Research Papers: Fundamental Issues and Canonical Flows

A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear

[+] Author and Article Information
T. F. Oliveira

 University of Brasilia, Faculty UnB Gama, Department of Energy, Gama-DF, Brazil 70910 900taygoara@unb.br

F.R. Cunha1

 University of Brasilia, Department of Mechanical Engineering, Fluid Mechanics of Complex Flows Lab–VORTEX, Brasilia-DF, Brazil 70910 900frcunha@unb.br

A :I  = 0, in order to preserve the drop volume.


Corresponding author.

J. Fluids Eng 133(10), 101208 (Oct 05, 2011) (8 pages) doi:10.1115/1.4005102 History: Received February 12, 2010; Accepted September 09, 2011; Published October 05, 2011; Online October 05, 2011

This theoretical work shows how the knowledge of the emulsion microscale, including drop stretching and orientation leads to a continuum description of emulsion flows. A first order small deformation theory is explored for describing the rheology of an emulsion of high viscosity drops undergoing unsteady shear flows. The stationary shape and the interfacial velocity of a drop are used in order to obtain the contribution of the drop to the effective stress tensor of the emulsion. A complex rheology including the nonlinear frequency response of the emulsion under oscillatory shear at arbitrary frequency forcing and strain amplitude is identified.

Copyright © 2011 by American Society of Mechanical Engineers
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