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Stability of a moving radial liquid sheet: Time-dependent equations

DSpace at IIT Bombay

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Title Stability of a moving radial liquid sheet: Time-dependent equations
 
Creator TIRUMKUDULU, MS
PARAMATI, M
 
Subject FLUID SHEETS
THIN SHEETS
INSTABILITY
DISINTEGRATION
DYNAMICS
CURTAIN
SHAPE
 
Description We study the stability of a radial liquid sheet produced by head-on impingement of two equal laminar liquid jets. Linear stability equations are derived from the inviscid flow equations for a radially expanding sheet that govern the time-dependent evolution of the two liquid interfaces. The analysis accounts for the varying liquid sheet thickness while the inertial effects due to the surrounding gas phase are ignored. The analysis results in stability equations for the sinuous and the varicose modes of sheet deformation that are decoupled at the lowest order of approximation. When the sheet is excited at a fixed frequency, a small sinuous displacement introduced at the point of impingement grows as it is convected downstream suggesting that the sheet is unstable at all Weber numbers (We rho(l)U(2)h/sigma) in the absence of the gas phase. Here, rho(l) is the density of the liquid, U is the speed of the liquid jet, h is the local sheet thickness, and sigma is the surface tension. The sinuous disturbance diverges at We = 2 which sets the size of the sheet, in agreement with the results of Taylor ["The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets," Proc. R. Soc. London, Ser. A 253, 313 (1959)]. Asymptotic analysis of the sinuous mode for all frequencies shows that the disturbance amplitude diverges inversely with the distance from the edge of the sheet. The varicose waves, on the other hand, are neutrally stable at all frequencies and are convected at the speed of the liquid jet. (C) 2013 AIP Publishing LLC.
 
Publisher AMER INST PHYSICS
 
Date 2014-10-14T13:28:01Z
2014-10-14T13:28:01Z
2013
 
Type Article
 
Identifier PHYSICS OF FLUIDS, 25(10)
1070-6631
1089-7666
http://dx.doi.org/10.1063/1.4824705
http://dspace.library.iitb.ac.in/jspui/handle/100/14516
 
Language en