Thermocapillary migration of fluid particles in tubes.
Item
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Title
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Thermocapillary migration of fluid particles in tubes.
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Identifier
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AAI9432334
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identifier
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9432334
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Creator
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Chen, Jinnan.
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Contributor
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Advisers: Charles Maldarelli | Zeev Dagan
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Date
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1994
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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, Mechanical
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Abstract
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This thesis studies the axial, thermocapillary-driven migration of fluid particles (drops and bubbles) through a continuous and otherwise quiescent liquid phase which fills a cylindrical tube. The hydrodynamic flows accompanying the thermocapillary migrations studies in this thesis are axisymmetric and creeping; the heat transfer is conductive with the tube wall insulated and the surface tension is expanded linearly in the temperature. Compact particles are examined, i.e. ones for which the equivalent spherical radius a{dollar}\sp\prime{dollar} is smaller than the tube radius, b{dollar}\sp\prime.{dollar} Numerical solutions of the hydrodynamic and conduction equations are obtained in order to determine the ratio of the quasisteady velocity in the tube (U{dollar}\sp\prime),{dollar} relative to that in an infinite medium {dollar}(U\sbsp{lcub}o{rcub}{lcub}\prime{rcub}).{dollar} The relative velocity is obtained as a function of a{dollar}\sp\prime{dollar}/b{dollar}\sp\prime,{dollar} the conductivity (k) and viscosity {dollar}(\kappa){dollar} ratio of the particle to the suspending phase, and the capillary number Ca (= {dollar}\mu\sp\prime\sp{lcub}(2){rcub}U\sbsp{lcub}o{rcub}{lcub}\prime{rcub}/\sigma\sp\prime,{dollar} where {dollar}\sigma\sp\prime{dollar} is the surface tension and {dollar}\mu\sp\prime\sp{lcub}(2){rcub}{dollar} is the suspending phase viscosity).;In the case of dominant interfacial tension forces (Ca = 0) for which the drop translates as a sphere, solutions using a collocation technique indicate that for a fixed ratio of a{dollar}\sp\prime{dollar}/b{dollar}\sp\prime,{dollar} as k decreases, a greater proportion of energy is conducted through the gap between the insulated tube wall and the particle. This conduction pattern creates a larger surface temperature gradient, and causes the relative migration velocity to increase. The enhancement in migration for decreasing k becomes more pronounced as a{dollar}\sp\prime{dollar}/b{dollar}\sp\prime{dollar} increases and the surface gradient intensifies. However, as the gap distance between the sphere and the tube decreases, hydrodynamic retarding forces develop, and these forces are overriding in the sense that the migration velocity in the tube never exceeds the value in an infinite medium.;In the case of deformable compact particles, capillary numbers must be restricted to values smaller(Ca {dollar}\ne{dollar} 0) than one to be consistent with the assumption that the tension is expanded linearly in the temperature. Calculations, by a boundary integral technique, for Ca = 0.05 and {dollar}\kappa{dollar} = 1, k = 0 and k = 1 demonstrate that for {dollar}\rm a\sp\prime/b\sp\prime\le 0.8{dollar} the particle is squeezed into the tube center by the hydrodynamic force due to the flow. This deformation reduces the hydrodynamic interaction of the particle with the wall causing an increase in the velocity.
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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.
