Creeping flows, definition

Kj / y, where K is the surface dilationcil modulus, defined in 13.6.19). An alter-native Marangoni number was introduced by Edwards et al., who considered creep flow around an emulsion droplet. Their definition is Ma s K° /kar/, where a is the radius of the droplet, rj the bulk viscosity and fc (in s ) a rate constant, characteristic of the rate of supply of surfactants to the interface by transport from the bulk. The second definition rather applies to Gibbs monolayers it is a measure of the extent to which surface tension gradients can develop against the counteracting replenishment of the surface. 

A sketch of the physical problem and a definition of the cylindrical polar coordinates (r, creeping-flow limit, the governing equations and boundary conditions are... 

For the pendant drop in figure I, the equations above are subjected to the no-slip boundary conditions at solid surfaces and the kinematic condition on the free surfaces. The kinematic condition implies that there is no liquid crossing the boundary into the gas phase, or in other words forms a definite boundary between the phases. For creeping flows into an atmosphere of gas with minimal velocities there will be no interfacial shear stress tangential to the surface and the normal stress inside the fluid is balanced by the surface tension as described by the famous Young-Laplace equation. 

---