Nozzle Ar blowing technology profoundly influences the production and quality of continuous casting slabs. Its primary objectives include minimizing nozzle nodules, eliminating inclusions, and enhancing slab quality. Extensive physical experiments and numerical simulations have been performed to reveal the metallurgical phenomena and principles in continuous casting molds. However, the high costs associated with physical experiments and constraints related to model size and measurement methods hinder the accurate depiction of the actual motion state of high-temperature liquid steel and bubbles. As a result, more researchers are using numerical simulation methods to investigate Ar blowing at the nozzle. The focus of these studies typically involves tracking bubbles' position, velocity, and diameter using the Euler-Lagrange method. Numerous scholars have explored the influence of process parameters such as casting speed and Ar blowing rate on the distribution of Ar bubbles in the mold via numerical simulations. These studies also examine how these parameters affect the capture of Ar bubbles in the solidified shell. However, few scholars have explored the interactions among bubbles, such as collision, coalescence, and fragmentation. Understanding these interactions is crucial for determining bubble distribution, particularly near the mold wall, which significantly impacts the quality of the solidified shell. A collision-polymerization-fragmentation-trapping model has been developed to address this gap and describe bubble behavior. This model aims to effectively manage the movement and distribution of Ar bubbles in the slab mold, enhance the efficiency of inclusion removal by bubbles, and minimize bubble entrapment in the solidified shell. The simulation study examined how casting speed, Ar blowing rate, nozzle angle, and nozzle immersion depth affect the movement of Ar bubbles in a 800 mm × 1300 mm × 230 mm continuous casting mold. The findings underscore the critical role of bubble collision, aggregation, and fragmentation in shaping their size distribution in the mold. Moreover, process parameters substantially influence the spatial distribution of bubbles: larger bubbles tend to accumulate and float up near the nozzle, medium-sized bubbles are located and float up farther from the nozzle, and smaller bubbles predominantly gather and float up near the mold's narrow surfaces. However, some small bubbles have the potential to migrate toward the deeper sections of the mold and become entrapped by the solidified shell, potentially causing defects in the slab quality. The distribution of bubbles is predominantly influenced by the nozzle immersion depth, which affects where bubbles are located in the mold. Meanwhile, the Ar blowing rate and the nozzle angle significantly affect the diameter and number of bubbles in the mold. Additionally, casting speed is crucial in influencing bubble distribution, number, and diameter in the mold. Optimal conditions, such as a casting speed of 1.4 m/min, an Ar blowing rate of 10 L/min, a nozzle angle of -15°, and a nozzle immersion depth of 180 mm, result in a well-dispersed bubble distribution in the mold. This favorable dispersion enhances the effectiveness of inclusion removal, improves the purity of liquid steel, minimizes bubble entrapment by solidified shells, and consequently enhances the overall quality of the slab.