Numerical simulation of the behaviour of magnetic liquids
- When?
- Friday 24 June 2011, 16:00 to 17:00
- Where?
- 39AA04
- Open to:
- Staff, Students
- Speaker:
- Gunar Matthies (University of Kassel, Germany)
Abstract: Magnetic liquid or ferrofluids are complex fluids which interact with external magnetic field. Many effects can be observed.
One of the most spectacular phenomena is the Rosensweig or normal-field instability where an external magnetic field is applied perpendicular to a flat and horizontal surface. For small magnetic field strength the surface remains flat. If the magnetic field strength exceeds a critical value then a regular pattern of so-called peaks occurs.
This phenomenon can be described by a coupled system of nonlinear partial differential equations. On the one hand we have to consider the Maxwell equations in the fluid and the surrounding. On the other hand we have to take into account the Navier-Stokes equations in the time-dependent domain which is occupied by the magnetic liquid. Finally, the force balance at the free surface given by the Young-Laplace equation is of importance.
If a constant magnetic field is applied then the magnetic fluid reaches a stationary state where the liquid is in rest. For the static case we present a decoupling strategy which is based on the subproblems. An error estimate for a finite element discretisation of the Young-Laplace equation will be given.
We use the ALE approach to deal with the time-dependent domain in the dynamic case. The whole problem is decoupled in a similar way as in the static case.
The simulations in both the static and the dynamic case show that finite element methods are able to calculate the peaks shapes and the critical value for the magnetic field strength for the onset of the instability.
Moreover, the differences between the static case and the stationary limit of the dynamic case are very small.
