Long wave and lubrication theories for core-annular flow

Chen, Kang Ping; Joseph, Daniel D.

doi:10.1063/1.858157

Cited by 20 publications

(14 citation statements)

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“…We note that stabilization has also been observed in the infinite case where ''inertial'' pressures, arising from finite Reynolds number flows, have been identified as responsible. [13][14][15] To the extent that the symmetries of the infinite case are quite different, it may not surprise that the physics also differs.…”

Section: Discussionmentioning

confidence: 99%

Suppression of the capillary instability in the Rayleigh–Taylor slot problem

Chen

Steen

1996

Physics of Fluids

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Stability of capillary-gravity interfacial waves between two bounded fluidsThe classical Rayleigh-Taylor instability for an interface of finite extent is modified by two independently controlled perturbation effects. A component of gravitational acceleration tangent to the interface is imposed and the interface is subjected to a flow-induced pressure field. The stability of the flat horizontal interface when surface tension holds heavier liquid above ambient gas is considered in a 2D model problem. The two perturbations are realized by tilting the interface to the horizontal and by inducing a flow with shear. It is found that the effect of tilt angle or shear on its own is destabilizing, while together, in the right combination, they can stabilize. It is thereby shown how to extend the stability limit over the classical Rayleigh-Taylor result. The framework for the analysis is the classical unperturbed pitchfork bifurcation ͑codimension 2͒. The coefficients in the unfolding are calculated by applying the Lyapunov-Schmidt technique to a pinned deformable interface that holds a shear-induced lubrication flow.

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Section: Discussionmentioning

confidence: 99%

Suppression of the capillary instability in the Rayleigh–Taylor slot problem

Chen

Steen

1996

Physics of Fluids

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“…The results of the bifurcation theory are consistent with observations of flows that are close to perfect core-annular flows. We also present a review and critique of various weakly nonlinear long wave equations used to describe waves on the interface [Chen and Joseph 1991b]. Viscoelastic effects have been investigated by Chen [1991aChen [ , 1992.…”

Section: V4 Stability Studiesmentioning

confidence: 99%

Fundamentals of Two-Fluid Dynamics

Joseph

Renardy

1993

Interdisciplinary Applied Mathematics

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112

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except for brief excerpts in connection wii" h reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software. or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names , trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.Production managed by Henry Krell; manufacturing supervised by Vincent Scelta. Photocomposed copy prepared from the authors' TeX file. 987654321ISBN 978-1-4615-7063-9ISBN 978-1-4615-7061-5 (eBook) vi Preface the interfaces between fluids. Viscosity segregation can be used to promote mixing and demixing, to promote say the displacement of one fluid by another as in the problem of oil recovery, or to segregate one molten plastic from another by encapsulation. The lubrication of one fluid by another is a particularly important branch of two-fluid dynamics; if one fluid has a surpassingly large viscosity, it may be lubricated by a less viscous fluid. The most beautiful of the lubricated flows are the rollers discussed in chapter II of the first part, Mathematical Theory and Applications. The most useful of the lubricated flows are the water-lubricated pipelines, which are discussed in chapters V through VIII in the second part, Lubricated Transport, Drops and Miscible Liquids. It is our hope that this book will lead to deeper understanding of the principles and applications of two-fluid dynamics.The topics treated in this book are displayed in the table of contents. Four of the six chapters in this part, Lubricated Transport, Drops and Miscible Liquids, are about water-lubricated pipelining. We have reported results of systematic studies of ideal flows and linear and nonlinear stability analyses with experimental and field observations. Some techniques of analysis which are applied here are discussed in the first part, Mathematical Theory and Applications, and they are also explained again here at the places where they appear. We present all the analysis with enough details to teach students. As always, it is certain that a number of excellent studies of two-fluid dynamics which deserve mention have not been mentioned.Water-lubrication of viscous materials is a nascent technology with a proven potential for great economy. This feature of the subject is a motivation for our work and we have tried to direct readers, wherever possible, to the remaining problems which impede the technology.Our research for this project could not have been done without the help of certain persons: . We are especially indebted to Chen, Hu and Preziosi for their excellent analytical and numerical studies of lubricated pipelining and to Bai for the design and execution of very elegant experiments. We thank Michael Renardy for reading through the manuscript.Our nominee for the "gold core ...

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“…Georgiou et al [18] and Kouris & Tsamopoulos [19,20] also found that when the core layer was more viscous than the annular layer, the shearing of basic flow acted to stabilize CAF at sufficiently high Reynolds numbers. Chen & Joseph [21] stated that the restraining effect of basic flow on capillary instability resulted from the fluid inertia.…”

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Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant

Sun

Peng

Zhu

2010

Sci. China Phys. Mech. Astron.

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The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability analysis. The flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble surfactant. Given the basic flow for this core-annular arrangement, the analytical solution is obtained with respect to the power-law fluid model. The linearized equations for the evolution of infinitesimal disturbances are derived and the stability problem is formulated as a generalized matrix eigenvalue problem, which is solved by using the software package Matlab based on the QZ algorithm. The shear-thinning property is found to have marked influence on the power-law fluid core-annular flow stability, which is reflected in various aspects. First, the capillary instability is magnified by the shear-thinning property, which may lead to an essential difference between power-law and Newtonian fluid flows. Especially when the interface is close to the pipe wall, the power-law fluid flow may be unstable while the Newtonian fluid flow is stable. Second, under disturbances to the interface a velocity discontinuity at the interface appears which is destabilizing to the flow. The magnitude of this velocity discontinuity is affected by the power-law index and the flow stability is influenced correspondingly. Besides, the shear-thinning property may induce new stability modes which do not appear in the Newtonian fluid flow. The flow stability shows much dependence on the interface location, the role of which was neglected in most previous studies. The shear-thinning fluid flow is more unstable to long wave disturbances when the interface is close to the pipe wall, while the Newtonian fluid flow is more unstable when the interface is close to the pipe centerline. But this trend is changed by the addition of interfacial surfactant, for which the power-law fluid flow is more stable no matter where the interface is located. core-annular flow, power-law fluid, interfacial surfactant, linear stability analysis PACS: 47.50. Gj, 47.55.Iv, 47.20.Ma

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Long wave and lubrication theories for core-annular flow

Cited by 20 publications

References 13 publications

Suppression of the capillary instability in the Rayleigh–Taylor slot problem

Suppression of the capillary instability in the Rayleigh–Taylor slot problem

Fundamentals of Two-Fluid Dynamics

Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant

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