Multi-wavelength Constraints on Dust Dynamics and Size Evolution in Protoplanetary Disk Rings. I. Method
Observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Jansky Very Large Array (JVLA) have revealed many dust rings in protoplanetary disks, often interpreted as dust traps at gas pressure bumps. Previous studies have typically modeled these rings by assuming a single dust species in drift-diffusion equilibrium, neglecting dust size evolution resulting from coagulation and fragmentation. In this work, we perform numerical simulations that incorporate both dust-gas dynamics (drift and diffusion) and dust size evolution. Our results show that the radial distributions of different dust species (up to the fragmentation limit) are nearly identical in the dust ring, as dust growth dominates over drift and diffusion (e.g., with a typical dust-to-gas ratio of $ε\sim 10^{-2}$). Building on this finding, we develop a comprehensive, self-consistent analytical theory that describes the dust ring structure while explicitly accounting for size evolution effects. Our model provides a unified framework for interpreting multi-wavelength observations by linking the physical dust distribution to the observed ring properties, thus laying the foundation for future observational modeling.