Paper Number
EF5 

Session
Emulsions, Foams & Interfacial Rheology

Title
Modeling microstructural inertia effects in dilute emulsions

Presentation Date and Time
February 13, 2017 (Monday) 11:40

Track / Room
Track 4 / Sandhill Crane

Authors (Click on name to view author profile)

1. Mwasame, Paul M. (University of Delaware, Department of Chemical and Biomolecular Engineering)
2. Wagner, Norman J. (University of Delaware, Chemical & Biomolecular Engineering)
3. Beris, Antony N. (University of Delaware, Chemical and Biomolecular Engineering)

Author and Affiliation Lines (in printed abstract book)
Paul M. Mwasame, Norman J. Wagner, and Antony N. Beris
Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE 19716

Speaker / Presenter 
Beris, Antony N.

Text of Abstract
Existing conformation tensor models for the rheology of emulsions in the limit of zero particle Reynolds number predict a positive first normal stress differences (N₁) and negative second normal stress differences (N₂), in agreement with simulations. On the contrary, emulsions of ellipsoidal droplets at finite particle Reynolds numbers display an interesting rheology where N₁ is negative and N₂ is positive. This rheological behavior is also accompanied by a reversed orientation of emulsion droplets towards the velocity gradient direction [1]. At the moment, there are no macroscopic theories that describe such behaviors. This work extends upon our previous model, rigorously developed for small Capillary and zero particle Reynolds numbers [2]. Here we outline a new application of non-equilibrium thermodynamics to allow for the incorporation of microstructural inertia effects into a conformation tensor model for emulsions. The resultant contravariant tensor model for such emulsions is rigorously validated through a comparison to known asymptotic theory in the limit of small but finite Reynolds numbers [3]. Among the findings is the emergence of a new extended co-deformational time to characterize microstructural inertia effects through an additional term weighted by a parameter ζ. ζ is inversely related to the Ohnesorge number (Oh≡μ/(ρaT)^1/2) as ζ∝Oh^-2∝Re/Ca and reflects the competition between Capillary and Reynolds number effects. The resultant model, with all parameters obtained from independent asymptotic theory, compares well with independent rheological data on emulsions at finite Reynolds numbers [1].

[1] X. Li and K. Sarkar, J. Rheol. 49, 1377 (2005). [2] P. M. Mwasame, N. J. Wagner, A. N. Beris “A Thermodynamically Consistent Macroscopic Model for Dilute Emulsion Behavior” (abstract submitted for SOR 2016 annual meeting) [3] R. V. Raja, G. Subramanian, and D. L. Koch, J. Fluid Mech. 646, 255 (2010).