Diffuse-Interface Simulations of Capillary Phenomena

Abstract: Fluid flows mainly driven by capillary forces are presented in this thesis. By means of modeling and simulations, interesting dynamics in capillary-driven flows are revealed such as coalescences, breakups, precursor films, flow instabilities, rapid spreading, rigid body motions, and reactive wetting.Diffuse-interface methods model a fluid interface as having a finite thickness endowed with physical properties such as surface tension. Two diffuse-interface models that are based on the free energy of the system are presented. The binary model, more specifically the coupled Navier-Stokes/Cahn-Hilliard equations, was used to study different two-phase flows including problems related to microfluidics. Numerical issues using this model have been addressed such as the need for mesh adaptivity and time-step restrictions. Moreover, the flexibility of this model to simulate 2D, axisymmetric, and 3D flows has been demonstrated.The factors affecting reproducibility of microdroplet depositions performed under a liquid medium are investigated. In the deposition procedure, sample solution is dispensed from the end of a capillary by the aid of a pressure pulse onto a substrate with pillar-shaped sample anchors. In both the experimental and numerical study it was shown that the deposited volume mainly depends on the capillary-substrate distance and anchor surface wettability. Furthermore, a critical equilibrium contact angle has been identified below which reproducible depositions are facilitated.The ternary model is developed for more complicated flows such as liquid phase sintering. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. Detailed analysis of the important capillary phenomena in liquid phase sintering such as reactive and nonreactive wetting and motion of two particles connected by a liquid bridge are presented. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Factors affecting the equilibrium configuration of the particles such as equilibrium contact angles and volume ratios are also investigated.