日本航空宇宙学会関西支部分科会「流体力学における現代的アプローチ」講演会

A conservative scheme for solving coupled surface-bulk convection-diffusion equations with an application to interfacial flows with soluble surfactant

Prof. Ming-Chih Lai
(Department of Applied Mathematics, National Chiao Tung University, Taiwan)

要旨

Many physical problems arising in biological or material sciences involve solving partial differential equations in deformable interfaces or complex domains. For instance, the surfactant (an amphiphilic molecular) which usually favors the presence in the fluid interface may couple with the surfactant soluble in one of bulk domains through adsorption and desorption processes. Thus, it is important to accurately solve coupled surface-bulk convection-diffusion equations especially when the interface is moving. In this talk, we present a new conservative scheme for solving this coupled surface-bulk concentration equations which the total surfactant mass is conserved in discrete sense. As an application, we extend our previous work to the interfacial flows with soluble surfactant. The effects of solubility of surfactant on drop deformations in a quiescent and shear flow are investigated in detail.

The Landau equation as the weak-coupling limit of interaction particle systems

Prof. Mario Pulvirenti
(Department of Mathematics, University of Rome, Italy)

要旨

In this talk we exploit the weak-coupling limit of a Hamiltonian particle system. We show, formally, that the Landau equation is the kinetic equation expected to be valid in this scaling limit. We also show that this is also true rigorously, up to the first order in the perturbative expansion.