The Society of Rheology 88th Annual Meeting

February 12-16, 2017 - Tampa, Florida


Emulsions, Foams & Interfacial Rheology

A thermodynamically consistent macroscopic model for dilute emulsion behavior

February 13, 2017 (Monday) 1:30

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

Mwasame, Paul M.

Conformation tensor models are important to describe the rheology of complex fluids including polymers, suspensions and emulsions at the macroscopic level of description [1,2,3]. However, only for viscoelastic systems is the foundation available, through microscopic kinetic theory, to make the use of these models widely acceptable. Existing conformation tensor models for emulsions have empirical parameters and are not always consistent with known limiting rheological behaviors. Here we describe how a contravariant tensor model for deformable ellipsoidal droplets, derived consistently within a non-equilibrium thermodynamics framework, is rigorously validated through a comparison against asymptotic theories in the limit of zero particle Reynolds numbers and for small Capillary numbers [4]. An additional benefit is that, through this asymptotic matching, all the parameters can be obtained from previous independent theoretical work. At the heart of this modeling success is the use of a more accurate expression for the surface area of the ellipsoid, needed to describe the surface energy of the emulsion. In addition, a simpler and more natural form for the relaxation that involves a lower order dependence on the conformation tensor than previous models [5,6] is adopted. The resultant a-priori predictions compare well against classic experiments [7].

[1] G. Batchelor, J. Fluid Mech. 41, 545-570 (1970). [2] M. Doi and T. Ohta, J. Chem. Phys. 95, 1242-1248 (1991). [3]A. N. Beris and B. J. Edwards, Thermodynamics of flowing systems (Oxford University Press, New York, 1994). [4] W. R. Schowalter, C. E. Chaffey and H. Brenner, J. Colloid Interf. Sci. 26, 152-160 (1968). [5]P. Maffetone and M. Minale, J. Non-Newton. Fluid. 78 227-241 (1998). [6] M. Grmela, A. Ammar, F. Chinesta and G. Maitrejean, J. Non-Newton. Fluid. 212, 1-12 (2014). [7] S. Torza, R. Cox and S. G. Mason, J. Colloid Interf. Sci. 38.2, 395-411 (1972).