Eglal Ellaban, who recently earned her master’s degree in Mathematics at Ryerson, has devoted her studies to advancing the scientific understanding of fluid mechanics.

If the mathematical modelling of fluid mechanics problems seems obscure at first glance, she emphasizes that real-life applications can be found everywhere. If you consider the dynamics involved when a liquid flows down an incline, for example – which happens to be the focus of Ellaban’s thesis research – everyday examples include everything from rain gutters and ketchup bottles, to sewers to canals.

Yet there are also much more complex applications, explains Ellaban. “Liquid films flowing down an inclined plane have widespread applications in both environmental phenomena and industrial settings,” she says, citing wide-ranging examples such as coating applications, polymer processing, lava flows and mud floods.

What continues to fascinate researchers like Ellaban are unanswered questions. Though the gravity-driven flow of liquid has a certain simplicity, the underlying dynamics are complex and still not fully mapped out, she says. “The formation of interfacial waves due to hydrodynamic instability exhibits complicated dynamics.”

Supervised by Jean-Paul Pascal, a professor in Ryerson’s Department of Mathematics, Ellaban’s thesis research goal was to advance scientific understanding and potential applications for society in this area. (Serge D’Alessio, a University of Waterloo mathematics professor, also worked with Ellaban on this project.)