Aldo Figueroa

Electrically driven vortices in a weak dipolar magnetic field in a shallow electrolytic layer

Steady dipolar vortices continuously driven by electromagnetic forcing in a shallow layer of an electrolytic fluid are studied experimentally and theoretically. The driving Lorentz force is generated by the interaction of a dc uniform electric current injected in the thin layer and the non-uniform magnetic field produced by a small dipolar permanent magnet (0.33 T). Laminar velocity profiles in the neighbourhood of the zone affected by the magnetic field were obtained with particle image velocimetry in planes parallel and normal to the bottom wall. Flow planes at different depths of the layer were explored for injected currents ranging from 10 to 100 mA. Measurements of the boundary layer attached to the bottom wall reveal that owing to the variation of the field in the normal direction, a slightly flattened developing profile with no shear stresses at the free surface is formed. A quasi-two-dimensional magnetohydrodynamic numerical model that introduces the non-uniformity of the magnetic field, particularly its decay in the normal direction, was developed. Vertical diffusion produced by the bottom friction was modelled through a linear friction term. The model reproduces the main characteristic behaviour of the electromagnetically forced flow.

Electromagnetically driven oscillatory shallow layer flow

We report experimental observations of the laminar flow in a thin horizontal layer of electrolyte, generated by a time-periodic Lorentz force produced by an alternate, unidirectional electric current and the field of a small permanent magnet. The force drives a periodically oscillating dipolar vortex which displays some spatial and temporal symmetries. The attention is focused on the motion of the oscillatory layer in vertical planes perpendicular to both the bottom wall and the injected current. For different frequencies of the injected current, velocity fields were obtained using particle image velocimetry in the zone of more intense magnetic field as well as close to the edges of the magnet where the inhomogeneity of the field is more pronounced. Velocity profiles as functions of the normal coordinate are determined in characteristic points at different phases and oscillation frequencies. Experimental results are compared with a simple analytical solution and a full three-dimensional numerical simulati...

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

We present a combination of experiment, theory, and modelling on laminar mixing at large Peclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, “The diffusive strip method for scalar mixing in two-dimensions,” J. Fluid Mech. 662, 134–172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement with quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimenta...