This project is an investigation into the fundamentals of flows involving free liquid-liquid or liquid-air interfaces where surface tension effects are dominant. The approach adopted is four-pronged and consists of modeling, analysis, computations, and comparisons with experiments, and it aims to establish theoretical and physically realistic models that are capable of describing phenomena of technological and strategic interest. Interfacial flows where surface tension is dominant arise in a plethora of classical and novel applications, including ink-jet printing and related technologies (DNA assays), solder-jet technologies and related advanced manufacturing processes, industrial emulsion processes, coating technologies, microfluidics and lab-on-a-chip technologies, and, micro- and nano-encapsulation techniques with applications to pharmaceutical slow drug release systems.
This project aims to contribute to understanding of such flows and in particular to incorporate, model, and analyze the effects of electric fields on the spatio-temporal interfacial dynamics which can lead to interfacial rupture (this is manifested as a singularity of the mathematical models). Another scope of the project is the use of electric fields in micron-sized multi-fluid systems where a controlled outcome is desired, for example enhanced mixing as in lab-on-a-chip technologies, or stabilization of capillary instability leading to longer threads as in extrusion processes or crystal growth liquid bridge geometries.
The research will develop novel nonlinear mathematical models capable of describing the phenomena referred to above and will use these to find mathematical solutions and describe their structure close to possible singular events. These solutions will in turn be used to guide and evaluate direct numerical simulations of the full problem with the aim of establishing simpler yet physically meaningful models that are highly efficient computationally, opening the way for large parametric studies of the phenomena. The mathematical study will also be used to obtain simple observable quantities, resulting from complex dynamics, that can be useful in experimental efforts.
