  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
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 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 actual configuration allow for similar models and
analysis.
