非理想体系多离子非稳态扩散模型及数值模拟

在众多工程领域中均存在扩散现象。大多数扩散模型均是采用经典的Fick定律,仅考虑理想溶液中离子浓度梯度对扩散的驱动,未考虑多离子溶液环境对扩散的影响。溶液中离子间的静电作用导致溶液偏离理想状态,使得各离子浓度不能完全有效发挥,实际的扩散现象得不到合理的解释。基于广义线性扩散通量方程,引入Guntelberg修正的活度系数表征理想溶液与实际溶液中离子浓度的偏差,结合质量平衡方程,建立了适用于非理想体系的多离子非稳态扩散模型。采用已有试验数据与模型结果进行了对比分析,验证了所建模型的正确性和有效性。选用有限元软件Comsol Multiphysics对所建模型进行数值求解,结果表明:溶液非理想性特征对离子扩散具有显著的阻滞作用。当离子价位一定时,初始浓度越高对离子扩散阻滞效果越明显;在源浓度一定的情况下,离子价位越高对扩散阻滞效果越强。

Multi-ion non-steady state diffusion model and numerical simulation in non-ideal system

Diffusion is a common phenomenon in many engineering fields. Most diffusion models use the classic Fick''s law, which only consider the driving force due to ion concentration gradient in ideal solution. However, the influence of multi-ions environment on ion diffusion fails to embody in Fick''s law. The electrostatic interaction between ions in the solution causes the solution to deviate from the ideal state which leads to the concentration of ions failing to fully exert, so the actual diffusion phenomenon cannot be properly explained. By applying the linear diffusion flux equation, introducing the modified Guntelberg activity coefficient to show the deviation of ion concentration between the ideal and actual solution, And combing with the mass balance equation together, a non-steady state diffusion model for multi-ions in non-ideal system was proposed. The effectiveness of the proposed model is verified and validated by comparing with the experiment results. The finite element software Comsol Multiphysics was used to conduct a series of numerical simulations. The results showed that the non-ideal of the solution has significant retardation effect on ion diffusion. When the ion valence state is fixed, the higher the initial concentration of ions, the more obvious the retardation effect on diffusion. When the concentration of contaminated source keeps constant, the greater retardation the retardation effect on diffusion.