The Printer’s Instability: The Dynamical Regimes of Directional Viscous Fingering

摘要: Important experimental and theoretical efforts have been devoted recently to the dynamical behaviours of extended systems (reviews can be found in References 1 2). In this spirit, experiments were done Rayleigh-Benard instability aimed at study onset chaos periodic structures with a large number cells3,4. On other hand electroconvection liquid crystals5,6, convection binary fluid mixtures7,8 Faraday experiment9,10 show rich dynamics due presence two independent control parameters. particular, propagative modes are observed, sometimes confined limited domains. Propagation also exists Taylor-Couette flows where it creates spiral structures11–13. For sake simplicity comparison models, one-dimensionality has sought systems. This is obtained by confinement above-mentioned experiments3,4 Another way reach boundary. boundary limit between convective rolls affected oscillatory instability14 or an interface two-dimensionally media. latter case, if front generates cells, their one dimensional good approximation. Such situations directional phase transition crystal15, eutectic crystallisation16 viscous fingering l7a,b. We presented previously17a results on widening gap. The present article reports development our work nonlinear regimes instability.