Coupled diffusion with classical elasticity models are utilized in various applications, e.g., the phase decomposition and coarsening of solder alloys [1] or microphase separation in hydrogels [2]. In the present contribution, we consider a coupled mechano-diffusion problem in the framework of Mindlin’s strain gradient elasticity and Cahn-Hilliard diffusion models [3]. This augments the modeling capabilities by incorporating elasticity-related length scales reflecting microstructural effects at the continuum level. The fourth-order boundary value problem of the coupled gradient elastic-diffusion model is formulated in a variational form within an H2 Sobolev space setting. Conforming Galerkin 2D discretizations for numerical results are obtained via an isogeometric approach and implemented as user subroutines in commercial FE software Abaqus [4]. We first consider a 1D problem and verify the implementation by comparing the results obtained via the finite-difference methods. Finally, we study an example of diffusional coarsening in solders and analyze the size effects in phase separation problems by extending the model in [1] towards the strain gradient elasticity framework. [1] Denis Anders, Christian Hesch and Kerstin Weinberg. Computational modeling of phase separation and coarsening in solder alloys. International Journal of Solids and Structures, 49(13):1557–1572, 2012 [2] Carla Fern ́andez-Rico et al. Elastic microphase separation produces robust bicontinuous materials. Nature Materials 23:124–130, 2024 [3] Tsagrakis, I. and Aifantis, E.C. Erratum to: Thermodynamic coupling between gra- dient elasticity and a Cahn–Hilliard type of diffusion: size-dependent spinodal gaps. Continuum Mechanics and Thermodynamics, 29:1181–1194, 2017 [4] Sergei Khakalo and Jarkko Niiranen. Isogeometric analysis of higher-order gradient elasticity by user elements of a commercial finite element software. Computer-Aided Design, 82:154–1697 2017