Retarding the growth of the Rosensweig instability unveils a new scaling regime

Abstract

Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the bifurcation parameter by six orders of magnitude, while this regime is tiny for standard ferrofluids and cannot be resolved experimentally there. We measure the growth of the pattern by means of a two-dimensional imaging technique, and find that the slopes of the growth and decay rates are not the same-a qualitative discrepancy with respect to the theoretical predictions. We solve this discrepancy by taking into account a viscosity which is assumed to be different for the growth and decay. This may be a consequence of the measured shear thinning of the ferrofluid.

Shape and fission instabilities of ferrofluids in non-uniform magnetic fields

“…Even though the magnetization is often considered linear, the case of a non-linear magnetization has also been studied by e.g. Knieling et al (2007); Lange et al (2016).…”

Ferrofluids and bio-ferrofluids: looking back and stepping forward

“…The growth rate and characteristics of Rosensweig instability patterns depends on ferrofluid viscosity, 531 finite depth of the container, 548 microgravity or hypergravity conditions 549 and also on non-linear field dependence of magnetization 550,551 evidenced experimentally in ref. 552–554.…”

“…Using a highly viscous magnetic fluid, obtained by cooling down a commercial sample (APG E32, Ferrotec Co), the growth rate of the Rosensweig instability can be slowed down by more than 2000 times 554–556 and, consequently, the growth of the pattern takes several tens of seconds, allowing for measurements with high temporal resolution using a 2D X-ray imaging technique. 543 The plain surface and domain-covering regular up-hexagonal ( i.e.…”

“…31C(b)), due to the formation of chains of magnetic particles in the static spikes and their subsequent destruction during the decay indicated by the observed magnetically enhanced shear thinning. 554 Large scale numerical simulation of magnetic field induced patterns using specific techniques (fast multipole method; smoothed particle hydrodynamics) allows for an accurate simulation of surface shape/topology considering ferrofluids as a deformable and paramagnetic continuum with surface tension. 559…”

“…533,540 The growth rate and characteristics of Rosensweig instability patterns depends on ferrofluid viscosity, 531 finite depth of the container, 548 microgravity or hypergravity conditions 549 and also on non-linear field dependence of magnetization 550,551 evidenced experimentally in ref. 552-554. Using a highly viscous magnetic fluid, obtained by cooling down a commercial sample (APG E32, Ferrotec Co), the growth rate of the Rosensweig instability can be slowed down by more than 2000 times [554][555][556] and, consequently, the growth of the pattern takes several tens of seconds, allowing for measurements with high temporal resolution using a 2D X-ray imaging technique. 543 The plain surface and domain-covering regular up-hexagonal (i.e.…”