The effect of tube corrugation on the stability of a core -annular flow.
Item
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Title
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The effect of tube corrugation on the stability of a core -annular flow.
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Identifier
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AAI9986389
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identifier
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9986389
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Creator
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Wei, Hsien-Hung.
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Contributor
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Adviser: David S. Rumschitzki
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Date
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2000
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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
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Abstract
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We focus on the problem of a core-annular flow in a corrugated tube. The motivation for this study derives from liquid-liquid displacement flows in small pores, as occur in secondary oil recovery and core-annular flow in the bronchi. We focus on the effect of tube, pore, or airway corrugation on the stability of such a flow arrangement and investigate whether and how the corrugation encourages or discourages instability compared with the situation of a straight, cylindrical tube. Both viscous (Chapter II & III) and inertial (Chapter IV) dominant theories have been asymptotically developed in the limit of thin annular films (epsilon → 0) and small corrugation (sigma → 0).;Chapter II examines the linear stability of a viscous core-annular flow. The wall corrugation leads to a spatially periodic base flow to leading order. This base flow contributes spatially periodic coefficients to the partial differential equations governing the system's stability. We employ Floquet-Bloch analysis to obtain the eigenvalue spectra of these linear stability equations. We compare the results with the direct numerical solution of the initial value problem of the interfacial dynamics for a given initial condition and a range of parameters. The eigenvalue spectra show multiple-branch structures. In contrast to the straight cylinder theory, an initial disturbance with wave length shorter than the circumference of the undisturbed fluid-fluid interface can be modified due to this interaction with higher wall corrugation harmonics to excite unstable longer waves and thus lead to a linear instability.;In Chapter III, we extend the linear analysis to the weakly non-linear regime. Linearly unstable long waves saturate in the weakly non-linear regime due to the non-linearity's wave steepening. The weakly non-linear analysis in a corrugated tube leads to the competition between unstable long waves being shortened and stabilized on the one hand, and these shorter waves exciting new unstable longer waves on the other. We derive and numerically solve the weakly non-linear amplitude equations for this situation and explore the results of this competition for various parameter regimes. For moderate or less strong interfacial tensions, the long wave linear instability excited by the corrugation, as discussed in Chapter II, still can be suppressed by the stabilization from the non-linear steepening.;In Chapter IV, we study the effect of corrugation on the linear stability of an inviscid core-annular flow, which is a complementary problem to the viscous system analyzed in Chapter II. Many qualitative features of the stability are similar to those in Chapter II. However, for a particular combination of the parameters, there is a regime where resonant corrections to the eigenvalue can be so large that a "bridge" of positive growth rates connecting the primary and secondary unstable eigenvalue branches can be present. In this case, the primary wave competes with its first harmonic wave and neither dominates at long (linear) times. The long-term interfacial evolution (in the linear regime) grows in an oscillatory manner.
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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.
