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85037779224
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-
note
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-4-0.005] for both modes.
-
-
-
-
29
-
-
85037764828
-
-
note
-
The effect of other parameters on the amplitude ratio has also been re-ported for the previously mentioned base case.
-
-
-
-
31
-
-
85037760491
-
-
note
-
Characteristic length and velocity for the nondimensionalization are the local radius of the surface interface and the average velocity determined from the volume flow rate.
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32
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Temporal and spatial instability of an inviscid compound jet
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A. Chauhan, C. Maldarelli, D. S. Rumschitzki, and D. T. Papageorgiou, "Temporal and spatial instability of an inviscid compound jet," Rheol. Acta 35, 567 (1996).
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33
-
-
85037766143
-
-
note
-
As pointed out by the authors, no slip at the liquid interface prevents the Kelvin-Helmholtz type of instability and allows focus onto the capillary driven instability phenomena.
-
-
-
-
34
-
-
85037751291
-
-
note
-
Here, s and k denote the transformed time and space coordinates.
-
-
-
-
35
-
-
85037754694
-
-
note
-
2 must be real.
-
-
-
-
36
-
-
85037762078
-
-
note
-
As before, R1 and R2 refer to the annular radii of the inner and outer interface, respectively.
-
-
-
-
37
-
-
85037778548
-
-
note
-
1 < R2.
-
-
-
-
38
-
-
85037760455
-
-
note
-
1s.
-
-
-
-
39
-
-
85037779765
-
-
note
-
As pointed out by the authors, similar results were found by Leib and Goldstein (reference in Part II) for the single inviscid jet.
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-
-
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40
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Capillary stability of a hollow inviscid cylinder
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42
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85037771712
-
-
note
-
As pointed out by Shkadov and Sisoev (see Ref. 30), the analysis by Sanz and Meseguer (see Ref. 41) corresponds to their own analysis in the inviscid limit and for the case of a constant axial velocity profile across the sheet.
-
-
-
-
43
-
-
85037765445
-
-
note
-
It was shown (for two limiting cases) that for a stable sheet the area of the disturbed surface is larger than that of the undisturbed annulus; for the unstable mode it was found to be smaller.
-
-
-
-
44
-
-
85037751666
-
-
note
-
1 were all real.
-
-
-
-
45
-
-
85037773629
-
-
note
-
i(kz+mt).
-
-
-
-
46
-
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85037772044
-
-
note
-
2, respectively.
-
-
-
-
47
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0022476234
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A theoretical model for the annular jet instability
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53
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85037776432
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-
note
-
The general linear analysis presented in Sec. IV shows that pure dilational and sinuous waves as observed on planar sheets do not exist on annular sheets. However, within the framework of the present analysis, waves primarily related to a variation of sheet thickness or sheet-centerline location are named dilational or sinuous waves respectively. The terminology parasinuous or paravaricose as adopted by Shen and Li (see Ref. 20) is not used here.
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54
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Mehring, C.1
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56
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-
85037759575
-
-
note
-
The subscript "10" denotes values of the undisturbed flow or base flow.
-
-
-
-
57
-
-
85037778365
-
-
note
-
g,+=0 is assumed here.
-
-
-
-
58
-
-
85037780082
-
-
note
-
Note that, for an ideal gas and isothermal or adiabatic pressure variations, K=1 or K=(f+2)/f with f(≥3), respectively. Here f denotes the total number of translational, rotational and vibrational degrees of freedom for one gas molecule.
-
-
-
-
59
-
-
85037776546
-
-
note
-
Nonlinear distorting planar liquid sheets in a void have been discussed by the authors elsewhere (see Ref. 55).
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-
-
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60
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0027459015
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85037771403
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note
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The shortcomings of the inviscid assumption will be addressed later.
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66
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0030766470
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Breakdown of scaling in droplet fission at high Reynolds number
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Mansour, N.N.1
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-
85037772986
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-
note
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2=1 for the infinite sheet analysis.
-
-
-
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70
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-
85037770307
-
-
note
-
d, in the range of interest.
-
-
-
-
71
-
-
85037755286
-
-
note
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-3) and higher neglected], the solution r(ξ,τ) can be determined without knowledge of h(ξ,τ).
-
-
-
-
72
-
-
85037758244
-
-
note
-
Note that a pure dilational distortion only exists for the lower-order linear solution.
-
-
-
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74
-
-
85037781677
-
-
note
-
Note that we are considering cases with small disturbance wave numbers only, i.e., k, l≪1.
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-
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75
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85037760381
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note
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Due to the long time-scale behavior of this instability, its analysis for the more practical semi-infinite case was rendered difficult and was not attempted within this work.
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78
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0021593959
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