Research interest in understanding the wetting and spreading phenomena of a droplet landing on a complex shape surface through numerical simulations has risen dramatically since the start of the era of scientific computing and high-speed/definition video camera.
This topic has attracted applied mathematicians, physicists, engineers, and computational scientists working together in a multidisciplinary environment due to its broad applications in industry, medicine, and biology. Many publications are related to this topic, ranging from laboratory experiments, mathematical and physical modeling to numerical simulations and visualizations. The hope is that the computer simulations based on the best mathematical model can closely match the flow behavior recorded with the high-speed camera.
Dr. Alfa Heryudono, associate professor of Mathematics, and Dr. Mehdi Raessi, associate professor of Mechanical Engineering, are the recipients of a $200,000 award from the National Science Foundation (NSF) for their three-year project "PUMA-VOF: Partition of Unity Multivariate Approximation for the Volume of Fluid Method." An essential focus of the application is in understanding the process of administering an eye drop on top of the tear film on the human cornea.
Computers (from "mini" to "super" version) used for these scientific simulations have become more advanced and faster year after year. Unfortunately, most number-crunching codes that are driving them still rely on legacy methods with lower accuracy. "Our goal is to utilize mathematical and numerical techniques to significantly improve accuracy without adding computational resources," says Heryudono. Having highly-accurate simulations may unravel features that cannot be captured with the low-order method."
“This project lies at the intersection of mathematical modeling, multiphase flow, and ophthalmology, which makes it particularly exciting," says Raessi. "Through advanced computational simulations, this project will, hopefully, lead to eye drop administering protocols that enable enhanced and targeted drug delivery, and avoid drug overdosage.”
The project has a strong component on research training and integrated education of students in an interdisciplinary setting. "Because the Volume-of-Fluid method is commonly used in studies of multiphase flow, this research will be extremely useful to researchers in academia, industry, and national labs for a wide variety of scientific and engineering applications," says Heryudono.