An enhanced wickability, i.e., permeability and capillary pumping capability, is crucial to two-phase thermal management and bio-medical systems, however, it is challenging to enhance them simultaneously. In this study, the enhanced wickability is examined using single-/three-columnar Bi-Particle-Size Wicks (BPSW). The enhanced pore-scale capillary flow with various particle/pore distributions is simulated using a two-phase single component free-energy-based Lattice Boltzmann Method (LBM). The results show that the cumulative liquid saturation of the single- and three-columnar BPSWs (measure of permeability) increases up to 53 and 18%, respectively, while their capillary pressure increases by 76 and 39%, respectively, compared to the Uniform-Particle-Size Wicks (UPSW). The enhancement is related to the fact that the localized larger pores allow for the primary liquid pathways, while the smaller pores increases the capillary pressure simultaneously. The increased pore size ratio leads to 13 and 26% improvement in the cumulative liquid saturation, while it shows the additional 38 and 30% increase in the capillary pressures in the single- and multi-columnar BPSWs. The simulation results provide insights into the optimal thin wick structures for high heat flux two-phase thermal management system by enhancing the wickability through the non-uniform pore sizes.