Exchange-Controlled Evaporative Transport: A Two-Border Boundary-Law Framework for Vapor Transport

Evaporation becomes a transport problem only when two-border surface physics is converted into boundary data for a vapor concentration field. This paper builds that conversion. Border 1 supplies the interfacial kinetic source; Border 2 supplies air-side clearing; together they determine the effective exchange flux placed on the transport boundary. The transported field is the vapor concentration or declared concentration-equivalent variable q(x, t), governed here by an advection-diffusion closure with an exchange law inherited from the evaporation mechanism. The main result is a conditional exchange-to-observation stability estimate: for a declared parabolic transport class, boundary-flux discrepancies and residual channels control the error seen by an observation map. Péclet, boundary Biot, ventilation, and supply numbers then classify the regime, while the validation record connects computations and measurements to supported inference. The result is a boundary-law framework that turns local evaporation physics into reviewable transport models.