Efficient particle sorting in microfluidic systems is vital for advancements in biomedical diagnostics and industrial applications. This study numerically investigates particle migration and passive sorting in symmetric serpentine microchannels, leveraging inertial and centrifugal forces for label-free, high-throughput separation. Using a two-dimensional numerical model, particle dynamics were analyzed across varying flow rates, diameter ratios (1.2, 1.5, and 2), and channel configurations. The optimized serpentine geometry achieved particle separation efficiencies exceeding 95% and throughput greater than 99%. A novel scaling framework was developed to predict the minimum number of channel loops required for efficient sorting. Additionally, the robustness of the proposed scaling framework is demonstrated by its consistency with findings from previous studies, which exhibit the same trend as predicted by the scaling laws, underscoring the universality and reliability of the model. Additionally, the study revealed the significant influence of density ratio (alpha) on sorting efficiency, where higher alpha values enhanced separation through amplified hydrodynamic forces. Optimal flow rates tailored to particle sizes were identified, enabling the formation of focused particle streaks for precise sorting. However, efficiency declined beyond these thresholds due to particle entrapment in micro-vortices or boundary layers. This work provides valuable insights and design principles for developing compact, cost-effective microfluidic systems, with broad applications in biomedical fields like cell sorting and pathogen detection, as well as industrial processes requiring precise particle handling.