The stability of an interface between two halfspaces of contrasting second-order fluids was examined through a perturbation scheme for small nonlinear stress terms and disturbances of small slope. The leading order problem is that for two linear fluids, a well-known result is retrieved. It is found that the rate of growth or damping periodic disturbances is independent of wavelength. This result can be anticipated simply by noting that the only parameters appearing in this problem with no imposed geometric length scale are the driving force and the linear viscosity from which no length scale can be constructed. The correction due to the nonlinear stress terms, however, leads to quite a different result. It is shown that a critical wavelength of order lambda exists, for which the instability is a maximum. The critical wavelength is such that the linear viscous problem must be carried out to second order in the interface slope.
Abstracts of the 20th Annual Meeting, Society of Engineering Science, Inc.
- Pub Date:
- Fluid Mechanics;
- Interfacial Tension;
- Viscous Fluids;
- Fluid Mechanics and Heat Transfer