Thermomagnetic convective flows in a vertical layer of ferrocolloid: Perturbation energy analysis and experimental study

Abstract

Flow patterns arising in a vertical differentially heated layer of nonconducting ferromagnetic fluid placed in an external uniform transverse magnetic field are studied experimentally and discussed from the point of view of the perturbation energy balance. A quantitative criterion for detecting the parametric point where the dominant role in generating a flow instability is transferred between the thermogravitational and thermomagnetic mechanisms is suggested, based on the disturbance energy balance analysis. A comprehensive experimental study of various flow patterns is undertaken, and the existence is demonstrated of oblique thermomagnetic waves theoretically predicted by Suslov [Phys. Fluids 20, 084101 (2008)] and superposed onto the stationary magnetoconvective pattern known previously. It is found that the wave number of the detected convection patterns depends sensitively on the temperature difference across the layer and on the applied magnetic field. In unsteady regimes its value varies periodically by a factor of almost 2, indicating the appearance of two different competing wave modes. The wave numbers and spatial orientation of the observed dominant flow patterns are found to be in good agreement with theoretical predictions.

Thermomagnetic convection in a layer of ferrofluid placed in a uniform oblique external magnetic field

“…This is consistent with a widely used Boussinesq thermal approximation adapted for magnetic fluids (Bashtovoy et al 1988) and is expected to be reasonable if the temperature and magnetic field variation across the layer remain small. The qualitative agreement between the computational results and the experimental observations reported in our previous work (Suslov et al 2012) indicates that indeed such a simplification preserves sufficient accuracy of the model and makes it tractable. We provide a further discussion and a quantitative justification of this simplification in § § 3 and 4.…”

“…Consistent with our previous studies (Suslov 2008;Suslov et al 2012) we consider a planar geometry: a fluid layer confined by long and wide non-magnetic plates. The choice of such a classical geometry is dictated by a number of factors.…”

“…In particular, it has been observed that when a normal magnetic field is applied to a sufficiently wide and long ferrofluid layer the convection patterns arising near the edges of the experimental layer differ drastically in both orientation and behaviour from their counterparts in the central part of the layer. Namely, while the most prominent pattern in the middle part of the layer is stationary, propagating structures have been detected near the edges that form some angle with the boundary, see figure 9 in Suslov et al (2012). The exact reasons for such a different behaviour of a ferrofluid near the edges of the flow domain remain unclear to date and our present study explores one of the plausible explanations.…”

“…There are a number of motivating factors for this study stemming from experimental observations reported by our collaborators (Bozhko & Putin 1991;Bozhko et al 1998;Bozhko & Putin 2003;Suslov et al 2012). In particular, it has been observed that when a normal magnetic field is applied to a sufficiently wide and long ferrofluid layer the convection patterns arising near the edges of the experimental layer differ drastically in both orientation and behaviour from their counterparts in the central part of the layer.…”

“…Bashtovoy et al 1988;Odenbach & Raj 2000;Odenbach 2002aOdenbach ,b, 2004Odenbach & Müller 2005;Pop & Odenbach 2006;Engler, Borin & Odenbach 2009) can significantly affect experimentally observed ferrofluid flows. The detailed set of specific assumptions and physical conditions under which the governing equations considered in § 2 are expected to be accurate has been discussed in Suslov et al (2012) and will be justified in § § 2-4. Here we just state that we assume that the concentration of the magnetic phase remains uniform in the current study and therefore we will only investigate the influence of the thermal and magnetic fields on the flow structure.…”