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By S. P. Lin

This publication is an exposition of what we all know concerning 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 rigorously defined. actual ideas are proven via arithmetic, exact numerical research and comparability of idea with experiments. workouts are supplied for college kids new to the topic. Researchers attracted to issues 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, medication or utilized arithmetic.

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In Free Surface Flows. Ed. by C. Heindrick and H. J. Roth, p. 45. Springer, New York. Crapper, G. , Jepson, W. , and Pyott, 1973. J. Fluid Mech. 57, 671. Crapper, G. , and Pyott, G. A. D. 1975. Proc. R. Soc. Lond. A 342, 209–224. , and Costa, M. 1997. J. Fluid Mech. 331, 127. Fraser, R. , and Hasson, D. 1962. AIChE J. 8, 672. Hagerty, W. , and Shea, J. F. 1955. J. Appl. Mech. 22, 509–514. , and Monkewitz, P. A. 1990. Ann. Rev. Fluid Mech. 22, 473–537. Lamb, H. 1945. Hydrodynamics. p. 395. Dover, New York.

Soc. Long. A 253, 296–321. Whitham, G. B. 1974. 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.

Thus the upper branch is relevant to the downstream region but the lower branch is relevant to the upstream region for the reasons just explained, dωr /dkr > 0 in both branches. Therefore the upper branch and the lower branch represent the downstream propagating wave packets which decay respectively in the downstream and upstream regions. 4 possess the same properties and thus represent decaying waves. Hence the same explanations apply, and will not be repeated again for these figures. 4. 28) must be replaced respectively here by (h 0 , ψe , ψg ) and r .

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