Numerical simulations of phase separation of deeply quenched mixtures.
Item
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Title
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Numerical simulations of phase separation of deeply quenched mixtures.
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Identifier
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AAI9908376
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identifier
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9908376
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Creator
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Vladimirova, Natalia Valerievna.
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Contributor
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Adviser: Roberto Mauri
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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
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Abstract
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In this work the phase separation of deeply quenched mixtures is studied. The theoretical model follows the standard model H, where convection and diffusion are coupled via a body force, which depends on the Peclet number {dollar}\alpha,{dollar} expressing the ratio of thermal to viscous forces. In the limit of sharp interfaces separating single-phase domains, the coupling term reduces to the capillary force.;For small Peclet numbers, {dollar}\alpha < 10\sp2,{dollar} the system forms single-phase domains, which can be drops or filaments depending on the mixture composition, separated from one another by sharp interfaces. These single-phase domains thicken as the system tries to minimize its interfacial area, with the typical domain size R growing in time as {dollar}t\sp{lcub}1/3{rcub},{dollar} in agreement with theoretical predictions. Phase separation for larger Peclet numbers is characterized by slower change of composition and faster domain growth. In fact, when {dollar}\alpha > 10\sp3,{dollar} the typical drop size increases linearly with time, with a growth rate proportional to the ratio between molecular diffusivity and interface thickness, in agreement with the experimental results. In addition, phase separation and domain growth occur simultaneously when the Peclet number is large, while, for small Peclet numbers, first sharp interfaces appear, and then the single-phase domains start to grow. The composition field within and without these microdomains appears to be non-uniform and time-dependent, even after the formation of sharp interfaces, thereby contradicting the commonly accepted assumption of local equilibrium at the late stage of phase separation.;This theoretical model was validated determining the velocity of a single drop immersed in a phase-separating continuum field with constant concentration gradient, finding that it is proportional to the concentration gradient and inversely proportional to the capillary number. A single drop, immersed in a homogeneous concentration field, it shrinks without moving, if the difference between the initial concentration of the continuum phase and its equilibrium value is negative. In the opposite case the drop grows linearly, consuming material from the surrounding field and moving randomly, propelled by the induced capillary driving force. Two drops, immersed in a continuum field, experience a mutual attraction, induced by the capillary force, which may or may not lead to the drop coalescence, depending on the concentration of continuum phase.
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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.
