<jats:p>The initial spreading of glycerol and silicon oil droplets on smooth, corrugated, and orthogonal surfaces is numerically investigated by an effective, sharp-interface modeling method. In this study, the temporal evolution of spreading radius during the initial phase is scaled by R/R0 = C(t/τi)α for inertial regime and R/R0 = C(t/τμ)α for the viscous regime. We focus on exploring how wettability, liquid properties, and substrate topography influence the exponent α and coefficient C. Instead of discussing the effects of density, viscosity, and surface tension separately, we use the Ohnesorge number Oh = μ/(ρD0γ)1/2 to unify the combined influence of liquid properties. The results show that in the inertial regime (Oh ≪ 1), α is determined by wettability and the capillary wave is observed to propagate along the droplet interface, whereas in the viscous regime (Oh ≫ 1), α is determined by Oh and no capillary wave is observed. Consequently, both qualitative (propagation of capillary wave) and quantitative (Ohnesorge number) criteria to distinguish the two distinct regimes are provided. Regarding the coefficient C, it is found to increase with the increasing hydrophilicity and decreasing Oh in the inertial regime. A larger C is also observed in orthogonal microgrooves with wider gap or narrower width. Besides, the hydrophobicity and hydrophilicity can be enhanced by the corrugated surfaces, inducing a higher and lower α on hydrophilic and hydrophobic corrugated surfaces, respectively. Meanwhile, some interesting phenomena are also observed, such as the faster contact line velocity on the inside of a single corrugation and the “stick-jump” advancing mode of the contact line on orthogonal surfaces.</jats:p>