Hector Gomez

University of A Coruna

Campus de Elvina, s/n

A Coruna, Spain

Tel: +34 981 167 000 Ext: 1415

e-mail: hgomez at udc dot es

Campus de Elvina, s/n

A Coruna, Spain

Tel: +34 981 167 000 Ext: 1415

e-mail: hgomez at udc dot es

## Separation of two immiscible liquids

Two premixed phobic liquids
tend to separate when they are quenched, leading to complex
patterns. The Cahn-Hilliard equation is a classical
continuum theory describing this phenomenon. This picture
shows a snapshot of a numerical simulation of the
Cahn-Hilliard equation using Isogeometric Analysis, and an
adaptive time-stepping technique that permitted computing,
apparently for the first time, stationary states in three
dimensions. The numerical simulation of phase separation may
have relevance, for example, in the development of
biodiesel.

## Crystal growth in a supercooled liquid

Crystals surrounded by
undercooled liquid tend to grow leading to fascinating
patterns, such as, for example dendrites. This picture shows
the atomic structure of two crystallites growing in a
supercooled liquid. The image has been obtain using
large-scale numerical simulation of the Phase Field Crystal
equation. We developed a new time integration scheme that
preserves the fundamental features of the continuum theory.

## Crack propagation in a ductile material

Material properties at the
macroscale are to a large extent controlled by complex
microstructures exhibiting topological defects, such as, for
example, vacancies, grain boundaries and dislocations. These
defects are the result of complicated non-equilibrium
dynamics that takes place on atomic length scales. This
picture shows the microstrucure evolution on atomic length
scales of a ductile material that undergoes fracture. The
simulation has been performed approximating the Phase Field
Crystal equation using a new time-stepping algorithm that
inherits at the discrete level the fundamental physical
features of the theory.

## Water/water-vapor two phase flow

Water/water-vapor two-phase flows are of great importance and appear, for example, in cavitation and implosion. This piecture show a simulation of two water-vapor bubbles right after having merged. We have employed large-scale numerical simulations of the Navier-Stokes-Korteweg equations.