March 23, 2023 11:00 am

Colloquium

Fiber coating dynamics: modeling, theory, and algorithms

Dr. Hangjie Ji, North Carolina State University

Thursday, March 23 – 11 :00AM; Location: 016 Manchester Hall

Thin liquid films flowing down vertical fibers spontaneously exhibit complex
interfacial dynamics, creating irregular wavy patterns and traveling liquid
droplets. Such fiber coating dynamics is a fundamental component in many
engineering applications, including mass and heat exchangers for thermal
desalination and water vapor and particle capture. Through experiments and
mathematical modelling, we demonstrate that flow regime transitions can be
triggered by varying inlet geometries. Theoretical predictions, based on a full
lubrication model and a weighted residual integral boundary-layer model,
explain the experimentally observed velocity and stability of traveling droplets
and their transition to isolated droplets. By coupling with the Marangoni
effects, a similar regime transition can also be triggered by imposing a
temperature field along the fiber. Using regularization techniques and a priori
estimates for energy-entropy functionals, we prove the existence of nonnegative
weak solutions for a fiber coating PDE model and analytically study
the traveling wave solutions. We will conclude by presenting our recent
results on developing positivity-preserving numerical methods and optimal
control for fiber coating dynamics.