Date of Award

Summer 2017

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Shahriar Afkhami

Second Advisor

Lou Kondic

Third Advisor

Linda Jane Cummings

Fourth Advisor

Philip D. Rack

Fifth Advisor

David Shirokoff


The volume of fluid (VoF) interface tracking methods have been used for simulating a wide range of interfacial flows. An improved accuracy of the surface tension force computation has enabled the VoF method to become widely used for simulating flows driven by the surface tension force. A general methodology for the inclusion of variable surface tension coefficient into a VoF based Navier-Stokes solver is developed. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation applies to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. The accuracy and convergence of the surface gradient computation are presented for various geometries, and for a classical problem of the thermocapillary migration of bubbles. The study of several applications of variable surface tension flows is presented, such as the breakup of liquid metal films and filaments, and the coalescence of drops characterized by different surface tension.

Included in

Mathematics Commons