On the spreading of one fluid over another

Abstract

Although particularly concerned with the spreading of oil over water, this paper deals with the gênerai problem of determining the nature and rate of spreading of any onè incompressible fluid over another of greater density. It is in three paris. PART I The two fluid layers are treated as the cornponents of a coupled System and a gênerai équation is derived for their chai'acteristics. The number of degrees of freedom of such a fluid System is redeflned and related to the capacities for wave propagation of the System. The number of characteristics in a coupled system is then related to the number of fluid components in the system, and the two types of uncoupled component are identified. It is shown that the effect of coupling is to separate the characteristics of the components and that, when the lower fluid is -m,uch deeper than the surface fluid, the surface fluid behaves as an uncoupled system. The Riemann invariants and "quasi-invariants" of this uncoupled system are investigated and a means of solving problems of reciitinear spreading obtained. PART II The analogous problem of a bursting dam is considered and a "wave front" introduced to better explain the behaviour observed experimentally. The front of the surface fluid is then studied in a simitar manner and the relations obtaining at the front are again verified by experiment. PART III The équations and characteristics obtaining in radial flow are derived. The characteristics are identical with those arising in rectilinear flow, but their invariant properties differ. These properties are investigated and a procédure devetoped whereby problems involving the radial flow of one fluid over another may be solved. In conclusion the présent work is compared with previous studies on the same subject.