Weroński Paweł, Elimelech Menachem
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, MS B284, Los Alamos, NM 87545, USA.
J Colloid Interface Sci. 2008 Mar 15;319(2):406-15. doi: 10.1016/j.jcis.2007.10.042. Epub 2007 Dec 21.
Using variable substitution, we present a general method for the numerical solution of stiff, ordinary, linear, homogeneous differential equations characteristic of colloid particle adsorption/deposition over an energy barrier. For the example of the radial impinging jet system, we demonstrate the application of this method of calculating the colloid concentration profile and initial particle flux in the presence of repulsive electrostatic interactions between the particle and adsorption surface. We show that our method works well in systems with energy barriers up to the order of hundreds of kT, at which point the adsorption flux vanishes. The numerical results obtained with our method are in good agreement with the known limiting analytical approximations for the particle flux through an energy barrier and for a low Péclet number. The developed numerical code is very stable over a wide range of physical parameters, and its accuracy for the most challenging parameter sets is on the order of 10(-4). To achieve this stability, we have derived and employed a single formula for the van der Waals dispersion interaction, working at both a small and a large separation distance. We show that this formula converges to the known available analytical expressions for dispersion forces in the limit of small and large separation distance. We also demonstrate that the maximum deviations between our formula and the other equations appear in the intermediate range of the separation distance and do not exceed 10%.
通过变量代换，我们提出了一种数值求解刚性、常、线性、齐次微分方程的通用方法，这类方程是胶体颗粒在能垒上吸附/沉积的特征。以径向冲击射流系统为例，我们展示了该方法在存在颗粒与吸附表面之间排斥性静电相互作用时计算胶体浓度分布和初始颗粒通量的应用。我们表明，我们的方法在能垒高达数百kT量级的系统中效果良好，此时吸附通量消失。用我们的方法获得的数值结果与已知的关于颗粒通过能垒的极限解析近似以及低佩克莱数的结果吻合良好。所开发的数值代码在广泛的物理参数范围内非常稳定，对于最具挑战性的参数集，其精度约为10^(-4)。为了实现这种稳定性，我们推导并采用了一个用于范德华色散相互作用的单一公式，该公式在小和大分离距离下均适用。我们表明，该公式在小和大分离距离极限下收敛于已知的色散力解析表达式。我们还证明，我们的公式与其他方程之间的最大偏差出现在分离距离的中间范围内，且不超过10%。
