An Electrochemical Investigation of Mass Transfer in a Pipe and a Simplified Bifurcation Model Nader Mahinpey A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Chernical Engineering and Applied Chemistry and the lnstitute of Biomaterials and Biomedical Engineering University of Toronto O Copyright by Nader Mahinpey, 2001 National Library Bibliothèque nationale I*l of Canada du Canada Acquisitions and Acquisitions et Bibliographie Sewices services bibliographiques 395 Wellington Street 395. rue Wellington Ottawa ON K 1A ON4 Ottawa ON KI A ON4 Canada Canada The author has granted a non- L'auteur a accordé une Licence non exclusive licence allowing the exclusive permettant a la National Library of Canada to Bildiothèque nationale du Canada de reproduce, loan, distriiute or selI reproduire, prêter, distribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la fome de rnicrofiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantiai extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. who have inspired me in many different ways, supported me during my academic career and life and encouraged me to achieve rny drearns. for making me what I am and for teaching me that: if you can imagine it. you can achieve it. if you can drearn it, you can become it. whose perpetual thoughts. attitude, smile and life have given me extraordinary strength to achieve seemingly unattainable goals. Mldmna-> -J for their unending love. An Electrochemical Investigation of Mass Transfer in a Pipe and a Simplified Bifurcation Model Nader Mahinpey Doctoral Thesis, 2001 Department of Chemical Engineering lnstiute of Biomaterials and Biomedical Engineering University of Toronto A novel technique was used to fabricate nickel flow models of a straight pipe and a Y-bifurcation. These were used to obtain integral mass transfer coefficients by the electrochemical technique with the ferri-ferrocyanide system at Reynolds numbers ranging from 250 to 8600, at the four Schmidt numbers of 1310, 2470, 3100 and 5655. For the straight pipe, good agreement was obtained with previously reported mass transfer correlations. As the Schmidt number increased, the effect of transition from laminar to turbulent flow on mass transfer was delayed to progressively higher Reynolds numbers. With the Y-bifurcation model, possible fiow separation and the formation of a new mass transfer boundary layer in the daughter branches significantly influence the mass transfer behavior. The electrochemical technique has been used to obtain transient mass transfer coefficients for smooth pipes. In contrast to the analytical solution of the corresponding heat transfer problem, two distinct transient periods are observed. The first is controlled by chemical reaction kinetics at the surface, followed by the diffusion-controlled period in agreement with the heat transfer solution. The transfer rate for laminar fiow is then proportional to (~lt)'~,in accordance with Higbie's penetration theory. In turbulent flow, the transient mass transfer rate, during the second transient period, is proportional to ~e''~(~lt)'~,higher than in laminar flow. The laser photochromic tracer method provided velocity and wall shear stress values in the plane of symmetry of a UV-transparent Plexiglas bifurcation model similar to that used in the mass transfer experiments at Reynolds numbers 500, 600, and 750. A novel copper electrodeposition technique has been used to obtain time-averaged convective local mass transfer coefficients in a straight pipe and a simplified bifurcation model. Laminar flow results for the pipe are in good agreement with the analytical Leveque solution. In the bifurcation. higher mass transfer coefficients along the inner wall and lower ones along the outer wall were observed. Both coefficients converge towards the same value further downstream. Within the branches, mass transfer and wall shear stress follow similar patterns both on the inner and outer walls. lt was found that stscY3and Cf/2 demonstrate analogous behavior. The lower transfer phenomena. both momenturn and mass. along the outer wall of the branches are coincident with the localization of atherosclerotic lesions and arterial plaques. I would like to express my sincere gratitude to my supervisors Professor O. Trass and Professor M. Ojha, for their continued advice, support and encouragement throughout this project. Without thern, would not have corne this far. I am sincerely grateful to Professor Basmadjian for his helpful suggestions for different parts of this study, especially in the transient mass transfer subject. I would also like to thank members of my reading cornmittee Professors. D. W. Kirk and D. E. Cormack, for their various suggestions and criticisrns. The technical support provided by Franz Schuh. Paul Jowlabar, and Fred Neub is gratefully appreciated. I would especially like to thank Franz Schuh whose innovative machine shop craftsmanship has been an asset not only for me but also for most of my fellow graduate students in the Institute. I thank Richard Leask who carried out the flow experiments and provided me with the velocity and wall shear stress data. 1 am grateful to al1 the members of the Doppler-Hemodynamics group at the lnstitute of Biomaterials and Biomedical Engineering: to Professors K. W. Johnston, R.S.C. Cobbold, and C.R. Ethier for their suggestions and support, and to al1 the students in the group for their helpfulness throughout this project. My thanks also go to the faculty members and staff of the Department of Chemical Engineering for their contribution to my career development during my studies in the Department. I also wish to thank al1 my family for their support during different stages of my life. Financial assistance from the University of Toronto Fellowship program is gratefully acknowledged. Page m.. ABSTRACT........................................................................................... I 1 I ACKNOWLEDGEMENTS........................................................................... v NOMENCLATURE.................................................................. .....m....m.m...xi LISTOF FIGURES................................................................................ xiv m.. m.. LISTOF TABLES............................................................................... XXI II INTRODUCTION....................m.m...........~........m.mm....m...........m..m...m...... 1 1 .1 Atherosclerosis and Hemodynamics .................................................. 2 1.2 Atherosclerosis and Mass Transfer ..................................................... .4 1.3 Objectives ........................................................................................ .7 2 LITERATUREREVIEW ...................m....m........m.......mm.......................m. 8 2.1 Atherosclerosis and the Artery Wall .................................................... .8 2.2. Mass Transfer between BIood and the Arterial Wall ..........................1 2 2.2.1 Cholesterol Transport ........................................................... 12 2.2.2 Oxygen Transport ................................................................ .14 Table of Contents vii 2.3 Macromolecule Transport between the Intima and Media ................. 16 2.4 Platelet Adhesion on the Arterial Wall ...................................... 19 2.5 Abdominal Aortic Geometry ............................................................... 21 2.6 Localization of Atherosclerosis ......................................A ~NTEGRATEDMASS TRANSFER IN A PIPEAND A SIMPLIFIED 3.1 Introduction ................................. ...,.,. ....................28 3.2 Experimental Methods ....................................................................... 29 3.2.1 The Geometry of the Bifurcation Model ................................29 3.2.2 Preparation of the Plating Electrolyte Solution ..................... 30 3.2.3 Fabrication of Electrodes ...................................................... 32 3.2.4 The Electrochemical Technique ........................................... 36 3.2.5 Electrical Circuit .................................................................... 38 3.2.6 Flow Loop and Expenmental Procedure .............................. 38 3.3 Results and Discussion ...................................................................... 43 3.3.1 Pipe Data .............................................................................. 43 3.3.2 Bifurcation Data ....................................................................47 3.4 Conclusions ........................................................................................ 52 TRANSIENTMASS TRANSFER ...................................................... 53 4.1 Introduction ...................................................................................... 33 4.2 Theory ................................................................................................56 ... Table of Contents ml1 4.3 Experimental Procedures .................................................................. -60 4.3.1 Flow System .......................................................................