By S. P. Lin
This ebook is an exposition of what we all know in regards to the physics underlying the onset of instability in liquid sheets and jets. Wave movement and breakup phenomena next to the onset of instability also are conscientiously defined. actual thoughts are proven via arithmetic, actual numerical research and comparability of thought with experiments. routines are supplied for college students new to the topic. Researchers attracted to subject matters starting from transition to turbulence, hydrodynamic balance or combustion will locate this publication an invaluable source, even if their history lies in engineering, physics, chemistry, biology, drugs or utilized arithmetic.
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Extra info for Breakup of liquid sheets and jets
43) Expanding ξ about ξ s , we have d f /dξ 1 + (d f /dξ ) 2 1/2 = α ( ξ + ξs ) + C , ξ + O ( ξ )2 1 2 where ξ = ξ − ξs . Thus the right side of this equation is ﬁnite in the limit of ξ → 0 if C = −αξs . This choice of C, however, dictates the deﬂection angle at ξ = 0 to be ﬁnite. 43) that θ at ξ = 0 is θ0 = sin−1 [α (1 + We0 )] . Finite θ0 can be understood to be the consequence of the upstream propagating, absolutely unstable disturbance near the slot exit where We < 1. Note that when P1 = P2 , α = 0 and thus θ0 = 0.
2) (∂τ + ∂x )2 f + We−1 f,x x x x = 0. 7. The decay with time of a packet of dispersive varicose capillary waves as they are convected downstream on a liquid sheet is depicted in the ﬁgure to show the nature of convective stability. Note that the initial response to an impulsively introduced disturbance for both modes remains essentially the same as that predicted by the large time asymptotic theory given previously. 3. Curved Falling Sheet Finnicum, Weinstein, and Ruschak (1993) showed that We < 1 can occur in a falling sheet without causing the sheet to disintegrate if the sheet is allowed to curve.
Linear and Nonlinear Waves. p. 374. John Wiley & Sons. New York. , 1994), and paper making (Soderberg and Alfredson, 1998). Many of the works cited below were motivated by applications in surface coating, fuel spray formation, nuclear safety, and other industrial processes. The spatial variation of sheet thicknesses in these applications is necessitated by the conservation of mass ﬂow across the cross section perpendicular to the ﬂow direction. For example, the thickness of a planar sheet of constant width must decrease in the ﬂow direction due to the gravitational acceleration.
Breakup of liquid sheets and jets by S. P. Lin