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Profile equations for film flows at moderate Reynolds numbers
Author(s) -
Kheshgi Haroon S.
Publication year - 1989
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690351017
Subject(s) - reynolds number , reynolds equation , mechanics , flow (mathematics) , mathematics , wavenumber , range (aeronautics) , newtonian fluid , reynolds averaged navier–stokes equations , reynolds decomposition , mathematical analysis , physics , classical mechanics , materials science , turbulence , optics , composite material
An approximate equation for the evolution of finite‐amplitude, long disturbances to Newtonian liquid films is found to be accurate over a wide range of Reynolds numbers. A long‐wave expansion leads to a film profile equation asymptotically correct when wave number and Reynolds number are small. Solutions of the film profile equation are compared to exact and other approximate solutions of the Navier‐Stokes system. An alternative form of the film profile equation results in remarkably accurate solutions, when Reynolds numbers are moderate, in the cases of standing or monotonically decaying waves in horizonatal films, rising film flow, final acceleration of a moving film, and film flow emerging from a slot coater.