Modeling Cryogenic Spray Temperature and Evaporation Rate Based on Single-Droplet Analysis

Cryogenic sprays are of interest in dermatology for cooling human skin during pulsed laser treatment of port wine stain (PWS) birthmarks. In the present study, a Phase Doppler Interferometer (PDI) was used to obtain preliminary measurements of mean diameters and mean velocities of tetrafluoroethane (HFC-134a) spray droplets, generated by an atomizing nozzle of a commercial dermatological instrument. Our measurements show significantly smaller diameters than those theoretically predicted for water sprays (by at least one order of magnitude), indicating a high evaporation rate due to the low boiling temperature of the cryogen at atmospheric pressure (Tb=-26 C). Using these preliminary measurements, along with a single-droplet evaporation model, we estimate the mean spray temperature, Tcryo, as a function of distance from the nozzle (z). In the model, we assume that a droplet decreases in diameter in accordance with the D-law. We further consider deceleration of the droplet due to the drag force. To compute Tcryo(z), we incorporate the instantaneous droplet velocity and diameter into a phase-change heat transfer balance, which includes heat convection with the surrounding air. The Tcryo(z) predicted by our single-droplet model are in reasonable agreement with the mean temperatures obtained experimentally using a straight-tube nozzle, similar to the commercial atomizing nozzle, in the measured range of z = 1.8-12.5 cm. Further studies are underway and will be presented in future papers. * Corresponding author. e-mail: [email protected]