The trajectory of an isolated solid particle dropped in the core of a vertical vortex is investigated theoretically and experimentally, in order to analyze the effect of the history force on the radial migration of the inclusion. Both the Stokes number (based on the particle radius and the fluid angular velocity) and the particle Reynolds number are small. The particle is heavier than the fluid, and is therefore expelled from the center of the vortex. An experimental device using spherical particles injected in a rotating cylindrical tank filled with silicone oil has been built. Experimental trajectories are compared to analytical solutions of the motion equations, which are obtained by making use of classical Laplace transforms. The analytical expression of the history force and the ejection rate are carried out. This force does not vanish, but increases exponentially and has to be taken into account for efficient predictions. In particular, calculations without history force overestimate particle ejection. The relative difference between the ejection rate with and without history force scales like the square root of the Stokes number, so that differences of the order of 10% are visible as soon as the Stokes number is of the order of 0.01. Also, agreement between experimental and theoretical trajectories is observed only if the acceleration term in the history integral involves the time derivative of the fluid velocity following the particle, rather than the acceleration of fluid points at the particle location, even for small particle Reynolds numbers. Finally, analytical calculations show that the particle ejection rate is more sensitive to the Boussinesq–Basset force than to Saffman’s lift.

A new kind of finite-amplitude convective oscillations in binary mixtures caused by the Soret effect is predicted. Such oscillations can be observed in colloidal solutions of nanoparticles whose diffusion coefficient is about two orders of magnitude less than that for molecules. Due to the small particle mobility the concentration gradient sets in so slowly, that Soret convection starts before this gradient reaches its stationary value. Soon after the onset, however, the convective motion mixes the fluid, that results in rapid damping of the motion. The concentration gradient is then formed again and the process is repeated. A period of these self-sustained oscillations is estimated for real magnetic colloids in the Bénard configuration.

This paper concerns a linear study of the convective parametric instability in the case of a Newtonian fluid confined in a Hele-Shaw cell and submitted to a vertical periodic motion. The gradient of temperature, applied to the fluid layer, is either in the same direction that gravity or in the opposite one. An asymptotic analysis shows that the Hele-Shaw approximation leads to two linear formulations depending on the order of magnitude of the Prandtl number. For these two asymptotic cases, the convective threshold is determined. It turns out that in the Hele-Shaw geometrical configuration, parametric oscillations have no influence on the criterion of stability when the Prandtl number is in the order of the unity or very superior to the unity. However, when the Prandtl number is small than unity, the parametric oscillations can affect the convective instability threshold.

The effect of a time-sinusoidal magnetic field on the onset of convection in a horizontal magnetic fluid layer heated from above and bounded by isothermal non magnetic boundaries is investigated. The analysis is restricted to static and linear laws of magnetization. A first order Galerkin method is performed to reduce the governing linear system to the Mathieu equation with damping term. Therefore, the Floquet theory is used to determine the convective threshold for the free-free and rigid-rigid cases. With an appropriate choice of the ratio of the magnetic and gravitational forces, we show the possibility to produce a competition between the harmonic and subharmonic modes at the onset of convection.