Theory

The phase-field model is based on a free energy functional written as function of the system's order parameter \(\phi\) (that distinguishes the different phases present in the system). In this formalism, the interface has a width \(\varepsilon\) and the order parameters vary continuously along its width. As a consequence of that, the system evolution as a whole is described by a unique set of equations applied to every phase of the system, without taking into account the boundary conditions at the interfaces.

Allen-Cahn Equation

\[ \left( \frac{\partial } { \partial t} + \mathbf{v}_m \cdot \nabla \right) \phi_m= -\frac{\delta F}{\delta \phi_m} \, , \]

Cahn-Hilliard Equation

\[ \left( \frac{\partial }{\partial t} + \textbf{v}_m \cdot \nabla \right) \phi_m = M(l_m) \nabla^2 \frac{\delta F}{\delta \phi_m} \textrm{ .} \]

Actomyosin model

Try it yourself our Python implementation in a live terminal.