Artículo
Abstract:
We investigate an unsteady plane viscous gravity current of silicone oil on a horizontal glass substrate. Within the lubrication approximation with gravity as the dominant force, this current is described by the nonlinear diffusion equation [Formula Presented]=([Formula Presented][Formula Presented][Formula Presented] (φ is proportional to the liquid thickness h and m=3>0), which is of interest in many other physical processes. The solutions of this equation display a fine example of the competition between diffusive smoothening and nonlinear steepening. This work concerns the so-called waiting-time solutions, whose distinctive character is the presence of an interface or front, separating regions with h≠/0 and h=0, that remains motionless for a finite time interval [Formula Presented] meanwhile a redistribution of h takes place behind the interface. We start the experiments from an initial wedge-shape configuration [h(x)≊[Formula Presented]([Formula Presented]-x)] with a small angle ([Formula Presented]⩽0.12 rad). In this situation, the tip of the wedge, situated at [Formula Presented] from the rear wall (15 cm⩽[Formula Presented]⩽75 cm), waits at least several seconds before moving. During this waiting stage, a region characterized by a strong variation of the free surface slope (corner layer) develops and propagates toward the front while it gradually narrows and [Formula Presented]h/∂[Formula Presented] peaks. The stage ends when the corner layer overtakes the front. At this point, the liquid begins to spread over the uncovered substrate. We measure the slope of the free surface in a range ≊10 cm around [Formula Presented], and, by integration, we determine the fluid thickness h(x) there. We find that the flow tends to a self-similar behavior when the corner layer position tends to [Formula Presented]; however, near the end of the waiting stage, it is perturbed by capillarity. Even if some significant effects are not included in the above equation, the main properties of its solutions are well displayed in the experiments © 1996 The American Physical Society.
Registro:
| Documento: | Artículo |
| Título: | Waiting-time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front |
| Autor: | Marino, B.M.; Thomas, L.P.; Gratton, R.; Diez, J.A.; Betelú, S.; Gratton, J. |
| Filiación: | Instituto de Fisica Arroyo Seco, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto, 399, Tandil, 7000, Argentina Instituto Fisica del Plasma, Consejo Nacional de Investigaciones Cientificas y Técnicas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina |
| Año: | 1996 |
| Volumen: | 54 |
| Número: | 3 |
| Página de inicio: | 2628 |
| Página de fin: | 2636 |
| DOI: | http://dx.doi.org/10.1103/PhysRevE.54.2628 |
| Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Título revista abreviado: | Phys Rev E. |
| ISSN: | 1063651X |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_1063651X_v54_n3_p2628_Marino.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v54_n3_p2628_Marino |
Referencias:
- Seshadry, R., Na, T.Y., (1985) Group Invariance in Engineering Boundary Value Problems, , Springer-Verlag, New York, and
- Peletier, L.A., (1981) Applications of Nonlinear Analysis in the Physical Sciences, p. 229. , H. Ammam, N. Bazley, Pitman, Boston, in, edited by, and, p
- Bear, J., (1982) Dynamics of Fluids in Porous Media, , American Elsevier, London
- Lacey, A.A., Ockendon, J.R., Tayler, A.B., (1982) J. Appl. Math., 42, p. 1252
- Buckmaster, J., (1977) J. Fluid Mech., 81, p. 735
- Huppert, H.E., (1982) J. Fluid Mech., 121, p. 43
- Lister, J.R., Kerr, R.C., (1989) J. Fluid Mech., 203, p. 215
- Hoult, D.P., (1972) Annu. Rev. Fluid, 4, p. 341
- Simpson, J.E., (1982) Annu. Rev. Fluid Mech., 14, p. 213
- Huppert, H.E., (1986) J. Fluid Mech., 173, p. 557
- Kerr, R.C., Lister, J.R., (1987) Earth Planet. Sci. Lett., 85, p. 241
- Marino, B.M., Thomas, L., Diez, J., Gratton, R., (1996) J. Colloid. Interf. Sci., 177, p. 14
- Kath, W.L., Cohen, D.S., (1982) Stud. Appl. Math., 67, p. 79
- Aronson, D.G., Caffarelli, L.A., Kamin, S., (1983) SIAM J. Anal., 14, p. 639
- Pattle, R.E., (1959) Q. J. Mech. Appl. Math., 12, p. 407
- Barenblatt, G.I., (1979) Similarity, Self-Similarity, and Intermediate Asymptotics, , Consultants Bureau, New York
- Diez, J.A., Gratton, R., Gratton, J., (1992) Phys. Fluids A, 4, p. 1148
- Gratton, J., (1991) Fund Cosmic Phys., 15, p. 1
- Ya. B. Zel'dovich and Yu. P. Raizer, (Academic, New York, 1967); Aronson, D.G., (1970) SIAM J. Appl. Math., 19, p. 299
- Knerr, B.F., (1977) Trans. Am. Math. Soc., 234, p. 381
- Kamin, S., (1980) Free Boundary Problems, , E. Magenes, Tecnoprint, Rome, in, edited by
- Smyth, N.F., Hill, J.M., (1988) IMAJ J. Appl. Math., 40, p. 73
- Gratton, J., Vigo, C., An. AFA (to be published); J. Gratton, E. Rossello, and J. A. Diez, An. Acad. Nac. Cien. Exactas Fis. Nat. Bue Aires, 51; Aronson, D.G., Caffarelli, L.A., Vazquez, J.L., (1985) Commun. Pure Appl. Math., 38, p. 375
- Vazquez, J.L., (1984) Trans. Am. Math. Soc., 285, p. 717
- Diez, J.A., Gratton, R., Thomas, L., Marino, B., (1994) Phys. Fluids, 6, p. 24
- Ruschak, K.J., (1985) Rev. Fluid Mech., 17, p. 65
- Barnes, H.A., Fulton, J.F., Walters, K., (1989) An Introduction to Rheology, , Elsevier, New York, and
- Rahalker, R.R., (1984) Proc. R. Soc. London Ser. A, 394, p. 207
- Tanner, L.H., (1979) J. Phys. D, 12, p. 1473
- Chen, J.D., (1987) J. Colloid. Interf. Sci., 122, p. 60
Citas:
---------- APA ----------
Marino, B.M., Thomas, L.P., Gratton, R., Diez, J.A., Betelú, S. & Gratton, J. (1996) . Waiting-time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 54(3), 2628-2636.http://dx.doi.org/10.1103/PhysRevE.54.2628
---------- CHICAGO ----------
Marino, B.M., Thomas, L.P., Gratton, R., Diez, J.A., Betelú, S., Gratton, J. "Waiting-time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front" . Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 54, no. 3 (1996) : 2628-2636.http://dx.doi.org/10.1103/PhysRevE.54.2628
---------- MLA ----------
Marino, B.M., Thomas, L.P., Gratton, R., Diez, J.A., Betelú, S., Gratton, J. "Waiting-time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front" . Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 54, no. 3, 1996, pp. 2628-2636.http://dx.doi.org/10.1103/PhysRevE.54.2628
---------- VANCOUVER ----------
Marino, B.M., Thomas, L.P., Gratton, R., Diez, J.A., Betelú, S., Gratton, J. Waiting-time solutions of a nonlinear diffusion equation: Experimental study of a creeping flow near a waiting front. Phys Rev E. 1996;54(3):2628-2636.http://dx.doi.org/10.1103/PhysRevE.54.2628
