(125b) Thin Film and Related Flows with Various Complexities

The recent passing of Jeff Davis is a tragic event. It is the sort of thing that is simply not supposed to happen. Instead, Jeff was supposed to continue to have a successful career leading his research group and his department to even greater heights. He was supposed to win even more awards and recognition, and become a member and fellow of prestigious learned societies. Alas, not to be... During his short time among us, however, Jeff made excellent contributions to the literature, mainly in the area of thin films; this started with his doctoral thesis work at Princeton. The purpose of this special symposium is to honour Jeff and celebrate his achievements. Although his loss is a painful one for the community, his legacy will live on through his outstanding body of work, the students that he taught and mentored so brilliantly, and the people whose lives he touched through his kindness. I am proud of my connection with Jeff who was my academic brother (Prof. Sandra Troian was our thesis adviser, though I was several years Jeff's senior); and we both worked on thin films (though I largely moved away from the area some time ago). Below, I offer a possible explanation for Jeff's fascination with this area of fluid mechanics.

The fluid dynamics of thin (or low aspect ratio) films and drops have enjoyed considerable attention over decades due to their relevance to numerous industrial, biological, environmental, and daily-life applications. These applications span microfluidics, coating flows, surfactant replacement therapy, rupture of tear films, reaction engineering and energy integration, and the dynamics of ice sheets and lava domes. The multi-physics of thin film flows reflects their truly multi-scale nature and the delicate interplay amongst intermolecular forces, capillarity, thermo-capillarity, chemically-driven stresses, and viscosity, as well as gravity and electromagnetic forces, depending on the application in hand. Additional complexities may arise from flows over rotating, compliant, structured, physically and/or chemically heterogeneous walls, and may involve heat transfer and phase change, as well as the presence of surfactants and nanoparticles; some flows also feature moving contact lines, which increases the level of complexity. As a result of this vast array of effects, thin film flows are accompanied by a range of fascinating, and visually appealing, phenomena, which include dewetting of thin polymeric films, fingering of flows down an incline and of surfactant-laden spreading drops, and large-amplitude waves on the surface of falling films. The theory, modelling, and simulation of thin film dynamics gives rise to highly nonlinear, high-order partial differential equations, which require a combined approach involving asymptotic methods and numerical techniques; and, Jeff, of course, was brilliant at both.

In my talk, I will touch on some previous and recent work, which my research group has carried out, together with many collaborators. This will include thin film flows with surfactants and moving contact lines, falling films and flows over rapidly rotating discs, and drying of particle-laden films with poroelasticity. I will also highlight connections with Jeff's important thin films work. I sincerely hope that this special symposium at AIChE 2024 will go some way towards highlighting Jeff's contributions, which will doubtless stand the test of time, and give him the send-off that his short yet glittering career thoroughly deserves.