2002/07/29 by Mitchell J. Feigenbaum, Feigenbaum, Mitchell J.
Engineering · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Pattern Formation and Solitons (nlin.PS) #Soft Condensed Matter (cond-mat.soft) #Theoretical and Computational Physics #cond-mat.soft #nlin.PS
paper · pdf · doi:10.48550/arxiv.cond-mat/0207690
arxiv created 2002/07/29 · openalex publication_date 2002/07/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Saffman-Taylor channel flow without surface tension on a\nhigh-pressure driven interface, but modify the usual infinite-fluid in\ninfinite-channel configuration. Here we include the treatment of efflux by\nconsidering a finite connected body of fluid in an arbitrarily long channel,\nwith its second free interface the efflux of this configuration. We show that\nthere is a uniquely determined translating solution for the driven interface,\nwhich is exactly the 1/2 width S-T solution, following from correct symmetry\nfor a finite channel flow. We establish that there exist no perturbations about\nthis solution corresponding to a finger propagating with any other width:\nSelection is unique and isolated. The stability of this solution is anomalous,\nin that all freely impressible perturbations are stabilities, while unstable\nmodes request power proportional to their strength from the external agencies\nthat drive the flow, and so, in principle, are experimentally controllable.\nThis is very different from the behavior of the usual infinite fluid: The limit\nof infinite length is singular, and not that of the literature. We argue that\nsurface tension on the efflux interface decreases the finger-width by the ratio\nof its surface tension to velocity of the high-pressure tip. The perturbation\ntheory created here to deal with transport between two free boundaries is novel\nand dependent upon a remarkable symmetry.\n