KnudsenModel: A Physically Consistent Python Framework for Computing Evaporative Cooling of Liquid Jets

We present KnudsenModel, an open-source Python implementation of the Knudsen model for computing evaporative cooling of microscopic liquid jets in vacuum. The code builds on widely used scientific Python packages and provides a transparent and flexible framework that can be applied to both cylindrical jets and spherical droplets. A fixed-mass radial discretization is employed to consistently account for the coupled evolution of mass loss and density, ensuring physically accurate predictions of both temperature and jet or droplet diameter. We analyze the numerical behavior of the method, including convergence properties and comparisons with literature calculations based on alternative discretization schemes, revealing that, in particular for water droplets, the present formulation captures a shallow minimum in the diameter that reflects the interplay between evaporation-induced mass loss and water's density anomaly-a feature absent in previous results. PROGRAM SUMMARY Program Title: temp_liq_jet Python package CPC Library link to program files: (to be added by Technical Editor) Developer's repository link: https://github.com/rgrisenti/temp_liq_jet Licensing provisions(please choose one): MIT Programming language: Python Nature of problem: Evaporative cooling drives the temperature evolution of microscopic liquid jets in vacuum. Accurate predictions of their temperature are essential for interpreting experiments employing such microjets. This evolution results from the coupled dynamics of evaporative mass loss at the liquid-vapor interface and radial heat transport within the fluid. While the Knudsen model provides a well-established theoretical framework, practical numerical implementations are often developed independently, with limited documentation or validation. Seemingly minor numerical choices-particularly in the radial discretization-can lead to inconsistencies that affect physically relevant observables, including droplet or jet radius. A physically consistent, reproducible implementation is therefore required to obtain reliable predictions and ensure reproducibility across studies. Solution method: The KnudsenModel class, provided in the temp_liq_jet Python package, implements a physically consistent numerical solution of the coupled mass and energy balance equations describing evaporative cooling of liquid jets or droplets. The liquid cross section is discretized into concentric shells of fixed mass, avoiding the inconsistencies associated with remapping procedures in previous implementations and addressing the radial discretization issues noted above. Evaporative mass loss at the surface is calculated using the Hertz-Knudsen expression, while radial heat transport is described by thermal conduction between neighboring shells. The resulting system of coupled ordinary differential equations is integrated along the propagation coordinate using robust ODE solvers from scipy.integrate. The code outputs the evolution of temperature and droplet or jet diameter, correctly capturing subtle physical effects arising from the interplay between evaporation and thermophysical properties, providing a transparent and reproducible reference implementation.