The squeezing of red blood cells through tubes and channels of near-critical dimensions.

Persistent Link:
http://hdl.handle.net/10150/184839
Title:
The squeezing of red blood cells through tubes and channels of near-critical dimensions.
Author:
Halpern, David Carlos Mohrer Judice.
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The aim of this dissertation is to develop theoretical models for the motion of rigid and flexible particles through very tight spaces. The geometries of conduits which will be investigated are cylindrical tubes, parallel plane walls and rectangular channels. This work is motivated by an interest in the flow and deformation of single red blood cells in very narrow capillaries, in spleen and in bone marrow. Mammalian red cells are highly flexible, but their deformations satisfy two significant constraints. They must deform at constant volume, because the contents of the cell are incompressible, and also at nearly constant surface area, because the red cell membrane strongly resists dilation. Consequently, there exists a minimal tube diameter below which passage of intact cells is not possible. A cell in a tube with this diameter has its critical shape: a cylinder with hemispherical ends. The motion of red cells is analysed using lubrication theory. When the tube diameter is slightly larger than the minimal value, the cell shape is close to its shape in the critical case. However, the rear end of the cell becomes flattened and then concave with a relatively small further increase in the diameter. The changes in cell shape and the resulting rheological parameters are analysed using matched asymptotic expansions for the high-velocity limit and using numerical solutions. A rapid decrease in the apparent viscosity of red cell suspensions with increasing tube diameter is predicted over the range of diameters considered. The red cell velocity is found to exceed the mean bulk velocity by an amount which increases with increasing tube diameter. The same type of analysis is applied to the flow and deformation of red blood cells between two parallel plates with near-minimal spacings. First, the critical shape of the particle and the minimum gap width are determined using calculus of variations. In this case, it is a disk with a rounded edge. The flow in the plasma layers between the cell and the plates is described using lubrication theory. Approximate solutions can be obtained using a locally two-dimensional analysis at each point of the rim of the cell. Cell shapes, pressure distributions, membrane stresses and particle velocities are deduced as functions of geometrical parameters. One significant finding is that the gap width between the cell and the wall decreases with distance from the axis of symmetry parallel to the flow direction. The red cell velocity may be smaller or larger than the mean fluid velocity far from the cell, depending on the spacing of the plates, with equality when the width of the red cell is about ninety percent of the spacing between plates. The same procedure is also applied to rectangular channels.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Cells -- Motility -- Mathematical models.; Erythrocytes -- Deformability.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Secomb, T. W.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleThe squeezing of red blood cells through tubes and channels of near-critical dimensions.en_US
dc.creatorHalpern, David Carlos Mohrer Judice.en_US
dc.contributor.authorHalpern, David Carlos Mohrer Judice.en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe aim of this dissertation is to develop theoretical models for the motion of rigid and flexible particles through very tight spaces. The geometries of conduits which will be investigated are cylindrical tubes, parallel plane walls and rectangular channels. This work is motivated by an interest in the flow and deformation of single red blood cells in very narrow capillaries, in spleen and in bone marrow. Mammalian red cells are highly flexible, but their deformations satisfy two significant constraints. They must deform at constant volume, because the contents of the cell are incompressible, and also at nearly constant surface area, because the red cell membrane strongly resists dilation. Consequently, there exists a minimal tube diameter below which passage of intact cells is not possible. A cell in a tube with this diameter has its critical shape: a cylinder with hemispherical ends. The motion of red cells is analysed using lubrication theory. When the tube diameter is slightly larger than the minimal value, the cell shape is close to its shape in the critical case. However, the rear end of the cell becomes flattened and then concave with a relatively small further increase in the diameter. The changes in cell shape and the resulting rheological parameters are analysed using matched asymptotic expansions for the high-velocity limit and using numerical solutions. A rapid decrease in the apparent viscosity of red cell suspensions with increasing tube diameter is predicted over the range of diameters considered. The red cell velocity is found to exceed the mean bulk velocity by an amount which increases with increasing tube diameter. The same type of analysis is applied to the flow and deformation of red blood cells between two parallel plates with near-minimal spacings. First, the critical shape of the particle and the minimum gap width are determined using calculus of variations. In this case, it is a disk with a rounded edge. The flow in the plasma layers between the cell and the plates is described using lubrication theory. Approximate solutions can be obtained using a locally two-dimensional analysis at each point of the rim of the cell. Cell shapes, pressure distributions, membrane stresses and particle velocities are deduced as functions of geometrical parameters. One significant finding is that the gap width between the cell and the wall decreases with distance from the axis of symmetry parallel to the flow direction. The red cell velocity may be smaller or larger than the mean fluid velocity far from the cell, depending on the spacing of the plates, with equality when the width of the red cell is about ninety percent of the spacing between plates. The same procedure is also applied to rectangular channels.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectCells -- Motility -- Mathematical models.en_US
dc.subjectErythrocytes -- Deformability.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSecomb, T. W.en_US
dc.contributor.committeememberGross, J. F.en_US
dc.contributor.committeememberGreenlee, W. M.en_US
dc.contributor.committeememberLomen, D. O.en_US
dc.identifier.proquest9005721en_US
dc.identifier.oclc703280275en_US
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