The aim of this proposal is to address, from the perspectives of modeling, simulation and experimentation, the critical issues related to the couplings between the bulk and interfacial flows, between the macroscale and the mesoscale dynamics, and between the inertial, viscous and surface rheological time-scales. These are essential for the development of designer surfactants: monolayer-forming materials for specified functions. It is expected that this project will provide (i) a general variational framework for the modeling of interfacial flows as well as for the coupling of mesoscale monolayer dynamics to the macroscale bulk flow; (ii) a robust and reliable numerical scheme for simulating the proposed multiscale model. The combined efforts of mathematical analysis, computer simulations and experimental measurements will significantly advance our knowledge on the multiscale interfacial dynamics associated to the monolayer forming surfactants.
Monolayer-forming surfactants are routinely applied in traditional technologies such as material and food processing, in liquid jets and atomization systems, as well as in emerging technologies such as lab-on-a-chip for parallel, low-cost DNA sequencing. These industries have a major economic impact. An example of surfactants playing a crucial role in biological systems is lung surfactants, without which respiration is impossible. In particular, recent developments in surfactant replacement therapy, used on premature infants, is a great success story where significant decreases in infant mortality are directly attributable to the surfactant therapy. Hence, a thorough understanding of the intrinsic physical processes associated with the multiscale interfacial monolayer hydrodynamics is of critical importance for the Nation's economic growth and well-being.
