This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.