A phase field model for droplets suspended in viscous liquids under the influence of electric fields
科研大讨论系列报告
报告题目(Title)：A phase field model for droplets suspended in viscous liquids under the influence of electric fields
报告人(Speaker)：徐士鑫 (Assistant Professor of Mathematics, Duke Kunshan University)
地点(Place)：后主楼1124
时间(Time)：2023 年 7月14日(周五), 10:00-11:00
邀请人(Inviter)：蔡永强
报告摘要
In this talk, we propose a Poisson-Nernst-Planck-Navier-Stokes-Cahn-Hillard (PNP-NS-CH) model for an electrically charged droplet suspended in a viscous fluid subjected to an external electric field. Our model incorporates spatial variations of electric permittivity and diffusion constants, as well as interfacial capacitance. Based on a time scale analysis, we derive two approximations of the original model, namely a dynamic model for the net charge (by assuming conductance remains unchanged) and a leaky-dielectric model (by assuming both conductance and net charge remain unchanged). For the leaky-dielectric model, we conduct a detailed asymptotic analysis to demonstrate the convergence of the diffusive-interface leaky-dielectric model to the sharp interface model as the interface thickness approaches zero.
Numerical computations are performed to validate the asymptotic analysis and demonstrate the model’s effectiveness in handling topology changes, such as electro-coalescence. Our numerical results of these two approximation models reveal that the polarization force, which is induced by the spatial variation of electric permittivity in the direction perpendicular to the external electric field, consistently dominates the Lorentz force, which arises from the net charge.
The equilibrium shape of droplets is determined by the interplay between these two forces along the direction of the electric field. Furthermore, in the presence of the interfacial capacitance, a local variation of effective permittivity leads to an accumulation of counter-ions near the interface, resulting in a reduction in droplet deformation. Our numerical solutions also confirm that the leaky-dielectric model serves as a reasonable approximation of the original PNP-NS-CH model when the electric relaxation time is sufficiently short. The Lorentz force and droplet deformation both decrease when the diffusion of net charge is significant. This work is collabortated with Yuzhe Qin, Huaxiong Huang, and Zilong Song.
主讲人简介
Professor Shixin Xu received the B.Sc. in Mathematics (Hons) from Ocean University of China and a Ph.D. in Mathematics from the University of Science and Technology, China, in 2013. From 2013 to 2017, he held post-doctorate positions at the National University of Singapore, the University of Notre Dame and University of California Riverside (U.S.), and the Fields Institute for Research in Mathematical Sciences (Canada). His research interests are machine learning and data-driven model for diseases, multiscale modeling of complex fluids, homogenization theory and numerical analysis.
