Abstract This study deals with the problem of diffusion for polydisperse colloids. The resolution of this complex problem usually requires computationally expensive numerical models. By considering the number of colloidal particles and their mass as independent variables, the equations of state for a dilute polydisperse colloid are derived on a statistical mechanics basis. Irreversible thermodynamics is then applied to obtain a simple two-moment diffusion model. The validity of the model is illustrated by comparing its results with those obtained by a classical size spectrum approach, in a sedimentation equilibrium problem and in an unsteady one-dimensional diffusion problem in Stokes–Einstein regime, and under the hypothesis that the size spectrum distribution is stochastic. In the first problem, the two-moment diffusion problem allows to represent rigorously the vertical size segregation induced by gravity, while in the second one, it allows a convenient description of the diffusion of polydisperse colloids by using two coupled diffusion equations, with an accuracy comparable with that of the classical size spectrum approach. The contribution of our work lies primarily in the application of a non-equilibrium thermodynamics methodology to a challenging issue of colloid modeling, namely, polydispersity, by going from statistical mechanics to the derivation of phenomenological coefficients, with the two-moment approach as a guideline.

中文翻译：

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基于不可逆热力学考虑的多分散胶体两矩扩散模型

摘要 本研究涉及多分散胶体的扩散问题。这个复杂问题的解决通常需要计算量很大的数值模型。通过将胶体粒子的数量和它们的质量作为独立变量，在统计力学的基础上推导出稀多分散胶体的状态方程。然后应用不可逆热力学来获得简单的两矩扩散模型。该模型的有效性通过将其结果与经典尺寸谱方法在沉积平衡问题和斯托克斯 - 爱因斯坦体系中的非稳态一维扩散问题中获得的结果进行比较来说明，并假设尺寸谱分布是随机的。在第一个问题中，两矩扩散问题允许严格地表示重力引起的垂直尺寸偏析，而在第二个问题中，它允许使用两个耦合扩散方程方便地描述多分散胶体的扩散，其精度与经典的尺寸谱方法。我们工作的贡献主要在于将非平衡热力学方法应用于胶体建模的一个具有挑战性的问题，即多分散性，通过从统计力学到现象学系数的推导，以两矩方法为指导. 其精度可与经典尺寸谱方法相媲美。我们工作的贡献主要在于将非平衡热力学方法应用于胶体建模的一个具有挑战性的问题，即多分散性，通过从统计力学到现象学系数的推导，以两矩方法为指导. 其精度可与经典尺寸谱方法相媲美。我们工作的贡献主要在于将非平衡热力学方法应用于胶体建模的一个具有挑战性的问题，即多分散性，通过从统计力学到现象学系数的推导，以两矩方法为指导.