Simulating particles at fluid-fluid interfaces using ALE
and the diffuse-interface model
Jaensson, N.O.; Hulsen, M.A.; Anderson, P.D.
Published: 01/01/2012
Document Version
Accepted manuscript including changes made at the peer-review stage
Please check the document version of this publication:
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences
between the submitted version and the official published version of record. People interested in the research are advised to contact the
author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
Citation for published version (APA):
Jaensson, N. O., Hulsen, M. A., & Anderson, P. D. (2012). Simulating particles at fluid-fluid interfaces using ALE
and the diffuse-interface model. Poster session presented at conference; Mate Poster Award 2012 : 17th Annual
Poster Contest, .
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
• You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal ?
Take down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Download date: 31. Jul. 2017
Structure and Rheology of Complex Fluids
Simulating particles at fluid-fluid
interfaces using ALE and the
diffuse-interface model
N.O. Jaensson, M.A. Hulsen and P.D. Anderson
Introduction
When two fluids are combined with particles new materials
can be created with unique properties. For example in the
widely used Pickering emulsions, drops of one fluid are stabilized in a second fluid by particles at the interface (see Figure
1).
fluid 2
solid particles
fluid 2
simulated a particle at an interface that is pulled out of equilibrium by a force F = (0, −Fy ) during forcing time tF . For
t > tF , the external force is removed, and the system is allowed to go back to its equilibrium state.
Results are presented for simulations with a Cahn number
C = 0.01, where the Cahn number is a dimensionless measure for the interface thickness. In Figure 3 the phase field
is shown for the beginning of the simulation (left) and after a
forcing time tF = 0.1 (right).
fluid 2
fluid 1
Figure 1: A Pickering emulsion consisting of drops of one fluid inside
another fluid which are stabilized by solid particles at the interface.
Recently, it has been shown that particles can also be used to
stabilize polymer blends (see e.g. [1]), but the mechanisms
remain not well understood. We use computational modeling
as a tool for better understanding the exact mechanisms of
stabilization of the interface by particles.
Method
We model the interface between the fluids (or “phases”) as a
diffuse interface by using the Cahn-Hilliard theory [2]. Stokes
flow is assumed to describe the flow dynamics. The interface
between the particle and the fluids is modeled as a sharp interface by creating a boundary fitted mesh and applying appropriate boundary conditions. The Arbitrary Lagrange Euler
(ALE) method is used where the mesh close to the particle is
moved with the particle, while the mesh further away is stationary. Remeshing is performed when the mesh becomes too
distorted (see Figure 2) and the phase-field variables are projected onto the new mesh.
Figure 3: The phase field at t = 0 (left) and at t = tF (right).
In Figure 4 the y-coordinate of the particle is shown as a function of time for several forcing times.
0
0
−0.01
−0.01
−0.02
−0.02
y
y
−0.03
−0.04
−0.05
0
−0.03
tF = 0.10
tF = 0.07
tF = 0.05
tF = 0.03
tF = 0.02
0.2
0.4
t
0.6
0.8
tF = 0.10
tF = 0.07
tF = 0.05
tF = 0.03
tF = 0.02
−0.04
1
−0.05
0
10
20
t
30
40
50
Figure 4: The y-coordinate of the particle as a function of time (left:
t ≤ 1, right: t ≤ 50) for several forcing times.
The results show good agreement with the results of Choi and
Anderson [3].
Conclusions and future work
A numerical method that combines ALE with the diffuseinterface model was successfully implemented to simulate a
particle at an interface. Future work includes extending the
model to axisymmetric and 3D, and using a viscoelastic model
for the fluids.
References
Figure 2: An initial mesh (left) is moved in the ALE method (middle)
and when it becomes too distorted, remeshing is performed (right).
Results
Following Choi and Anderson [3], who used the Extended Finite Element Method (XFEM) to handle the sharp interface, we
/w
[1] L. Elias et al. Morphology and rheology of immiscible polymer blends
filled with silica nanoparticles. Polymer , 48(20):6029-6040, 2007.
[2] J.W. Cahn and J.E. Hilliard. Free Energy of a Nonuniform System. I. Interfacial Energy. J. Chem. Phys. , 28(2):258-267, 1958.
[3] Y.J. Choi and P.D. Anderson. Cahn-Hilliard modeling of particles suspended in two-phase flows. Int. J. Numer. Meth. Fluids, 69(5):9951015, 2012.