The entrance and viscous flow zones of capillary dynamics are critical in anti-slip surfaces. Here we propose the numerical modelling of capillary filling, based on the phase-field method, incorporating dynamic contact angle and wetted wall boundary conditions. The entrance and inertial effects of single-phase water rising naturally in a millimeter-sized vertical cylinder are demonstrated. The numerical approach is validated through experimental capillary assays of polyethylene oxide (PEO) bulk modified polydimethylsiloxane (PDMS). The study examines the effect of the cylinder radius, height and water-surface contact angles. The results show: 1) The meniscus creation by reorientation of the fluid surface due to entrance effect, not observed in real-world scenarios; 2) the viscous-inertial or crossover stage with h-t^2 and h-t^(1/3) relations; and 3) the impact of various wetting potentials of the liquid on the capillary rise dynamics. The results show that the radius influences the rising time (t) and h–t curve, whereas, the conduit height is directly proportional to the filling time, with negligible effect on the curve. Moreover, the liquid wetting potential does not affect the rising time or the characteristic curve. The retrieved flow parameters can be useful in developing slip-resistance surfaces for usage in harsh situations, like icy surfaces.