On models of spreading pools

Abstract

The spread of liquid pools floating on water is commonly modelled by the assumption of a constant (densimetric) Froude number at the front. This can be understood in terms of a balance between the pressure difference across the front of the spreading pool, and the resistance at the front from having to push displaced water out of the way. Some early models of pools spreading on land also assumed constant Froude number, but in this case there is absolutely no credible justification for such an assumption. This was highlighted by Webber and Jones (1987) who noted that resistance will come from friction with the ground under the whole base of the pool, resulting in a very different spreading law. Nevertheless, the assumption of constant Froude number spreading of pools on land continues in some circles to this day, and a recent paper by Raj (2011) even goes as far as to assert that Webber and Jones (1987) assumed the spreading law, which in actual fact they were at pains to debunk. This paper is intended to set the record straight, with a detailed discussion of the physical phenomena controlling the way pools spread on land.