An Investigation of the Boundary-Layer Equations of a Dilute and Monodispersed Emulsion of Very Viscous Drops
Rodrigo Bento Rebouças1; Ivan Rosa de Siqueira1; Taygoara Felamingo de Oliveira2
1 Pontifícia Universidade Católica do Rio de Janeiro; 2 Universidade de Brasília
doi:10.20906/CPS/COB-2015-0030
Resumo
This work deals with the rheology of the boundary-layer of a dilute and monodispersed emulsion of very viscous drops. Assuming a regime of small deformations for the drops, which occurs in high-drop viscosity ratios, a constitutive model to describe the macroscopic behavior of the emulsion is presented. This model is based on two equations: the first, describes how the geometry of the drop varies along the flow; the second, calculates the additional stress that arises from the development of the droplet shape on the microscopic scale. Using this model and invoking the boundary-layer hypothesis, we present a system of two partial differential equations that describes the boundary-layer behavior of an emulsion. The numerical solution is performed by a Galerkin Finite Element Method with an additional stabilization technique. The results for the emulsion boundary-layer show the existence of a similar velocity profile and nonlinear effects when compared to a Newtonian fluid. Based on the numerical results for some terms of the boundary-layer model, we also propose some simplifications on the original equation, obtaining a formulation similar to that of Newtonian fluids.
Palavras-chave: Emulsions; Boundary-Layer; Finite Element Method