Date of Award


Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

College, School or Department Name

Department of Mathematical Sciences


Kathleen A. Feigl


The dynamic meshing procedure in an open source three-dimensional solver for calculating immiscible two-phase flow is modified to allow for simulations in two-dimensional planar and axisymmetric geometries. Specifically, the dynamic mesh refinement procedure, which functions only for the partitioning of three-dimensional hexahedral cells, is modified for the partitioning of cells in two-dimensional planar and axisymmetric flow simulations. Moreover, the procedure is modified to allow for computing the deformation and breakup of drops or bubbles that are very small relative to the mesh of the flow domain. This is necessary to avoid mass loss when tracking small drops or bubbles through flow fields. Three test cases are used to validate the modifications: the deformation and breakup of a two-dimensional drop in a linear shear field; the formation and detachment of drops in a two-dimensional micro T-junction channel; and an axisymmetric bubble rising from a pore into a static liquid. The tests show that the modified code performs very well, giving accurate results for much less computational time when compared to corresponding simulations without dynamic meshing.

The modified code is then applied to study drop breakup conditions inside a spray nozzle when an emulsion is sprayed to produce a powder. This is done by tracking droplets of various sizes through the flow field within the nozzle and determining conditions under which they break up. The particular interest is in determining the largest drop sizes for which breakup does not occur. The effects of viscosity ratio, capillary number, shear rate, and fluid rheology on the critical drop sizes are determined.

Although the code modifications performed for this research were implemented for dynamic mesh refinement of cells close to fluid-fluid interfaces, they may be adapted to other regions in the domain and for other types of flow problems.