Particle motion in a Brinkman medium with applications to biological transport.
Item
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Title
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Particle motion in a Brinkman medium with applications to biological transport.
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Identifier
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AAI9946161
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identifier
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9946161
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Creator
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Feng, Jianjun.
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Contributor
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Mentors: Sheldon Weinbaum | Peter Ganatos
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Date
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1999
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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 | Engineering, Biomedical | Biophysics, General
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Abstract
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A thin polyelectrolyte layer of loose fibers which coats the surface of endothelial cells, known as a surface glycocalyx, appears to be ubiquitous throughout the vascular system. This fiber matrix, which is composed of various proteins and other extracellular components, forms a highly compressible structure, that performs at least two vital functions at the cellular level. This fiber matrix layer both determines the Starling (oncotic) forces that act across vascular the endothelium and modulates the interaction of red and white cells with the endothelial surface. In this research we attempt to provide a framework for understanding the hydrodynamics of this fiber layer and the motion of solutes in a fiber matrix more generally. We shall develop methods and models for analyzing a range of problems arising in molecular mechanics, transport through capillaries and blood rheology. The general approach is based on effective medium theory (Brinkman equation) as applied to porous materials.;Analytic and numerical solutions to the Brinkman equation which describe the fluid or particle motion in a fiber-filled medium exhibit some unusual hydrodynamic features that are absent for a pure fluid medium. We first show by examining the arbitrary translation and rotation of a disk that the resistance and the torque on the disk depend significantly on the particle orientation. We then consider the inverse problem of flow through an orifice or pore in a Brinkman medium as a model for the flow through fenestrated pores in capillary endothelium. This problem is of fundamental fluid mechanical interest because it bridges the transition from a slow viscous flow characterized by Sampson's classic solution to the Stokes equation to a Darcy flow which is described by a potential equation for the pressure as the Darcy permeability decreases. The effect of confining boundaries on particle motion in a Brinkman medium is then examined for the first time. Here we examine the shielding effect of the fibers on the boundary interaction near a planar boundary when the clearance between the particle and the boundary decreases to distances of the order of the fiber spacing. The theory is applied to the motion of tagged lipid molecules in membrane bilayers in single particle tracking experiments and the penetration of leukocyte microvilli in the endothelial glycocalyx. Finally, a new type of lubrication theory is developed for highly compressible porous media which shows that there is an unexpected striking similarity between the gliding motion of a red cell moving over the endothelial glycocalyx that lines our microvessels and a human skier or snow boarder skiing on fresh powder. In both cases one finds that the pressure and lift force generated within the compressed matrix are four orders of magnitude greater than heretofore realized. These huge repulsive forces may explain why red cells do not experience constant molecular interactions with the endothelial plasmalemma.
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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.
