We propose a model for isothermal mass transport into immiscible complex fluids. The interface is described by two, space and time dependent, structural variables: a scalar Q(r,t) denoting the interfacial area density and a traceless symmetric second order tensor q(r,t) accounting for the shape anisotropy. The mass flux expression includes new contributions attributed to the dynamical changes of the interface. The diffusion-morphology coupling is found to influence both the mass transfer and the dynamics of the interface. The former exhibits non-Fickian behavior while the latter undergoes interfacial deformations that affect both its size and shape, creating internal stresses at the same time.

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