A comprehensive understanding of the combined effects of surface roughness and wettability on the dynamics of the trapping process is lacking. This can be primarily attributed to the contradictory experimental and numerical results regarding the impact of wettability on the capillary trapping efficiency. The discrepancy is presumably caused by the surface roughness of the inner pore‐solid interface. Herein, we present a comparative μ‐CT study of the static fluid‐fluid pattern in porous media with smooth (glass beads) and rough surfaces (natural sands). For the first time, a global optimization method was applied to map the characteristic geometrical and morphological properties of natural sands to 2‐D micromodels that exhibit different degrees of surface roughness. A realistic wetting model that describes the apparent contact angle of the rough surface as a function surface morphology and the intrinsic contact angle was also proposed. The dynamics of the trapping processes were studied via visualization micromodel experiments. Our results revealed that sand and glass beads displayed opposite trends in terms of the contact angle dependence between 5° and 115°. Sand depicted a nonmonotonous functional contact angle dependency, that is, a transition from maximal trapping to no trapping, followed by an increase to medium trapping. In contrast, glass beads showed a sharp transition from no trapping to maximal trapping. Since both porous media exhibit similar morphological properties (similar Minkowski functions: porosity, surface density, mean curvature density, Euler number density), we deduce that this difference in behavior is caused by the difference in surface roughness that allows complete wetting and hence precursor thick‐film flow for natural sands. Experimental results on micromodels verified this hypothesis. Key Points Wettability, surface roughness, and pore space structure have an impact on trapping efficiency Porous media with rough surface, as natural sands and glass‐ceramic micromodels, were studied Wettability‐controlled crossover from snap‐off to by‐pass trapping and spontaneous precursor thick‐film flow were observed