The study presented in this dissertation concerns the evaporation, in normal ambient conditions, of sessile droplets (pinned and freely receding) of various HFE liquids (instead of the widely used water), which are considered so far as environmentally friendly and are often used as heat-transfer fluids in thermal management applications. They are pure perfectly-wetting and volatile liquids with low thermal conductivity and high vapor density. These properties affect in their own way many aspects concerning droplet evaporation such as the evaporation-induced contact angles, evaporation rate of a droplet, contact line pinning and Marangoni flow, all of which are treated in the present dissertation.<p>In general, the thesis starts with a general introduction including but not limited to sessile droplets (Chapter 1). In Chapter 2 we provide a general overview of capillarity-related concepts. Then, in Chapter 3 we present the interferometric setup, along with the liquids and the substrate that is used in the experiments, and also explain the reasons why this particular method is chosen. In Chapter 4 we address, among others, the issue of evaporation-induced contact angles under complete wetting conditions. The behavior of the global evaporation rate is also examined here, whereas in Chapter 5 we discuss the influence of thermocapillary stresses on the shape of strongly evaporating droplets. Finally, before concluding in Chapter 7, we address in Chapter 6 the still open question of the influence of non-equilibrium effects, such as evaporation, on the contact-line pinning at a sharp edge, a phenomenon usually described in the framework of equilibrium thermodynamics. The experimental results obtained are also compared with the predictions of existing theoretical models giving rise to interesting conclusions and promising perspectives for future research.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results. / Doctor of Philosophy / When a liquid droplet is sliding along a solid surface, a moving contact line is formed at the intersection of the three phases: liquid, air and solid. This work develops a numerical method to study problems with moving contact lines. The partial differential equations describing the problem are solved by finite element methods. Our numerical method is validated against experiments and theories. Furthermore, we have implemented our method in three-dimensional problems.