Second-Order Perturbation Solutions to a Liquid Pool Spreading Model with Instantaneous Spill

Abstract

Second-order perturbation solutions have been obtained for the simple physical model describing the liquid pool spreading with an instantaneous spill, and are shown to improve over the first-order perturbation solutions. The second-order solutions to the non-dimensional governing equations for the model are derived to obtain more general solutions. Non-dimensional parameters are sought as the governing parameters for the non-dimensional equations, and the non-dimensional evaporation rate per unit area is used as the perturbation parameter. It is revealed that the number of governing parameters is reduced to two from three by non-dimensionalization. The second-order solutions exhibit a definite improvement over the first-order solutions with respect to the pool volume and the pool radius. The second-order solutions for the pool volume agree remarkably with the numerical solutions; however, there is still a little difference between the second-order solutions and the numerical ones for the pool radius at the final stage of spread.