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Particle Image Velocimetry (PlY) is a technique for measuring instantaneous twodimensional fluid velocity fields from a chosen plane of interest within a flow field. This thesis presents new developments and applications of the technique which have been used to study both the non-reacting and reacting flow fields within cylindrical combustion chambers. Non-reacting, swirling laminar flow fields near the transitional flow regime have been investigated by both Computational Fluid Dynamics (CFD) modelling and PIV experiments. Direct comparisons between CFD, PlY and other published results are made and close agreements are found. Additionally, the PlY technique has been optimised by careful use of a thin laser illumination sheet and correct choice of laser pulse separation. This has enabled successful PlY measurements in the boundary layers of the flow field where high velocity gradients exist. The PlY technique has been applied to measure the flame development and propagation process within the chamber under both quiescent and swirling flow conditions. Representative sequences of PIV results at different flame propagation stages are obtained and the accuracy in the extraction of the flame location is discussed. They clearly reveal the instantaneous flame front position and the unburned gas velocity field simultaneously. These features provide further insight into the combustion process itself and also the interaction between the combustion and flow field. A new application of PIV, combined with a flame speed detection technique, has been proposed and developed to obtain direct measurements of the laminar burning velocity of combustible mixtures. The laminar burning velocity is determined as the difference between the flame speed and the unburned gas velocity immediately ahead of the flame front. PIV is used to measure the unburned gas velocity field and either a pair of ionisation probes or a laser beam refraction technique is used to measure the local flame speed simultaneously. The relative merits of each technique are compared. The laminar burning velocities of propane-air mixtures initially at atmospheric conditions for equivalence ratios ranging from 0.7 - 1.4 were measured. The measured values show close agreement with previously published results based on other techniques. The advantages and limitations of the PIV techniques used in this work are examined and the prospects of their improvement and further application are discussed.

This research presents a novel capacitive-sensing-based method to measure fluid velocity for microfluidics devices. To illustrate the importance of fluid velocity measurement, a case study was first conducted for a split and recombine micromixer. The study underscored the influence of fluid velocity on micromixer efficiency and mixing quality. The proposed fluid velocity measurement method employs two capacitance sensing electrodes placed along the fluid channel, capable of detecting small capacitance changes as fluid passing through the sensing area. The relation between capacitance changes and fluid velocity in the proposed sensing structures was developed and hence used to estimate fluid velocity. The proposed technique does not require extensive bench equipment and is suitable for point-of-care applications. To validate our approach, we implemented a two-step 3D printing process, creating a Polylactic acid (PLA) micro platform with embedded graphene–PLA composite electrodes. The accuracy of the developed method was investigated by cross-verifying the obtained velocities with an optical measurement method. Most absolute percentage discrepancies between the results from the proposed method and the optical method are under 12%, validating the precision of the proposed method. Future research will focus on integrating this velocity measurement method into microfluidic devices produced using advanced microfabrication technologies.

A poroelastic finite element model of a heterogeneous articular cartilage disc was created to examine the tissue response to low amplitude (± 2% strain), low frequency (0.1 Hz) dynamic unconfined compression (UCC). A strong correlation has been made between the relative fluid velocity and stimulation of glycosaminoglycan synthesis. A contour plot of the model shows the relative fluid velocity during compression exceeds a trigger value of 0.25 μm/s at the radial periphery. Dynamic UCC biochemical results have also reported a higher glycosaminoglycan content in this region versus that of day 0 specimens. Fluid velocity was also found not to be the dominant physical mechanism that stimulates collagen synthesis; the heterogeneity of the fluid velocity contour plot conflicts with the homogeneous collagen content from the biochemical results. It was also found that a Tresca (shear) stress trigger of 0.07 MPa could provide minor stimulation of glycosaminoglycan synthesis. A feasibility study on modeling a heterogeneous disc was conducted and found convergence issues with the jump in properties from the superficial to middle layers of the disc. It is believed that the superficial layer contains material properties that allow the tissue to absorb much of the compressive strain, which in turn increases pressure and causes convergence issues in ABAQUS. The findings in this thesis may help guide the development of a growth and remodeling routine for articular cartilage.

Turbulent gas-particle suspensions are of great practical importance in many naturally phenomena, such as dust storms and snow avalanches, as well as in industrial applications such as fluidised, circulating bed reactors and pneumatic transport. Due to the difference in mass density of about three orders of magnitude between solids and gases, the mass loading is large, but the volume fraction of the particles is usually small. Since the length scale of these flows ranges from tens of centimeters to hundreds of meters, the Reynolds number based on the flow dimension and velocity is usually large. Due to this, these flows are almost always in the turbulent regime, and the fluid velocity fluctuations are significant. The particle sizes are typically small in these applications, of the order of 100 m or less. Due to this, the Reynolds number (based on the particle size and velocity) is usually low. This implies that the fluid inertia is not important, and the flow dynamics is dominated by fluid viscosity at the particle scale. At the same time, due to the density contrast between the particles and fluid, the Stokes number (ratio of particle inertia and fluid viscosity) is large. The inertia is sufficiently large that the particles cross the fluid streamlines. In this situation, there is a two-way coupling between the fluid turbulence and the particle dynamics. The turbulent fluid velocity fluctuations result in particle velocity fluctuations due to the drag force exerted by the particles on the fluid. In turbulent gas-particle suspensions, the fluctuating velocity of the particles results in a force on the fluid, which could either enhance or dampen the turbulent velocity fluctuations. The finite size of the particles could also result in fluid velocity effects which can not be captured by considering the particles as point masses. The dynamics of turbulent particle suspensions is analysed in the limit of low particle Reynolds number and high particle Stokes number, where there is a balance between particle inertia and fluid viscosity. The turbulent gas flow in a channel is considered for definiteness, in order to analyse the effect of turbulent fluctuations, as well as the effect of cross-stream variations in the turbulent statistics. The particle size is considered to be comparable to the Kolmogorov scales, which are the smallest scales in the turbulent flow. In addition, the fluid inertia at the particle scale is neglected, and the particles are dynamics is modeled using the Stokes equations. However, inertial effects are included at the macroscopic scale, where the Navier-Stokes equations are solved by Direct Numerical Simulations (DNS) using Chebyshev-Fourier spectral techniques. There are three important objectives in the present analysis. 1. The first is to examine the turbulence modification due to the reverse force of the particles. There are two models used for the reverse force of the particles on the fluid. The first is a point force, which is modeled as a delta function in real space. Instead of using smoothing functions for the delta function, we prefer to incorporate the point force in the momentum conservation equation in spectral space. A more complicated representation proposed here involves the inclusion of the symmetric and anti-symmetric force moments, calculated from the solution of Stokes equations for the flow around the sphere. These are represented as gradients of delta functions, and are also included in the momentum conservation equations in the spectral co-ordinates. 2. The second objective is to examine the effect of particle rotation and collisions on the flow dynamics. While particle rotation is usually included in the analysis of granular flows, this is not normally included in the treatment of particle collisions. 3. The third objective is to examine whether the effect of the fluid turbulence can be modeled as a fluctuating force. When the viscous relaxation time of the particles is larger than the integral time for the fluid velocity fluctuations, the fluid velocity fluctuations can be considered as delta function correlated in time, and the effect of these fluctuations can be incorporated using a Langevin description. In this case, the diffusion coeffcients in the Langevin equation for the particles is calculated from the correlation in the fluid velocity fluctuations. The new objective here is to include both the drag force and the torque exerted on the particles in the presence of particle rotation, and to examine whether these are sufficient to capture the effect of ff fluid turbulence on the particle phase. The Direct Numerical Simulations show that there is a significant attenuation of the turbulent velocity fluctuations when the reverse force exerted by the particles is added in the fluid momentum equations, and the particles are considered to be smooth. This turbulence attenuation is greater when the particle volume fraction increases, and when the particle mass density increases. However, when particle rotation is included, the turbulent velocity fluctuations are significantly larger than those without rotation, and in come cases are close the fluctuation levels when the reverse force is included. Thus, the particle rotation has a significant enhancement on the turbulent velocity fluctuations. The attenuation in the fluid turbulence is also reflected in the magnitude of the particle fluctuating velocities. The particle fluctuating velocities are higher when the effect of particle rotation is included. The reason for this is that there is particle rotation induced due to mean fluid shear, and this rotational energy gets transformed into translational energy in inter-particle collisions. The effect of inclusion of the symmetric and anti-symmetric force moments does not result in a significant change in the turbulence intensities for the range of volume fractions and mass densities considered here. There is a small but discernible increase in the turbulence for the largest volume fraction and mass density considered here, but this increase is much smaller than the significant turbulence attenuation due to the inclusion of particle rotation. Systematic trends are also observed in the particle linear and angular velocity distributions. The particle stream-wise linear velocity distribution, and the span-wise angular velocity distribution are broader than a Gaussian distribution near the zero, and exhibit steep decrease at larger velocity. They are also asymmetric, and the distribution depends on the location across the channel. The distribution of the cross-stream and span-wise linear velocity and the stream-wise and cross-stream angular velocity, is narrower than a Gaussian distribution at the center, and exhibits long tails for high velocities. Thus, there are systematic variations in the distribution functions for both the linear and angular velocities, which need to be included in kinetic theory descriptions for the particle phase. The fluctuating force model has also been simulated, where particle dynamics is explicitly simulated, the fluid velocity fields are not simulated, but are modeled as fluctuating forces and torques acting on the particles. The variance in the fluctuating force and torque are determined from the correlations in the fluid velocity and the vorticity fields, and these are modified to include the turbulence attenuation due to the reverse force exerted by the particles. The fluctuating force simulations do accurately capture the trends observed in the mean and fluctuating velocities. They are also able to capture the non-Gaussian nature of the linear and angular velocity distributions of the particles, even though the random forcing is considered to be a Gaussian function. Thus, the fluctuating force formulation can be used to accurately capture the effect of the fluid on the particles, only if the forces are modified to include the effect of turbulence attenuation due to the reverse force exerted by the particles.

Longitudinal growth of long bone occurs at growth plates by a process called endochondral ossification. Endochondral ossification is affected by both biological and mechanical factors. This thesis focuses on the mechanical modulation of femoral bone growth occurring at the proximal growth plate, using mechanobiological theories reported in the literature. Finite element analysis was used to simulate bone growth. The first study analyzed the effect of subject-specific growth plate geometry over simplified growth plate geometry in numerical prediction of bone growth tendency. Subject-specific femur finite element model was constructed from magnetic resonance images of one able- bodied child. Gait kinematics and kinetics were acquired from motion analysis and analyzed further in musculoskeletal modelling to determine muscle and joint contact forces. These were used to determine loading on the femur in finite element analysis. The growth rate was computed based on a mechanobiological theory proposed by Carter and Wong, and a growth model in the principal stress direction was introduced. Our findings support the use of subject- specific geometry and of the principal stress growth direction in prediction of bone growth. The second study aimed to illustrate how different muscle groups’ activation during gait affects proximal femoral growth tendency in able-bodied children. Subject-specific femur models were used. Gait kinematics and kinetics were acquired for 3 able-bodied children, and muscle and joint contact forces were determined, similar to the first study. The contribution of different muscle groups to hip contact force was also determined. Finite element analysis was performed to compute the specific growth rate and growth direction due to individual muscle groups. The simulated growth model indicated that gait loading tends to reduce neck shaft angle and femoral anteversion during growth. The muscle groups that contributes most and least to growth rate were hip abductors and hip adductors, respectively. All muscle groups’ activation tended to reduce the neck shaft and femoral anteversion angles, except hip extensors and adductors which showed a tendency to increase the femoral anteversion. The third study’s aim was to understand the influence of different physical activities on proximal femoral growth tendency. Hip contact force orientation was varied to represent reported forces from a number of physical activities. The findings of this study showed that all studied physical activities tend to reduce the neck shaft angle and anteversion, which corresponds to the femur’s natural course during normal growth. The aim of the fourth study was to study the hypothesis that loading in the absence of physical activity, i.e. static loading, can have an adverse effect on bone growth. A subject-specific model was used and growth plate was modeled as a poroelastic material in finite element analysis. Prendergast’s indicators for bone growth was used to analyse the bone growth behavior. The results showed that tendency of bone growth rate decreases over a long duration of static loading. The study also showed that static sitting is less detrimental than static standing for predicted cartilage-to-bone differentiation likelihood, due to the lower magnitude of hip contact force. The prediction of growth using finite element analysis on experimental gait data and person- specific femur geometry, based on mechanobiological theories of bone growth, offers a biomechanical foundation for better understanding and prediction of bone growth-related deformity problems in growing children. It can ultimately help in treatment planning or physical activity guidelines in children at risk at developing a femur or hip deformity. / <p>QC 20170616</p>