Shear rheology of concentrated emulsions at finite inertia: a numerical study
Date
2013
Authors
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Journal ISSN
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Publisher
University of Delaware
Abstract
The dynamics and rheology of an emulsion of viscous drops in shear flow is
investigated computationally. The simulations are performed using a three-dimensional
front tracking method. An emulsion gives rise to an effective non-Newtonian rheology
with finite normal stress differences and shear-dependent viscosity.
Previous estimates about the bulk properties of emulsions were limited to Stokes
conditions under which a positive first normal stress difference and a negative second
normal stress difference are predicted. However, the introduction of finite inertia significantly
modifies the behaviour of emulsions. The normal stress differences change
sign and the emulsion shows a shear-thickening behaviour with inertia. Computed
rheological properties (effective shear viscosity and first and second normal stress differences)
in conditions close to Stokes limit match well with the existing theoretical
and simulated results. The first component of the rheology arising from the interfacial
stresses at the drop surface is investigated as functions of particle Reynolds number,
capillary number and volume fraction. The sign change is caused by the increase in
drop inclination in presence of inertia, which in turn directly affects interfacial stresses
due to drops. Increasing volume fraction or capillary numbers increases the critical
Reynolds numbers for sign reversals due to increasing alignment of the drops with the
flow directions. The Reynolds stresses which form the second component of the stress
formulation are also considered in detail. The primary components of the Reynolds
stress showed a simple scaling with Reynolds number for moderate values of inertia.
They showed a non-linear increase at larger values of Reynolds number. A comparison
of the estimated effective viscosity with an established empirical relation is also
presented. Presence of finite surface tension results in a characteristic stress relaxation
time scale for emulsions. This is investigated for both dilute and concentrated systems
and the results are verified against the standard theoretical expressions. Finally, to
enhance the capabilities of the current computational method to handle extremely low
Reynolds number flows, a parallel version of the Alternate Direction Implicit method
is implemented.