Capillary instability of jets.
Item
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Title
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Capillary instability of jets.
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Identifier
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AAI9908303
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identifier
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9908303
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Creator
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Chauhan, Anuj.
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Contributor
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Advisers: Charles Maldarelli | David S. Rumschitzki | Demetrios T. Papageorgiou
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Date
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1998
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Chemical | Physics, Fluid and Plasma
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Abstract
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This thesis studies the capillary instability of a compound jet. A compound jet comprises an inner core of a primary fluid surrounded by an annulus of an immiscible secondary fluid. The compound jet is unstable due to capillarity. A compound jet finds applications in a variety of fields, such as, ink jet printing, particle sorting, extrusion, molding, particle production etc. In some of these applications such as molding, the disturbances that could cause the jet breakup start as periodic spatial disturbances of Fourier wave number k and grow in time. This is the temporal instability. In some other applications, such as, ink-jet printing, the disturbances initiate at the edge of the nozzle from which the jet issues out. These disturbances grow in space. This is the spatial instability. At small velocities, even if the initial disturbances are periodic in time, they grow exponentially in time. This is the absolute instability. We perform the temporal, spatial and the absolute stability analysis of an inviscid compound jet in a unified framework using the theory of transforms. Further, we solve the temporal instability problem for a viscous jet to understand the effect of viscosity on breakup dynamics. In the temporal analysis, we show that each interface of the compound jet contributes one mode to the instability. The modes contributed by the inner and outer interfaces grow for waves longer than the inner and the outer circumference of the undisturbed jet, respectively. The inner interface mode has a higher growth rate and hence dominates the breakup. The two interfaces grow exactly in phase in this mode and hence it is refereed to as the stretching mode. The other mode is the squeezing mode because the two interfaces grow exactly out of phase. The same two modes are also present in the spatial analysis. At high Weber numbers the predictions of the spatial theory reduce to those of the temporal theory because the waves simply convect with the jet velocity and there is no dispersion. At Weber numbers below a critical value, the compound jet becomes absolutely unstable. There are three absolutely unstable modes and as the Weber number approaches zero, one of them is stabilized and the other two reach growth rates that are same as the maxima of the stretching and the squeezing modes in the temporal theory. Viscosity reduces the spatial and the temporal growth rates and also the critical Weber number. Experimentally, we verify the predictions of the spatial theory for a single jet at high and intermediate Weber numbers and observe a backward propagating modes at smaller Weber numbers which could signify absolute instability.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
