This thesis contributes to the continuum hydrodynamic modeling and simulations for two-phase (liquid-gas) flows on solid substrates. It has been known for decades that the liquid-gas flows on solid substrates present challenges to the classical paradigm of continuum hydrodynamics due to the presence of three-phase contact line, i.e., the intersection of the free (liquid-gas) interface with the solid wall. One classical problem is the non-integrable stress singularity due to the incompatibility between the moving contact line (MCL) and the no-slip boundary condition. The other problem is the thermal singularity (characterized by a diverging heat flux) occurring at the contact line of an evaporative (volatile) liquid droplet/slug/film on heated/cooled substrate. To resolve the stress and...[ Read more ]

This thesis contributes to the continuum hydrodynamic modeling and simulations for two-phase (liquid-gas) flows on solid substrates. It has been known for decades that the liquid-gas flows on solid substrates present challenges to the classical paradigm of continuum hydrodynamics due to the presence of three-phase contact line, i.e., the intersection of the free (liquid-gas) interface with the solid wall. One classical problem is the non-integrable stress singularity due to the incompatibility between the moving contact line (MCL) and the no-slip boundary condition. The other problem is the thermal singularity (characterized by a diverging heat flux) occurring at the contact line of an evaporative (volatile) liquid droplet/slug/film on heated/cooled substrate. To resolve the stress and thermal singularities, numerous models have been proposed for various systems that involve contact lines. However, a general continuum model capable of describing liquid-gas flows on solid substrates is still not available, where phase transitions (evaporation/condensation) and hydrodynamics are coupled, and various fluid-solid interfacial dissipative processes are present and may play an important role. The purpose of this thesis is to construct such a model for one-component fluids near the critical point and to use it to numerically study the behaviors of one-component liquid-gas flows on solid substrates for three typical scenarios: (i) isothermal liquid-gas (Couette) flows confined between two planar solid walls with a constant shear rate, (ii) a droplet moving on cooled/ordinary/heated solid substrates with wettability gradients, (iii) a droplet moving on solid substrates with thermal gradients. By fully taking into account the various dissipative processes (e.g., velocity slip and temperature slip) at the fluid-solid interface, this thesis presents a physically more complete and quantitatively more accurate description for the liquid-gas flow phenomena involved in confined geometries and wetting dynamics, which are important to many industrial processes.