Abstract: When a densely-packed monolayer of hydrophobic particles is placed on a fluid surface, the particles interact through capilary bridges, leading to the formation of a particle raft or “praft”. Densely packed monolayers exhibit a two-dimensional elastic response, and they are capable of supporting both tension and compression. The introduction of a controlled amount of surfactant generates a surface tension gradient, producing Marangoni forces and causing the surfactant to spread, fracturing the monolayer. These systems are of interest to materials scientists and engineers because they provide an idealized setting for investigating the interplay between fluid flow and fracture. Previous studies of the surfactant-induced fracture of prafts have examined the role of viscosity and the initial packing fraction on the temporal and spatial evolution of the fractures. The potentially important role of differences in surface tension between the surfactant and the underlying fluid has not been explored.
This seminar will describe a new continuum-based model and simulations that account for the interplay between the pressure exerted by a spreading surfactant and the elastic response of the praft, including the fracture toughness. This is affected through the use of a “surfactant damage” field that serves as both an indicator function for the surfactant concentration, as well as the damage to the monolayer. Stochastic aspects of the particle packing are incorporated into the model through a continuum mapping approach. The model gives rise to a coupled system of nonlinear partial differential equations, with an irreversibility constraint. We recast the model in variational form and discretize the system with an adaptive finite element method. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. Based on the model, we determine a dimensionless parameter that characterizes the ratio between this driving force and the fracture resistance of the praft. Interestingly, while our results indicate that the stochastic aspects of the packing are important to the fracture process, we find that regimes of fracture are largely governed by the differences in surface tension. Finally, we support our findings with newly designed experiments that validate the model and confirm the trends inferred from the simulations.
Bio: John Dolbow is a Professor of Civil and Environmental Engineering at Duke
University, where he directs the Duke Computational Mechanics Laboratory. Professor Dolbow received his BS in Mechanical Engineering from the University of New Hampshire in 1995, and his Ph.D. in Theoretical and Applied Mechanics from Northwestern University in 1999. He has been a faculty member in the Department of Civil and Environmental Engineering at Duke University since 1999, and his research concerns the development of numerical methods for evolving interface problems. He has received various awards for his research, including Young
Investigator awards from both the USACM and the IACM. He has held visiting appointments at Harvard University, the Okinawa Institute of Science and Technology, and Sandia National Laboratories. He is the Editor-In-Chief of the journal Finite Elements in Analysis and Design. He currently serves as the Vice President for the USACM, as well as on the DOE’s Advanced Scientific Computing Advisory Committee.