國立清華大學 數學系

Abstract: The Poisson-Boltzmann (PB) equation is widely used to model the electrical double layer in a colloidal system. For better understanding properties of the electrical double layer around a spherical colloidal particle, we study asymptotic behavior for solutions of the PB equation with a small dielectric parameter ε in an annular domain. In addition, we establish the precise asymptotic formulas for the slope of the boundary layers with the leading order term O(1/ε) and the second-order term O(1) as ε goes to zero. These asymptotic formulas also show that the boundary curvature exactly appears in the second-order term. Our mathematical results provide a way to see the influence of ionic concentrations and the curvature of the boundary on the thickness of the boundary layer. Tea Time: 3:30pm, R707