论文标题
吸附动力学的多尺度建模
Multiscale Modeling of Sorption Kinetics
论文作者
论文摘要
在本文中，我们提出并验证一个多尺度模型，以描述存在陷阱边界的粒子扩散。我们从漂移扩散方程开始，其中漂移术语描述了气泡陷阱的效果，并以具有吸引力的术语和排斥核心的短距离电位进行建模。 Lennard-Jones电位模拟了被气泡表面吸引的颗粒的相互作用，从而简化了由于离子的疏水性能而导致的捕获。在我们的模型中，电势的效果被质量保护和渐近分析得出的合适边界条件所取代。假定潜力具有小尺寸$ \ varepsilon $。考虑了$ \ varepsilon $中的渐近扩展，边界条件是通过在扩展中保留最低订单项来获得的。 我们研究的另一个方面是来自气泡表面接近的高浓度的饱和效应。仔细检查模型的有效性，并在1D，2D和不同的几何形状中进行了几个测试。
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps, and is modeled by a short range potential with an attractive term and a repulsive core. The interaction of the particles attracted by the bubble surface is simulated by the Lennard-Jones potential that simplifies the capture due to the hydrophobic properties of the ions. In our model the effect of the potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The potential is assumed to have a range of small size $\varepsilon$. An asymptotic expansion in the $\varepsilon$ is considered, and the boundary conditions are obtained by retaining the lowest order terms in the expansion. Another aspect we investigate is saturation effect coming from high concentrations in the proximity of the bubble surface. The validity of the model is carefully checked with several tests in 1D, 2D and different geometries.
