa mmpe 2014 - kit€¦ · xuan cai1, holger marschall2, martin wörner1 and olaf deutschmann1 1...

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Page 1: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

76021 Karlsruhe, Germany 2 Technische Universität Darmstadt, Center of Smart Interfaces,

64287 Darmstadt, Germany

In this paper, we use a phase field method coupled with the Navier-Stokes equations for numerical investigation of wetting phenomena. Simulations on capillary rise and droplet wetting on a flat substrate with fixed grids produce steady computational results in good agreement with analytical solutions and experimental data in the literature. As key element to achieve CPU-time efficient simulations, we present the first 3D finite-volume based phase-field simulations for wetting phenomena with adaptive mesh refinement around interface, to the best of our knowledge. Results for the droplet motion on an inclined plane indicate that the droplet speed depends critically on the mobility. Since in our phase-field method, the mobility (respectively the corresponding Peclet number) is rather a numerical than a physically measurable parameter, we conclude that the method is not yet predictive for droplet sliding on inclined surface.

2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

116

Page 2: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

2.1 The phase field method

CC

C A B C CA CB

C

C Ct Pe

C C Cn C

C C CCn

e

2.2 Equations of fluid flow

C Re p Ct

C CCa Cn

Eo CCa

B

A

C C C

B

A

C C C

A,B μA,Bt p

Re AL U μACa μAU

Eo A B gL g

PeL U Cn L

Pe

Cn

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.2.3 Numerical treatment

PeCn

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3.1 2D static-mesh simulations 3.1.1 Capillary rise

w

2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

117

Page 3: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

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3.1.2 Partial droplet wetting 3.1.2.1 Final droplet shape

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L H

e e

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2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

118

Page 4: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

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3.1.2.2 Spreading dynamics

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μ

μ

μ

Pe

Pe

Re Ca , Cn Eo e μ

3.2 3D adaptive mesh simulations

dynamicRefineFvMesh

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2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

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Page 5: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

3.2.1 Droplet wetting on flat substrate

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e

0 eRe Ca , Pe Cn Eo μ

e

e

e

e

0 e

Re Ca , Pe Cn Eo μ

3.2.2 Droplet wetting on inclined plane

0 e Re Ca , Pe Cn Eo μ

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2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

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Page 6: BoA MMPE 2014 - KIT€¦ · Xuan Cai1, Holger Marschall2, Martin Wörner1 and Olaf Deutschmann1 1 Karlsruhe Institute of Technology, Institute of Catalysis Research and Technology,

Pe

s0 e Re Ca , Cn Eo μ V

Pe

Pe

2nd International Symposium on Multiscale Multiphase Process Engineering - Hamburg, 24-27 September 2014

121