The effective viscosity of a mixture of two Stokes fluids.
Homogenization of the Stokes system, and with the averaging of equations for two phase flow is discussed.. In the former direction, section one reports on a new, optimal lower bound for the energy dissipation rate of a mixture of two Stokes fluids. In the latter direction, section two explores the relevance of homogenization to the derivation of averaged equations. Linking the two is the (highly speculative) "maximum lubrication hypothesis," that the effective viscosity of a mixture should saturate the lower bound. Surface tension effects are ignored in the first two parts, but discussed in section three along with other directions for future work.
Kohn, R., & Lipton, R. (1986). The effective viscosity of a mixture of two Stokes fluids.. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/811