A Study on the Continuous Spill with Limited Period of Release

In this study, the spread of cryogenic liquid due to a limited period of release is investigated for the first time. This physical phenomenon is governed by three parameters: the evaporation rate per unit area, release time, and spill quantity. However, it is found that two dimensionless parameters, the dimensionless evaporation rate and the dimensionless spill rate, are determined by non- dimensionalizing the governing equation of this phenomenon. Third-order perturbation solutions are obtained and compared with a numerical solution to verify the perturbation solution. For the same spill quantity, continuous and subsequent instantaneous models are necessary for small release times, whereas continuous models are only required for large release times. Additionally, two consecutive spread models are necessary for a small spill quantity at a fixed release time. These two spread regimes are clearly distinguished using the perturbation solution.