Paper Number
SC43 

Session
Suspensions & Colloids

Title
Conformation tensor-based macroscopic models of particulate and multiphase systems

Presentation Date and Time
October 18, 2018 (Thursday) 10:25

Track / Room
Track 1 / Galleria I

Authors (Click on name to view author profile)

  1. Mwasame, Paul M. (Corning Incorporated, Sullivan Park Science & Technology Center)
  2. Wagner, Norman J. (University of Delaware)
  3. Beris, Antony N. (University of Delaware, Chemical and Biomolecular Engineering)

Author and Affiliation Lines (in printed abstract book)
Paul M. Mwasame1, Norman J. Wagner2, and Antony N. Beris2
1Sullivan Park Science & Technology Center, Corning Incorporated, Erwin, NY 14870; 2Chemical and Biomolecular Engineering, University of Delaware, Newark, DE

Speaker / Presenter 
Beris, Antony N.

Text of Abstract
Recently [1], the Maffetone-Minale model for dilute emulsions has been recast and extended for arbitrary (dispersed/continuum) viscosity ratios using the non-equilibrium thermodynamics bracket framework [2]. More recently, we also developed a generalization of that model for conditions where particle inertia effects are important [3]. In both cases, all the model parameters have been obtained based on comparisons against previous asymptotic microscopic theory results. In the present work, we offer two additional extensions. In the first one, we describe how a two conformation tensors-based model can be developed through which we can describe the rheology of emulsions in the presence of Ostwald ripening. We are thus able to describe a population of droplets and their evolution in time along with the evolution of the rheology. In the second application, a model for the rheology of concentrated non-Brownian suspensions is presented. Following Phan-Thien [4], the microstructure is represented through a conformation tensor that represents now the second moment of the unit vector along the center to center line connecting two generic spheres. However, unlike that work, the thermodynamically-based model formulated here following an extension of the bracket approach of [2] is consistent with all viscometric functions in non-Brownian suspensions. In shear flows, the model predicts negative first and second normal stress differences that have been observed in both experimental and simulation studies. These are accompanied by microstructure orientation and localization along the compressional axis of the shear flow field.
Acknowledgment
NSF, Grant No. CBET 312146.
References
1. Mwasame, P.M., Wagner, N.J., Beris, A.N. 2017. J. Fluid Mech., 831:433-73.
2. Beris, A.N. and Edwards, B.J., 1994. Thermodynamics of Flowing Systems. Oxford U. Press.
3. Mwasame, P.M., Wagner N.J., Beris, A.N., 2018. Phys. Fluids, 30:030704.
4. Phan-Thien, N., 1995. J. Rheol., 39:679-95.