Asymptotics for Dilute Emulsions with Surface Tension

Grigor Nika, Bogdan Vernescu
2015 Journal of Elliptic and Parabolic Equations  
We consider an emulsion formed by two newtonian fluids, one being dispersed in the other under the form of droplets, in the presence of surface tension. We investigate the dilute case where the droplet size a is much smaller than the distance between the droplets' centers. We prove that the limit behavior when → 0 is described by the unperturbed Stokes flow and estimate the order of convergence rate of the velocity to be a n/2 . We improve the convergence result and determine the first
more » ... the first corrector in the velocity expansion. Taylor's and Einstein's viscosity formulas are recovered. 2010 Mathematics Subject Classification. Primary 35J25, 35J20; Secondary 76D07, 76T20.
doi:10.1007/bf03377377 fatcat:vcwqm7mp5jc25lbuphvmeijtem