By S. P. Lin
This ebook 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 techniques are demonstrated via arithmetic, exact numerical research and comparability of conception with experiments. workouts are supplied for college kids new to the topic. Researchers drawn to issues starting from transition to turbulence, hydrodynamic balance or combustion will locate this publication an invaluable source, no matter if their historical past lies in engineering, physics, chemistry, biology, medication or utilized arithmetic.
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Extra info for Breakup of liquid sheets and jets
The solution for ψ 0 is ψ0 = C z/ h(ξ ), where C is a constant to be determined from the dynamic boundary condition. Similarly, collecting O(ε1 ) solution terms and solving for ψ 1 , we have ψ1 = C1 z/ h(ξ ), where C1 is to be determined together with C. The irrotational and the free surface kinematic conditions for the O(ε2 ) solution are respectively ψ2 ,zz = ψ0 ,ξ − ψ0 , ξ ξ ξ and ψ2 ,z h,ξ = −ψ2 ,ξ . 30 Nonuniform Inviscid Liquid Sheets The solution for ψ 2 that satisﬁes the above two equations is ψ2 = C h,2ξ h,ξ z3 − h, − 2 + C2 (ξ )z, ξ ξ 2 6h h ξ where the arbitrary function C2 (ξ ) is so chosen that the free surface z = h(ξ ) remains a stream surface.
The larger the inertial force imparted to the sheet for a given surface tension, the smaller the rate of decrease of h in the direction of the ﬂow, as it should be. Note that the ﬂuid velocity increases in the radial direction, but its rate is much smaller than the rate of decrease of h. The variation of the local Weber number is given by We = (r uh)2 ρ(U0 u)2 (H0 h) = We0 2 . 13) Since 2πruh is the constant discharge and rh = 1 to the ﬁrst order of approximation, the local Weber number decreases inversely with the distance in the downstream condition.
Varicose mode; - - -, sinuous mode. 3. Absolute Instability 19 sheet atomization processes to produce smaller droplets by increasing the ambient gas density (by increasing the gas pressure, for example). For We = O(10), the ampliﬁcation rate of the varicose mode is much smaller than that of the sinuous mode. 3. Absolute Instability In the previous section we considered the case of We > 1 and found that the uniform sheet in the presence of ambient gas is convectively unstable. In this section we show that when the Weber number is reduced to less than one, the sheet becomes absolutely unstable.