Incollection,
Numerical Vesicle Dynamics:\boundary tracking & phase phield approach
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Vesicles are fluid droplets surrounded by a fluid and incompressible membrane.
They constitute a simple model able to describe cell (and some subcellular entitiy) dynamics.
Despite their simplicity compared to the biological systems, vesicles show an extremely rich behaviour
even in simple situations like when embedded in an external shear flow.
Two different types of approach have so far been used for vesicle dynamics: an explicit tracking of
the membrane and a phase field approach.\\
While the latter can be implemented in more general situations, i.e. when the vesicle is positioned
in a viscoelastic fluid, the former allows a faster and for some aspects simpler numerical resolution.
In my work I adopted both techniques. My aim is then to show their challanges,
some possible solutions and which results I obtained (and which in general can be obtained)
more conveniently with one or the other.\\
The main challenge of the explicit boundary tracking is the high precision needed for the computation of the
differential operators involved, which are as high as $4^th$ order.\\
On the other hand, phase field techniques suffer for the lack of agreed governing equations,
fact due to the arbitrarity of the definition of the phase field.
In this context I will discuss the advantages brought by a thermodynamically consistent derivation of the
equations.
Tags
- boundary
- consistentcy
- differential
- element
- field
- operator
- phase
- statphys23
- thermodynamical
- topic-7
- vesicle
