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This thesis is concerned with time-dependent free-boundary problems at low Reynolds numbers. The primary objective is to use a combined experimental and numerical investigation to examine the deformation and breakup characteristics of a single phase Newtonian liquid drop suspended in a second immiscible Newtonian fluid undergoing a prescribed linear flow. Two related studies grew naturally out of this work and are also discussed here: (1) an analytic and numerical examination of the behaviour of concentric double emulsion droplets in linear flows, and (2) an introduction to the effect surfactants have on drop deformation in extensional flows.

This thesis is concerned with time-dependent free-boundary problems at low Reynolds numbers. The primary objective is to use a combined experimental and numerical investigation to examine the deformation and breakup characteristics of a single phase Newtonian liquid drop suspended in a second immiscible Newtonian fluid undergoing a prescribed linear flow. Two related studies grew naturally out of this work and are also discussed here: (1) an analytic and numerical examination of the behaviour of concentric double emulsion droplets in linear flows, and (2) an introduction to the effect surfactants have on drop deformation in extensional flows.

This work analyses the role of small but finite particle inertia on the microstructure of suspensions of heavy particles subjected to an external flow. The magnitude of particle inertia is characterized by the Stokes number, St, defined as the ratio of the inertial relaxation time of a particle to the flow time scale. Fluid inertia is neglected so that the fluid motion satisfies the quasi-steady Stokes equations. The statistics of the particles is governed by a Fokker-Planck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phase-space probability density of a single spherical Brownian particle in a linear flow. Though valid for an arbitrary flow field, the method fails for a spatially varying mass and drag coefficient. In all cases, however, a Chapman-Enskog-like formulation provides a valid multi-scale description of the dynamics both for a single Brownian particle and a suspension of interacting particles. For long times, the leading order solution simplifies to the product of a local Maxwellian in velocity space and a spatial density satisfying the Smoluchowski equation. The higher order corrections capture both short-time momentum relaxations and long-time deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a non-Fickian term at O(St).

This work analyses the role of small but finite particle inertia on the microstructure of suspensions of heavy particles subjected to an external flow. The magnitude of particle inertia is characterized by the Stokes number, St, defined as the ratio of the inertial relaxation time of a particle to the flow time scale. Fluid inertia is neglected so that the fluid motion satisfies the quasi-steady Stokes equations. The statistics of the particles is governed by a Fokker-Planck equation in position and velocity space. For small St, a multiple scales formalism is developed to solve for the phase-space probability density of a single spherical Brownian particle in a linear flow. Though valid for an arbitrary flow field, the method fails for a spatially varying mass and drag coefficient. In all cases, however, a Chapman-Enskog-like formulation provides a valid multi-scale description of the dynamics both for a single Brownian particle and a suspension of interacting particles. For long times, the leading order solution simplifies to the product of a local Maxwellian in velocity space and a spatial density satisfying the Smoluchowski equation. The higher order corrections capture both short-time momentum relaxations and long-time deviations from the Maxwellian. The inertially corrected Smoluchowski equation includes a non-Fickian term at O(St).

The refractive index, for [gamma][subscript Na]=5893 [angstroms], of dense fluid argon was measured by the determination of the angle of minimum deviation. The study covered states from 133 to 173[degrees]K for pressures 20 to 100 atm. The density data of J. Levelt were used to calculate values of the Lorentz-Lorenz function for these states.

The refractive index, for [gamma][subscript Na]=5893 [angstroms], of dense fluid argon was measured by the determination of the angle of minimum deviation. The study covered states from 133 to 173[degrees]K for pressures 20 to 100 atm. The density data of J. Levelt were used to calculate values of the Lorentz-Lorenz function for these states.

The creeping motion of a neutrally buoyant drop in Poiseuille flow is studied numerically using the boundary integral technique. The effects of the viscosity ratio, interfacial tension and drop size on steady shapes and velocities of the deformed drop are considered. Particular attention is given to cases involving large deformation which occurs when the interfacial tension becomes small. The critical value of the capillary number, for a given viscosity ratio, above which a steady shape for the drop does not exist is determined.

The stability of annular flow of two fluids of different viscosities through a circular tube is studied. The instability considered in the present study occurs at the interface between two fluids. Linear stability analysis is carried out for axisymmetric disturbances when the mechanisms of instability due to a viscosity difference between two fluids and interfacial tension are simultaneously present. The growth factor of instability is nonlinear in the viscosity ratio and the interfacial tension because the governing equations and boundary conditions are linearized with respect to a disturbance amplitude function, but not linearized with respect to the viscosity ratio and the interfacial tension. The effects of the viscosity ratio, interfacial tension, radius ratio and Reynolds number on the stability of the interface as well as the modes of maximum instability are studied.

The creeping motion of a neutrally buoyant drop in Poiseuille flow is studied numerically using the boundary integral technique. The effects of the viscosity ratio, interfacial tension and drop size on steady shapes and velocities of the deformed drop are considered. Particular attention is given to cases involving large deformation which occurs when the interfacial tension becomes small. The critical value of the capillary number, for a given viscosity ratio, above which a steady shape for the drop does not exist is determined.

The stability of annular flow of two fluids of different viscosities through a circular tube is studied. The instability considered in the present study occurs at the interface between two fluids. Linear stability analysis is carried out for axisymmetric disturbances when the mechanisms of instability due to a viscosity difference between two fluids and interfacial tension are simultaneously present. The growth factor of instability is nonlinear in the viscosity ratio and the interfacial tension because the governing equations and boundary conditions are linearized with respect to a disturbance amplitude function, but not linearized with respect to the viscosity ratio and the interfacial tension. The effects of the viscosity ratio, interfacial tension, radius ratio and Reynolds number on the stability of the interface as well as the modes of maximum instability are studied.

Fluid flow through flexible tubes is of interest due to its dynamic similarity to that of fluid flow in veins, arteries, bronchial air ways, urethra, vocal codes peristaltic tubes, and flexible micro-fluidic devices. Similar behavior can be observed in diagnostic and therapeutic devices pressurized cuffs, prophylaxis, intra-aortic balloon counterpulsation, prosthetic heart devices, vein cannulation and prosthetic vocal codes. Due to the flexible material that constitutes the tube a state of total collapse is highly likely when the tube is subjected to excessive external forces. Thus, muscle contraction and expansion and external forces that act upon the vessel wall all serve to deform the flexible tube thereby affecting the fluid flow area and fluid flow behavior. It is reasonable to conclude that fluid flow within a flexible vessel is a function of the fluid properties, material prosperities of the flexible structures and any external forces. Furthermore within the flexible tube, the presence of attached internal structures can impose further limitations on the fluid flow. Such systems can be found in vein and valves, heart valves and also in nebulizers.

Fluid flow through flexible tubes is of interest due to its dynamic similarity to that of fluid flow in veins, arteries, bronchial air ways, urethra, vocal codes peristaltic tubes, and flexible micro-fluidic devices. Similar behavior can be observed in diagnostic and therapeutic devices pressurized cuffs, prophylaxis, intra-aortic balloon counterpulsation, prosthetic heart devices, vein cannulation and prosthetic vocal codes. Due to the flexible material that constitutes the tube a state of total collapse is highly likely when the tube is subjected to excessive external forces. Thus, muscle contraction and expansion and external forces that act upon the vessel wall all serve to deform the flexible tube thereby affecting the fluid flow area and fluid flow behavior. It is reasonable to conclude that fluid flow within a flexible vessel is a function of the fluid properties, material prosperities of the flexible structures and any external forces. Furthermore within the flexible tube, the presence of attached internal structures can impose further limitations on the fluid flow. Such systems can be found in vein and valves, heart valves and also in nebulizers.

Published data on flow field variation caused by various blade design patterns are scarce. Most designs exhibit significant flow separation and adverse pressure gradients effects that lower mixing efficiency. In view of the design potentials of the CFD methodology, the flow field variations caused by different blade designs could be classified in order to be able to predict the spread of the low pressure regions behind blades while retrofitting existing equipment towards energy-saving performance without decreasing the impeller blending and dispersing capacity related to the geometry considered.

The aim of the present study is to reveal such variations for some conventional flat blade modifications. The performance of three flat and hollow blade design modifications comprising slotted and perforated blades are examined. The specific power drawn, pumping capacity, deformation rate and turbulence intensity are determined and compared. The impeller power effectiveness is discussed in terms of the strain deformation rate produced. Evidence for enhanced performance of slotted and perforated designs is presented.

Published data on flow field variation caused by various blade design patterns are scarce. Most designs exhibit significant flow separation and adverse pressure gradients effects that lower mixing efficiency. In view of the design potentials of the CFD methodology, the flow field variations caused by different blade designs could be classified in order to be able to predict the spread of the low pressure regions behind blades while retrofitting existing equipment towards energy-saving performance without decreasing the impeller blending and dispersing capacity related to the geometry considered.

The aim of the present study is to reveal such variations for some conventional flat blade modifications. The performance of three flat and hollow blade design modifications comprising slotted and perforated blades are examined. The specific power drawn, pumping capacity, deformation rate and turbulence intensity are determined and compared. The impeller power effectiveness is discussed in terms of the strain deformation rate produced. Evidence for enhanced performance of slotted and perforated designs is presented.

THIS PAPER is certainly not intended to be a history of the subject, but a few important milestones are recalled in this and the next five sections.

The purpose of the exercise is to submit that the discipline of fluid mechanics, as taught in engineering schools and practiced in industry, is perhaps ripe for a major overhaul equal in significance to the changes that took place early in the twentieth century. The different eras to be discussed are seen from the perspective of the history of the universe
time line depicted in Fig. 1.

The art of fluid mechanics arguably has its roots in prehistoric times when streamlined spears, sickle-shaped boomerangs and fin-stabilized
arrows evolved empirically [1] by the sheer perseverance of archaic Homo sapiens who knew nothing about air resistance or aerodynamic principles.

Three aerodynamically correct wooden spears were recently excavated in an open-pit coal mine near Hanover, Germany [2]. Archeologists dated the carving of those complete spears to about 400,000 years ago [3] which strongly suggests early Stone Age ancestors possessing resourcefulness and skills once thought to be characteristics that came only with fully-modern Homo sapiens.

THIS PAPER is certainly not intended to be a history of the subject, but a few important milestones are recalled in this and the next five sections.

The purpose of the exercise is to submit that the discipline of fluid mechanics, as taught in engineering schools and practiced in industry, is perhaps ripe for a major overhaul equal in significance to the changes that took place early in the twentieth century. The different eras to be discussed are seen from the perspective of the history of the universe
time line depicted in Fig. 1.

The art of fluid mechanics arguably has its roots in prehistoric times when streamlined spears, sickle-shaped boomerangs and fin-stabilized
arrows evolved empirically [1] by the sheer perseverance of archaic Homo sapiens who knew nothing about air resistance or aerodynamic principles.

Three aerodynamically correct wooden spears were recently excavated in an open-pit coal mine near Hanover, Germany [2]. Archeologists dated the carving of those complete spears to about 400,000 years ago [3] which strongly suggests early Stone Age ancestors possessing resourcefulness and skills once thought to be characteristics that came only with fully-modern Homo sapiens.