The steady thermocapillary motion in shallow enclosures is studied. Two different configurations, imposed heat flux and differentially heated side walls, are considered. A numerical simulation of the problem in the imposed heat flux case is made. The Pressure Correction Method is used to treat the pressure velocity coupling, in particular, the SIMPLER approximation. The discretization is made using central differences along with an appropriate non-uniform grid. The computed results show the streamlines and temperature field in different Marangoni number, Prandtl number, Capillary number and aspect ratio

Abstract The steady thermocapillary motion in shallow enclosures is studied. Two different configurations, imposed heat flux and differentially heated side walls, are considered. A numerical simulation of the problem in the imposed heat flux case is made. The Pressure Correction Method is used to treat the pressure velocity coupling, in particular, the SIMPLER approximation. The discretization is made using central differences along with an appropriate non-uniform grid.

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The possibility to stabilize the oscillatory thermocapillaryconvection is demonstrated using a proportional feedbackcontrol. This topic has a strong industrial motivation inconnection with a container-less crystal growth method calledthe floating-zone technique. The thermocapillary oscillation isknown to cause detrimental striations, microscopicinhomogeneity of the dopant distribution, in the final productof the crystal growth process. The feedback control is realizedby locally modifying the surface temperature by using the localtemperature measured at dierent locations fed back through asimple control law. Placing sensor/actuator pairs (controllers)in a strategical manner using the knowledge of the modalstructures, a simple cancellation scheme can be constructedwith only a few controllers. In this method, the state can bestabilized without altering the base flow appreciably whichcould be advantageous compared with other available controlmethods targeting the base convection. As an initial study of such kind of control method, thisthesis work explores the possibility of applying the control insimplified geometries such as the annular configuration and thehalf-zone for high Prandtl number liquids by means ofexperiments, numerical simulations, and formulation of a simplemodel equation system. Successful suppression of theoscillation was obtained especially in the weakly nonlinearregime where the control completely suppresses theoscillations. With a right choice of actuators, even with thelocal control, it was shown that it is possible to modify thelinear and weakly-nonlinear properties of the three-dimensionalflow system with linear and weakly nonlinear control. On theother hand, the method exhibits certain limitations. Dependingon the geometry of the system and actuators, the limitation canbe caused by either the enhancement of nonlinear dynamics dueto the finite size of the actuators or the amplification of newlinear modes. The former case can be attenuated by increasingthe azimuthal length of the actuators to reduce the generationof broad wavenumber waves. In the latter case, having an ideaof the structures of the newly appearing modes, thedestabilization of those modes can be delayed by optimizing theconfiguration of controllers. On the whole, the oscillation canbe attenuated significantly in a range of supercritical Maup to almost twice the critical value. <b>Keywords:</b>Fluid mechanics, Marangoni convection,thermocapillary convection, annular configuration, half-zone,feedback control, flow visualization, low dimensional model,bifurcation.

In this thesis, a new model is formulated for a piezoelectric membrane and fluid motion in a microchannel heat engine. A new slug flow model is developed for droplet motion in a circular cross-section channel. The model includes friction, pressure, viscous and thermocapillary forces on the droplet. This thesis examines the concept of a piezoelectric device at one end of the channel to generate electricity from thermocapillary pumping of the droplet within the microchannel. The slug flow model is used to predict the flow energy needed to convert the thermocapillary pumping into electrical energy. A thin membrane design of a piezoelectric device is developed and modelled with the slug flow approximation. The deformation of the piezoelectric membrane is analyzed. The deformation is found to be a function of the air pressure in the closed microchannel and the displacement of the droplet along the microchannel. This was formulated based on the bending of a thin plate (representing the membrane). The displacement relates to the final output voltage of the design. The direct piezoelectric effect was also examined to determine a relationship between the output voltage and induced stress on the membrane by the force of air. Results are presented for a micro heat engine configuration containing a single membrane on one side of the droplet. It was found that the deformation of the membrane and the output voltage were directly proportional to the displacement of the droplet. A relatively small output voltage was gained from a complete cycle of the droplet. A sensitivity study was performed by varying the channel dimensions along with the dimensions of the piezoelectric membrane. The coupling factor of the piezoelectric membrane was varied to examine its effect on the output voltage. It was found that a larger channel and thinner membrane resulted in a larger output voltage. Materials with a large piezoelectric constant were found to have the largest output voltage, as opposed to those with a lower dielectric constant. / UOIT

<p>The possibility to stabilize the oscillatory thermocapillaryconvection is demonstrated using a proportional feedbackcontrol. This topic has a strong industrial motivation inconnection with a container-less crystal growth method calledthe floating-zone technique. The thermocapillary oscillation isknown to cause detrimental striations, microscopicinhomogeneity of the dopant distribution, in the final productof the crystal growth process. The feedback control is realizedby locally modifying the surface temperature by using the localtemperature measured at dierent locations fed back through asimple control law. Placing sensor/actuator pairs (controllers)in a strategical manner using the knowledge of the modalstructures, a simple cancellation scheme can be constructedwith only a few controllers. In this method, the state can bestabilized without altering the base flow appreciably whichcould be advantageous compared with other available controlmethods targeting the base convection.</p><p>As an initial study of such kind of control method, thisthesis work explores the possibility of applying the control insimplified geometries such as the annular configuration and thehalf-zone for high Prandtl number liquids by means ofexperiments, numerical simulations, and formulation of a simplemodel equation system. Successful suppression of theoscillation was obtained especially in the weakly nonlinearregime where the control completely suppresses theoscillations. With a right choice of actuators, even with thelocal control, it was shown that it is possible to modify thelinear and weakly-nonlinear properties of the three-dimensionalflow system with linear and weakly nonlinear control. On theother hand, the method exhibits certain limitations. Dependingon the geometry of the system and actuators, the limitation canbe caused by either the enhancement of nonlinear dynamics dueto the finite size of the actuators or the amplification of newlinear modes. The former case can be attenuated by increasingthe azimuthal length of the actuators to reduce the generationof broad wavenumber waves. In the latter case, having an ideaof the structures of the newly appearing modes, thedestabilization of those modes can be delayed by optimizing theconfiguration of controllers. On the whole, the oscillation canbe attenuated significantly in a range of supercritical M<i>a</i>up to almost twice the critical value.</p><p><b>Keywords:</b>Fluid mechanics, Marangoni convection,thermocapillary convection, annular configuration, half-zone,feedback control, flow visualization, low dimensional model,bifurcation.</p>

This thesis focuses on investigating the stability, dynamics and physical mechanisms of thermocapillary flows undergoing phase change by means of direct numerical simulations and experiments. The novelty of the general approach developed in this work lies in the fact that the problems under consideration are addressed with novel fully-coupled transient two-phase flow models in 3D. Traditional simplifications are avoided by accounting for deformable interfaces and by addressing advection-diffusion mechanisms not only in the liquid but also in the gas. This strategy enables a realistic investigation of the interface energy and mass transfer at a local scale for the first time. Thorough validations of the models against theory and experiments are presented. The thesis encompasses three situations in detail: liquid layers in saturated environments, liquid layers in unsaturated environments and evaporation of liquid droplets. Firstly, a model grounded in the volume-of-fluid method is developed to study the stability of laterally-heated liquid layers under saturated environments. In this configuration, the planar layer is naturally vulnerable to the formation of an oscillatory regime characterized by a myriad of thermal wave-like patterns propagating along the gas-liquid interface, i.e. hydrothermal waves. The nonlinear growth of the instabilities is discussed extensively along with the final bulk flow for both the liquid and gas phases. Previously unknown interface deformations, i.e. physical waves, induced by, and enslaved to, the hydrothermal waves are reported. The mechanism of heat transfer across the interface is found to contradict previous single-phase studies since the travelling nature of the hydrothermal waves leads to maximum heat fluxes not at the points of extreme temperatures but somewhere in between. The model for saturated environments is extended in a second stage to assess the effect of phase change in the hydrothermal waves for the first time. New numerical results reveal that evaporation affects the thermocapillary instabilities in two ways: the latent energy required during the process tends to inhibit the hydrothermal waves while the accompanying level reduction enhances the physical waves by minimizing the role of gravity. Interestingly, the hydrothermal-wave-induced convective patterns in the gas decouple the interface vapour concentration with that in the bulk of the gas leading to the formation of high (low) concentrations of vapour at a certain distance above interface cold (hot) spots. At the interface the behavior is the opposite. The phase-change mechanism for stable layers is also discussed. The Marangoni effect plays a major role in the vapour distribution and local evaporation flux and can lead to the inversion of phase-change process, i.e. the thermocapillary flow can result into local condensation in an otherwise evaporating liquid layer. The third problem discussed in this thesis concerns with the analysis of evaporating sessile droplets by means of both experiments and 3D numerical modeling. An experimental apparatus is designed to study the evaporation process of water droplets on superheated substrates in controlled nitrogen environments. The droplets are simultaneously recorded with a CCD camera from the side and with an infrared camera from top. It is found that the contact line initially remains pinned for at least 70% of the time, period after which its behaviour changes to that of the stick-slip mode and the drop dries undergoing contact line jumps. For lower temperatures an intermediate stage has been observed wherein the drop evaporates according to a combined mode. The experimental work is complemented with numerical simulations. A new model implementing the diffuse-interface method has been developed to solve the more complex problems of this configuration, especially those associated with the intricate contact-line dynamics. Further insights into the two-phase flow dynamics have been provided as well as into the initial transient stage, in which the Marangoni effect has been found to play a major role in the droplet heating. For the first time, a fully-coupled two-phase direct numerical simulations of sessile drops with a moving contact line has been performed. The last part of this work has been devoted to the investigation of three-dimensional phenomena on drops with irregular contact area. Non-sphericity leads to complex three-dimensional drop shapes with intricate contract angle distributions along the triple line. The evaporation rate is found to be affected by 3D features as well as the bulk flow, which become completely non-axisymmetric. To the best of our knowledge, this work is the first time that three-dimensional two-phase direct numerical simulations of evaporating sessile drops have been undertaken.

The growth of energy demand in the world requires addressing the increasing power requirements of industrial and residential consumers. Optimizing the design of new and existing large power producing systems can efficiently increase energy supply to meet the growing demand. Hydrogen as an energy carrier is a promising sustainable way to meet the growing energy demand, while protecting the environment. This thesis investigates the efficient production of hydrogen from the electrolysis of copper chloride, by predicting entropy production as a result of diffusive mass transfer. Also, this thesis investigates the possibility of producing electrical energy from waste heat produced by industrial or other sources. The thermocapillary motion of fluid droplet in a closed rectangular microchannel is used to generate electrical energy from waste heat in a piezoelectric membrane by inducing mechanical deformation as a result of the droplet motion. Modeling, fabrication, and experimental measurement of a micro heat engine (MHE) are investigated in this study. Analytical and experimental results are reported for both circular and rectangular microchannels. A novel fabrication technique using lead zirconate titanate (PZT) as substrate in microfluidic application is presented in this study. This thesis develops a predictive model of the entropy production due to thermal and fluid irreversibilities in the microchannel. Thermocapillary pressure and friction forces are modelled within the droplet, as well as surface tension hysteresis during start-up of the droplet motion. A new analytical model is presented to predict the effect of transient velocity on the voltage production in the MHE. In order to predict the effect of the applied stress on voltage, the different layers of deposition are considered for thin film laminates. The highest efficiency of the system from simulated taking into iv account the electromechanical coupling factor is about 1.6% with a maximum voltage of 1.25mV for the range of displacement considered in this study. In addition, new experimental and analytical results are presented for evaporation and de-pinning of deionised water and toluene droplets in rectangular microchannels fabricated from Su-8 2025 and 2075. / UOIT

The transient two-dimensional thermocapillary convection and molten pool shape in melting or welding with a time-dependent and distributed incident flux are numerically predicted in this study. Determination of the molten pool shapes is crucial, because of its close relationships with the strength, microstructure, and mechanical properties of the fusion zone. In the work, the time-dependent incident flux is assumed to be a function of scanning speed and energy distribution parameter. Transport processes at the time corresponding to the maximum cross section can be identical to those under steady three-dimensional condition. The computed flow patterns and molten pool shapes under the flat free surface exhibits distinct regions for different Marangoni and Prandtl numbers. The effects of Peclet number and beam power on flow and temperature fields and fusion zone shapes are also presented. The computed results are confirmed by comparing the predicted peak speed on the free surface and molten pool width with those obtained from scale analysis provided in the literature.

A half-zone experimental set-up was used to study the effects of various liquid bridge and helium flow parameters on the onset of thermocapillary convection in silicone oil liquid bridges. Experiments confirmed that helium flow has a stabilizing effect, with the effect increasing with helium velocity. Furthermore, helium flow in the same direction as surface flow due to Marangoni convection had a more stabilizing effect than countercurrent flow. It was established that increasing helium temperature has a mixed effect, producing a less stable bridge at low helium flow rates, but a more stable flow pattern at higher helium flow rates. Finally, it was confirmed that decreasing the cold disk temperature results in a decrease in critical temperature difference.