THESIS
2017
xix, 110 pages : illustrations ; 30 cm
Abstract
Moving contact line problem plays an important role in fluid-fluid interface motion
on solid surfaces. The problem can be described by a phase-field model
consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with the
generalized Navier boundary condition (GNBC). In this thesis, we generalize
the GNBC to surfaces with complex geometry and introduce a finite element
method on unstructured 3D meshes. In order to construct a stable and efficient
solver for the case of large density and viscosity ratio, we combine the idea of
convex-splitting [34] for the Cahn-Hilliard equation and the pressure stablization
formulation [46] for the Navier-Stokes equations. Two efficient numerical methods
are presented, including a linear decoupled scheme and a linearized coupled
sche...[
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Moving contact line problem plays an important role in fluid-fluid interface motion
on solid surfaces. The problem can be described by a phase-field model
consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with the
generalized Navier boundary condition (GNBC). In this thesis, we generalize
the GNBC to surfaces with complex geometry and introduce a finite element
method on unstructured 3D meshes. In order to construct a stable and efficient
solver for the case of large density and viscosity ratio, we combine the idea of
convex-splitting [34] for the Cahn-Hilliard equation and the pressure stablization
formulation [46] for the Navier-Stokes equations. Two efficient numerical methods
are presented, including a linear decoupled scheme and a linearized coupled
scheme. Numerical experiments are carried out to validate the effectiveness and
efficiency of the proposed schemes.
Accurate simulation of the interface and contact line motion requires very fine
meshes, and the computation in 3D is even more challenging. Thus, the use of
high performance computers and scalable parallel algorithms are indispensable.
A highly parallel solution strategy using different solvers for different components of the discretization is presented. More precisely, we apply a restricted additive
Schwarz preconditioned GMRES method to solve the systems arising from implicit
discretization of the Cahn-Hilliard equation and the velocity equation, and
an algebraic multigrid preconditioned CG method to solve the pressure Poisson
system. Parallel performances show that the strategy is efficient and scalable for
3D problems on a supercomputer with a large number of processors.
We apply the proposed schemes and solution algorithms to study three important
application problems, particularly for those phenomena that can not be achieved
by 2D simulations. In the first application, we study numerically the dynamics
of a droplet spreading on a rough solid surface. A mass compensation algorithm
is introduced to preserve the mass of the droplet. On a surface with circular
posts, we study how wettability of the rough surface depends on the geometry
of the posts. The contact line motion for a droplet spreading over some periodic
rough surfaces are also efficiently computed. Moreover, we study the motion of
a droplet on an inclined surface with hydrophilic or hydrophobic properties.
In the second application, we investigate the contact line motion and flow features
for a solid object impacting on a liquid surface. The motion of impact object
is governed by Newton’s second law and the surface is imposed with the GNBC
that accounts for the effect of interface tension. For 2D problems, we apply the
technique of adaptive refinement based on a posteriori error estimation in order
to achieve high numerical accuracy. We also present 3D simulations for impact
objects with different flow conditions and different geometries.
In the last application, we study the capillary force hysteresis and pinning-depinning
events by direct simulations of a fiber intersecting a liquid-air interface.
A 3D cylindrical fiber is used to model the surface with real geometric feature
as in the Atomic-Force-Microscope (AFM)-based experiments. In the numerical
experiments, we investigate how the flow velocity and wetting property affect the capillary force that generated by a defect with chemical heterogeneity or geometrical roughness.
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