BALANCE-EQUATIONS FOR FLUID LINES, SHEETS, FILAMENTS AND MEMBRANES

Fluid structures can be classified into two categories: fluid filaments and fluid membranes. If the cross section of a fluid filament vanishes, the fluid filament is called a fluid line, whereas if the thickness of a fluid membrane vanishes, the fluid membrane is called a fluid sheet. In this paper, the local instantaneous balance equations are derived for a line and a sheet of fluid moving in a three-dimensional geometrical space. For a filament, the balance equations are obtained by using quantities averaged over the cross section of the filament. For a membrane, the balance equations are obtained by using quantities averaged over the height of the membrane. It is shown that the local and averaged formulations are consistent. All these balance equations have been rigorously derived by applying original mathematical theorems given in the appendices to the paper. Such balance equations can be used to model single-phase flow in bends or coils, the dynamic centering of thin liquid shells in capillary oscillations and the instability of an annular jet.