A new icing model has been developed to predict the sponginess (liquid fraction) and growth rate of freshwater ice accretions growing under a surface film of unfrozen water. This model is developed from first principles and does not require experimental sponginess data to tune the model parameters. The model identifies icing conditions that include no accretion, dry accretion, glaze accretion, spongy nonshedding, and spongy shedding regimes. It is a steady state model for a stationary vertical cylinder intercepting horizontally directed spray. The model predicts both the accretion mass growth flux and the accretion sponginess. The model results suggest that spongy shedding and spongy nonshedding regimes are common under the high liquid flux conditions typical of freshwater ship icing. Moreover, the unfrozen liquid incorporated into the spongy ice matrix can substantially increase the ice accretion load over that which would be predicted purely thermodynamically. Despite differences in the experimental setup, the model's performance compares well with two independent freshwater experimental data sets for icing on horizontal rotating cylinders. The model performs well in its prediction of both accretion sponginess and growth rate. The model predicts sponginess with a variation in liquid mass fraction of about 0.2--0.5, over the range of air temperature of 0¿C to -30¿C, in agreement with observations.