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We report numerical simulations of wicking through micropores of two types of geometries, axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation. The aim is to gain a detailed understanding of the interfacial dynamics in these geometries, with an emphasis on the motion of the three-phase contact line. We adopt a diffuse-interface formalism and use Cahn-Hilliard diffusion to model the moving contact line. The Stokes and Cahn-Hilliard equations are solved by finite elements with adaptive meshing. The results show that the liquid meniscus undergoes complex deformation during its passage through contraction and expansion. Pinning of the interface at protruding corners limits the angle of expansion into which wicking is allowed. For sufficiently strong contractions, the interface negotiates the concave corners, thanks to its diffusive …