#### Statistical Physics

# Complex fluids

The characteristics of normal fluids may change substantially when small amounts of nano-scale objects like polymers, membranes, or particles are added. A particular interesting example of such complex fluids are magnetic liquids which are suspensions of ferromagnetic grains in an appropriate carrier liquid. They combine the hydrodynamic properties of Newtonian fluids with a super-paramagnetic response to external magnetic fields (the prefix 'super' refers to the unusually high value of the relative magnetic permeability of up to ). Since almost all of their hydrodynamic properties can be modulated by external magnetic fields ferrofluids have many interesting technical and medical applications as intelligent fluids (see e.g. ferrotec).

The theoretical description of ferrofluids requires the simultaneous solution of the Navier-Stokes and continuity equations of hydrodynamics and the magneto-static Maxwell equations. The interesting and often surprising properties of ferrofluids stem from the corresponding interplay between their hydrodynamic and magnetic degrees of freedom.

#### Rolling ferrofluid drop on the surface of a liquid

V. Sterr, R. Krauß, K. I. Morozov, I. Rehberg, A. Engel, R. Richter *New J. Phys.* **10 **(2008) 063029

Rotating magnetic fields spin up the tiny magnetic grains in a ferrofluid. Due to the viscous coupling to the carrier liquid the angular momentum is transferred to the whole fluid. In this way a drop of ferrofluid that floats on the surface of a non-magnetic liquid can be propelled forward (rolldrop.mpg). The velocity with which the drop advances can be both measured experimentally and described theoretically in terms of the physical parameters characterizing the fluids and the magnetic field. The understanding of this problem is crucial if one is to construct a ferrofluid pump which operates without moving mechanical parts.

#### Suppressing the Rayleigh-Taylor instability

D. Rannacher, A. Engel, *Phys. Rev.* E** 75** (2007) 016311

The free surface of a ferrofluid is rather sensitive to external magnetic fields since its shape determines the boundary conditions for the magnetic field problem. This interplay between surface deformation and field modulation may be utilized to prevent the Rayleigh-Taylor instability of a ferrofluid layered on top of a non-magnetic liquid of smaller density. The stabilization of this potentially unstable situation is achieved by a magnetic field rotating in the plane of the flat interface. The method offers a convenient possibility to establish clean initial conditions for an experimental investigation of the Rayleigh-Taylor instability which sets in at the moment when the field is switched off.

#### Cylindrical Korteweg-deVries solitons

D. Rannacher, A. Engel, *New J. Phys.* **8** (2006) 108

The magnetic field build up by a straight, current carrying wire may stabilize a cylindrical column of ferrofluid surrounded by a non-magnetic liquid of the same density. The dispersion relation of axis-symmetric waves on the surface of the cylinder is to leading order linear which is similar to the case of shallow water waves. Accordingly, in the weakly non-linear regime cylindrical Korteweg-deVries solitons show up which may be observed experimentally. The movie on the left shows a larger and therefore faster soliton overtaking a smaller one.

#### Rotating ferrofluid drops

A. V. Lebedev, A. Engel, K. I. Morozov, H. Bauke *New. J. Phys.* **5** (2003) 57

Rotating magnetic fields spin up the tiny magnetic grains in a ferrofluid. Due to the viscous coupling to the carrier liquid the angular momentum is transferred to the whole fluid. In this way drops of magnetic fluid floating in or on a nonmagnetic liquid of appropriate density may by set into rotation. When completely immersed they show various shape bifurcations (rotdrop.mpg) with similarities to heavenly bodies.

#### Ferrofluid ratchet

A. Engel, H. W. Mueller, P. Reimann, A. Jung *Phys. Rev. Lett.* **91** (2003) 060602

A. Engel und P. Reimann, *Phys. Rev. *E** 70** (2004) 051107

V. Becker, A. Engel, *Phys. Rev.* E** 75** (2007) 031118

Due to their nanoscopic size the magnetic grains in a ferrofluid are subject to strong thermal fluctuations generated by the molecules of the carrier liquid which induce random changes of their positions and orientations. Using an appropriate time-dependent external magnetic field the orientational fluctuations may be rectified resulting in a rotation of the whole fluid probe. The combination of a deterministic force without rotating component and nondirectional thermal fluctuations to bring about directed rotation is an example for a so-called ratchet or Brownian motor representing a non-equilibrium variant of Maxwell's demon.