Μελέτη Εξαναγκασμένης Διάχυσης σε Ταλαντούμενη Ροή Ιξωδοελαστικού Ρευστού

Abstract

In this thesis we examine the phenomenon of forced diffusion of a substance which is dissolved in a viscoelastic fluid that oscillates between parallel plates. The phenomenon of forced diffusion consists of simultaneous convection and diffusion of substances in moving fluids, which was first studied by G.I. Taylor. As shown by Taylor the phenomenon of forced diffusion can be used as a method for determining the diffusion coefficient of substances in viscous fluids and has great importance in physiology, for the circulatory and pulmonary system of organisms and of course the humans. The phenomenon of forced diffusion has applications in modern medical science, mainly by introducing high-frequency ventilators. In addition, measurements of the speed of blood which are based on the time required to transfer a substance from one point of an artery or vein to another, are based on the theoretical study of this phenomenon. In the first chapter we present some of the most important experimental studies the phenomenon. The second chapter is a reference to Taylor’s theory for the case of dispersion of a substance in Newtonian fluid, moving with steady flow in a cylindrical pipe. Then, we present Watson’s work which studied the oscillatory flow of a Newtonian fluid in a random cross-section pipe. Chapter three presents general perspectives for modeling the behavior of blood. Also, there is reference to unidirectional shear flows, with which we examine experimentally the properties of fluids. We also analyze the model of Jeffrey’s viscoelasctic fluid for which it is studied in this thesis, the forced dispersion of a substance when it oscillates between parallel plates. We present the calculations and the results and we consider critical for the calculations the parameters ξ,ξ1 and ξ2 in order to have expressions similar to those of Watson, and the charts for the percentage increase in the rate of diffusion. Finally, the Annex presents the calculations which are made for the expressions of the augmented diffusion coefficient Rv and the programs used to calculate the diagrams D1-D16.