Temperature-concentration (activator-inhibitor) model of the magnetic fluid free surface autooscillations induced by absorption of light

A. Cebers^1,2 - T. Du¹ - W. Luo¹

¹ Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
² Institute of Physics, Latvian Academy of Sciences, Salaspils-1, LV-2169, Latvia

Abstract
Competitive influence of the temperature and concentration perturbations on the position of the free surface of magnetic liquid film under the heating by laser is considered. Assuming that characteristic thermal relaxation time is small in com-parison with characteristic hydrodynamic time of motion of magnetic liquid film and diffusion time of magnetic particles across the Gaussian beam the simple physical model for the free surface and concentration dynamics is formulated which has much in common with activator-inhibitor model considered with respect to different problems in chemistry and biology. It is shown that small parameter - ratio of hydrodynamic and diffusion times exists in the problem and set of equations is reduced to the similar one considered in mathematical literature concern-ing the singular Hopf bifurcation. The existence of the Hopf bifurcation in the pro-posed model is illustrated and characteristic properties of the corresponding bifur-cation diagram are indicated. Considering the oscillating solutions with large am-plitude it is shown that the model proposed gives the saw-tooth oscillations similar to the observed in experiment for the diameter of the diffraction rings arising in magnetic liquid due to thermal lens effect. Figs 7, Refs 11.