The diffusion driven by the gradient of the chemical potential (by the Fick/Darcy law) in deforming continua at large strains is formulated in the reference configuration with both the Fick/Darcy law and the capillarity (i.e. concentration gradient) term considered at the actual configurations deforming in time. Static situations are analysed by the direct method. Evolution (dynamical) problems are treated by the Faedo-Galerkin method, the actual capillarity giving rise to various new terms as e.g. the Korteweg-like stress and analytical difficulties related to them. Some other models (namely plasticity at small elastic strains or damage) with gradients at an actual configuration allow for similar models and analysis.

中文翻译：

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在实际变形配置中具有毛细作用的Cahn-Hilliard方程

在大应变下连续变形中化学势梯度（由菲克/达西定律）驱动的扩散是在参考构型中制定的，其中菲克/达西定律和毛细作用（即浓度梯度）均考虑了实际配置随时间变形。静态情况通过直接方法进行分析。进化（动力学）问题用Faedo-Galerkin方法处理，实际的毛细作用引起了各种新术语，例如类似Korteweg的应力和与之相关的分析困难。在实际配置中具有渐变的其他一些模型（即在较小的弹性应变或损坏时具有可塑性）可以进行类似的模型和分析。