Applied Mathematics and Mechanics >
Dripping retardation with corrugated ceiling
Received date: 2018-01-12
Revised date: 2018-03-06
Online published: 2018-08-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 91752203, 11490553, and 11521091)
The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.
Dong LUO, Jianjun TAO . Dripping retardation with corrugated ceiling[J]. Applied Mathematics and Mechanics, 2018 , 39(8) : 1165 -1172 . DOI: 10.1007/s10483-018-2357-6
[1] CHANDRASEKHAR, S. Hydrodynamic and Hydromagnetic Stability, Dover, New York (1981)
[2] NETTLETON, L. L. Fluid mechanics of salt domes. Bulletin of the American Association of Petroleum Geologists, 18, 1175-1204(1934)
[3] SELIG, F. A theoretical prediction of salt dome patterns. Geophysics, 30, 633-643(1965)
[4] LISTER, J. R. and KERR, R. C. The effect of geometry on the gravitational instability of a buoyant region of viscous fluid. Journal of Fluid Mechanics, 202, 577-594(1989)
[5] YIANTSIOS, S. G. and HIGGINS, B. G. Rayleigh-Taylor instability in thin viscous films. Physics of Fluids A, 1, 1484-1501(1989)
[6] LIN, C. D., XU, A. G., ZHANG, G. C., LUO, K. H., and LI, Y. J. Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows. Physical Review E, 96, 053305(2017)
[7] FERMIGIER, M., LIMAT, L., WESFREID, J. E., BOUDINET, P., and QUILLIET, C. Twodimensional patterns in Rayleigh-Taylor instability of a thin-layer. Journal of Fluid Mechanics, 236, 349-383(1992)
[8] LIMAT, L., JENFFER, P., DAGENS, B., TOURON, E., FERMIGIER, M., and WESFREID, J. E. Gravitational instabilities of thin liquid layers-dynamics of pattern selection. Physica D, 61, 166-182(1992)
[9] LAPUERTA, V., MANCEBO, F. J., and VEGA, J. M. Control of Rayleigh-Taylor instability by vertical vibration in a large aspect ratio containers. Physical Review E, 64, 016318(2001)
[10] CARNEVALE, G. F., ORLANDI, P., ZHOU, Y., and KLOOSTERZIEL, R. C. Rotational suppression of Rayleigh-Taylor instability. Journal of Fluid Mechanics, 457, 181-190(2002)
[11] TAO, J. J., HE, X. T., YE, W. H., and BUSSE, F. H. Nonlinear Rayleigh-Taylor instability of rotating inviscid fluids. Physical Review E, 87, 013001(2013)
[12] BURGESS, J. M., JUEL, A., MCCORMICK, W. D., SWIFT, J. B., and SWINNEY, H. L. Suppression of dripping from a ceiling. Physical Review Letters, 86, 1203-1206(2001)
[13] ALEXEEV, A. and ORON, A. Suppression of the Rayleigh-Taylor instability of thin liquid films by the Marangoni effect. Physics of Fluids, 19, 082101(2007)
[14] WEIDNER, D. E., SCHWARTZ, L. W., and ERES, M. H. Suppression and reversal of drop formation in a model paint film. Chemical Product and Process Modeling, 2, 1-30(2007)
[15] XIE, C. Y., TAO, J. J., SUN, Z. L., and LI, J. Retarding viscous Rayleigh-Taylor mixing by an optimized additional mode. Physical Review E, 95, 023109(2017)
[16] CIMPEANU, R., PAPAGEORGIOU, D. T., and PETROPOPULOS, P. G. On the control and suppression of the Rayleigh-Taylor instability using electric fields. Physics of Fluids, 26, 022105(2014)
[17] BRUN, P. T., DAMIANO, A., RIEU, P., BALESTRA, G., and GALLAIRE, F. Rayleigh-Taylor instability under an inclined plane. Physics of Fluids, 27, 084107(2015)
[18] POPINET, S. An accurate adaptive solver for surface tension driven interfacial flows. Journal of Computational Physics, 228, 5838-5866(2009)
[19] ALMGREN, A. S., BELL, J. B., COLLELA, P., HOWELL, L. H., and WELCOME, M. L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. Journal of Computational Physics, 142, 1-46(1998)
[20] LISTER, J. R., RALLISON, J. M., and REES, S. J. The nonlinear dynamics of pendent drops on a thin film coating the underside of a ceiling. Journal of Fluid Mechanics, 647, 239-264(2010)
/
| 〈 |
|
〉 |
Email Alert
RSS