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.
A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear
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Oliveira, T. F., and Cunha, F. (October 5, 2011). "A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear." ASME. J. Fluids Eng. October 2011; 133(10): 101208. https://doi.org/10.1115/1.4005102
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