Dripping retardation with corrugated ceiling

• Published in: Applied mathematics and mechanics Vol. 39; no. 8; pp. 1165 - 1172
• Main Authors: Luo, Dong, Tao, Jianjun
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01-08-2018; Springer Nature B.V; CAPT-HEDPS, SKLTCS, Collaborative Innovation Center of IFSA, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Ceilings; Classical Mechanics; Film thickness; Fluid- and Aerodynamics; Interface stability; Lubrication; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; 70K50; pendent film; Rayleigh-Taylor instability (RTI); corrugated wall; surface tension; O347.2
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-018-2357-6

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.