Singularities and stability of inviscid, planar liquid membranes

• Published in: International journal of engineering science Vol. 39; no. 17; pp. 1935 - 1948
• Main Author: Ramos, Juan I.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.11.2001; Elsevier
• Subjects: Computational methods in fluid dynamics; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Inviscid flow; Linear stability; Materials science; Methods of deposition of films and coatings; film growth and epitaxy; Physics; Planar liquid membranes; Singularities; Sinuous mode; Theory and models of film growth; Inviscid flow; Linear stability; Sinuous mode; Singularities; Planar liquid membranes; Fluid mechanics; Singularity; Liquids; Membranes; Stability; Fluid dynamics; Non viscous fluid; Falling film; Spin-on coating; Numerical method; Asymptotic approximation; Deposition process
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(01)00032-5

The equations governing the fluid dynamics of inviscid, planar liquid membranes subject to pressure differences are first derived along and normal to the membrane, and then written in Cartesian coordinates. It is shown both algebraically and differentially that the steady-state equations may have removable singularities at or below the nozzle exit if the Weber number is equal to or less than one, and that these singularities indicate that the liquid exits the nozzle at an angle which is different from the nozzle exit. It is also shown that vertically falling membranes are stable and oscillate in both space and time. Finally, some asymptotic solutions of the equations are obtained.