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

Aldo Figueroa (1) , Patrice Meunier (2) , Sergio Cuevas (3) , Emmanuel Villermaux (2) , Eduardo Ramos (3)

1 UAEM - Universidad Autonoma del Estado de Morelos
2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
3 Instituto de Energıas Renovables, Universidad Nacional Autonoma de Mexico, A.P. 34, Temixco, Morelos 62580, Mexico

We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet 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 experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.

Domaines: Mécanique des fluides [physics.class-ph]

Aldo Figueroa, Patrice Meunier, Sergio Cuevas, Emmanuel Villermaux, Eduardo Ramos. Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions. Physics of Fluids, 2014, 26 (1), pp.013601. ⟨10.1063/1.4861004⟩. ⟨hal-01174033⟩