Text only print
Full screen print
PDE Real Analysis Seminar
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|
2012/03/21
10:00-11:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Chiun-Chang Lee (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
Chiun-Chang Lee (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ Abstract ]
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.
