The Society of Rheology 88th Annual Meeting

February 12-16, 2017 - Tampa, Florida


Emulsions, Foams & Interfacial Rheology

Modeling microstructural inertia effects in dilute emulsions

February 13, 2017 (Monday) 11:40

Track 4 / Sandhill Crane

(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)

(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

Beris, Antony N.

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).