Numerical simulation of cell motility is one of the difficult problems in computational science. It belongs to a class of problems which involve moving interfaces between flowing or deforming media. Different numerical techniques are being developed for different application areas and in this work an attempt is made to apply two popular numerical techniques used in the field of computational multiphase flows to a cell motility problem. An unsteady cell motility problem is considered to simulate numerically based on a two-dimensional mathematical model. Two important numerical methods, the Level set method and the Front tracking methods are applied to the cell motility problem to study several cases and to verify the convergence of the solution. With the assumption of no mechanical or physical obstructions to the cell, the results of the numerical simulations show that the domain shapes converge to a circular shape as they reach the steady state condition. The final steady state velocities with which the domains move and the final steady state area to which they converge are observed to be independent of domain shapes. Moreover all shapes converge to exactly same radius of circle and move with same velocity after reaching steady state condition.

In this thesis we report the results of investigations on the rheological response of emulsions to the application of the electric field. A front-tracking finite difference scheme is used in conjunction with Taylor-Melcher leaky dielectric theory to study the problem. The numerical results in different regions of the deformation-circulation map show that the structure formation in regions I and III can be hindered by the hydrodynamic effect. This is opposite to what is observed in the perfect dielectric cases and region II of the map. For perfect dielectric systems, where the electrohydrodynamics effects are absent, droplets form chain-like structures spanning the distance between the electrodes after the application of the electric field. Subsequently, the chains interact with each other to form columns comprising two or more chains. Point-dipole approximation is used to analyze the structure formation and it is shown that it is also applicable to region II where the hydrodynamic effect is weak and the behavior of the system is mainly governed by the dielectrophoretic forces. It is shown that the chain formation is not possible in regions I and III due to the competition between the dipolar force and torque on one side and hydrodynamic effect on the other side. In region I, the hydrodynamic torque prevents the chain formation by competing with the dipolar torque, which tends to align the drops with the electric field. On the other hand, in region III, the repulsive nature of the hydrodynamic effect opposes the attractive dipolar force and does not allow the particles to form stable chains.

Ce travail de thèse est consacré à la modélisation et simulation numérique d'écoulements diphasiques liquide-gaz mettant en jeu des transferts de chaleur. La simulation de configurations où la prise en compte des effets de compressibilité de la phase gazeuse est indispensable (micropompes, microactionneurs, etc...) a nécessité l'utilisation d'un modèle original, considérant le liquide incompressible et le gaz compressible sous l'hypothèse faible Mach. Lors de cette thèse, ce modèle a été implémenté dans un code diphasique prenant en compte l'interface à l'aide d'une méthode de front-tracking. Des cas tests ont été développés spécifiquement afin de vérifier la conservation de l'énergie pour des configurations de complexité croissante. Les résultats des cas tests ont permis de mettre en évidence la difficulté à assurer la conservation de l'énergie lorsque l'interface n'est pas discontinue mais lissée, comme c'est le cas dans la méthode de front-tracking standard. Une méthode de traitement d'interface hybride a été proposée, rétablissant le caractère discontinu de l'interface avec la reconstruction d'une fonction indicatrice de phase échelon, tandis que le déplacement de l'interface est assuré d'un pas de temps à l'autre à l'aide du front-tracking. Les résultats obtenus avec cette nouvelle méthode hybride sont très satisfaisants, la méthode hybride permettant d'assurer la conservation de l'énergie et de la masse avec précision dans les simulations. / This thesis is devoted to the modeling and the numerical simulation of liquid-gas flows in non isothermal micro-cavities or micro-channels. The objective is to describe two-phase flows in which compressibility of the gaseous phase plays a key role (as for instance in micropumps, microactuators, etc...). An original model is developed, considering in the same computational domain, an incompressible liquid and a compressible gas under the low Mach approximation. This model has been implemented in a code using the front-tracking method for the interface description. In order to check the proper satisfaction of the energy balance, specific test cases have been developed considering several configurations of increasing complexity. It has been shown from these test cases that energy conservation can hardly be satisfied when the interface is described by the means of a smooth function, which is done in the front-tracking method. An hybrid method has been proposed, restoring the discontinous nature of the interface. It makes use of a step function combined with the front tracking method. Results obtained with this new hybrid method show that mass conservation and energy balance are very properly enforced during the computations. This thesis is devoted to the modelling and numerical simulation of liqui-gas flow envolving heat transfer. Simulation of configurations where it is essential to take into account the compressibility nature of the gaseous phase(for instance micropumps, microactuators, etc...) require the use of an original model, considering an incompressible liquid and a compressible gas under the low Mach assuption. During this thesis, the model has been implemented in a multiphase flow code using the front-tracking method to handle the interface. Test cases have been developped specifically to check the energy conservation for differents configurations of an increasing complexity. Numerical results highlighted difficulties encountered to ensure the energy conservation while using smooth description of the interface, as it is the case in the standard front-tracking method. An hybrid method has been proposed, restoring the discontinous character of the interface by reconstructing a step maker function, whereas the front displacement from a time step to the next, is still handled with the front-tracking. Results obtained using this new hybride method are very satisfactory, the hybrid method allowing the code to ensure accurately the energy and mass conservation during the computations.

One of the most demanding engineering issues in Inertial Fusion Energy (IFE) reactors is the design of a reaction chamber that can withstand the intense photons, neutrons and charged particles due to the fusion event. Rapid pulsed deposition of energy within thin surface layers of the fusion reactor components such as the first wall may cause severe surface erosion due to ablation. One particularly innovative concept for the protection of IFE reactor cavity first walls from the direct energy deposition associated with soft X-rays and target debris is the thin liquid film protection scheme. In this concept, a thin film of molten liquid lead is fed through a silicon carbide first wall to protect it from the incident irradiations. Numerous studies have been reported in the literature on the thermal response of the liquid film to the intermittent photon and ion irradiations, as well as on the fluid dynamics and stability of liquid films on vertical and upward-facing inclined surfaces. However, no investigation has heretofore been reported on the stability of thin liquid films on downward-facing solid surfaces with liquid injection through (i.e. normal to the surface of) the bounding wall. This flow models the injection of molten liquid lead over the upper end cap of the reactor chamber. The hydrodynamics of this flow can be interpreted as a variation of the Rayleigh-Taylor instability due to the effect of the bounding wall which is continuously fed with the heavier fluid. In order to gain additional insight into the thin liquid film protection scheme, experiments have been conducted to investigate the critical issues associated with this concept. To this end, an experimental test facility has been designed and constructed to simulate the hydrodynamics of thin liquid films injected normal to the surface of and through downward-facing flat walls. In this doctoral thesis, the effect of different design parameters (film thickness, liquid injection velocity, liquid properties and inclination angle) on liquid film stability has been examined. The results address the morphology of the film free surface, the frequency of droplet formation and detachment, the size and penetration depth of the detached droplets, and the interface wave number. These experimental data have been used to validate a novel mechanistic numerical code based on a level contour reconstruction front tracking method over a wide range of parameters. The results of this investigation will allow designers of IFE power plants to identify appropriate windows for successful operation of the thin liquid film protection concept for different coolants.