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Rime icing on messenger wires of electrified railways poses a serious threat to train operational safety. To elucidate the growth behavior of rime accretion on messenger wires in cold regions, this study develops an icing growth model grounded in the Makkonen framework and the dry-growth regime, with particular emphasis on the dominant role of collision efficiency. A flow-particle coupled finite-element approach is employed to resolve the airflow around the messenger wire and to track the trajectories of supercooled water droplets, yielding spatial distributions of both overall and local collision efficiencies. In conjunction with the Macklin ice-density model, a predictive method for the evolution of accretion thickness is constructed. The simulations indicate that ice accumulates primarily on the windward side; as time progresses, the thickness increases and the accreted profile becomes distinctly asymmetric. These findings provide a theoretical basis for icing prediction and for the formulation of anti-icing and de-icing strategies for messenger wires, offering significant engineering value for enhancing train safety and the reliability of railway power supply.