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A diffuse-interface method for simulating two-phase flows of complex fluids

Published online by Cambridge University Press:  09 September 2004

PENGTAO YUE
Affiliation:
Department of Chemical and Biological Engineering and Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
JAMES J. FENG
Affiliation:
Department of Chemical and Biological Engineering and Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
CHUN LIU
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
JIE SHEN
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Abstract

Two-phase systems of microstructured complex fluids are an important class of engineering materials. Their flow behaviour is interesting because of the coupling among three disparate length scales: molecular or supra-molecular conformation inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. In this paper, we propose a diffuse-interface approach to simulating the flow of such materials. The diffuse-interface model circumvents certain numerical difficulties in tracking the interface in the classical sharp-interface description. More importantly, our energy-based variational formalism makes it possible to incorporate complex rheology easily, as long as it is due to the evolution of a microstructure describable by a free energy. Thus, complex rheology and interfacial dynamics are treated in a unified framework. An additional advantage of our model is that the energy law of the system guarantees the existence of a solution. We will outline the general approach for any two-phase complex fluids, and then present, as an example, a detailed formulation for an emulsion of nematic drops in a Newtonian matrix. Using spectral discretizations, we compute shear-induced deformation, head-on collision and coalescence of drops where the matrix and drop phases are Newtonian or viscoelastic Oldroyd-B fluids. Numerical results are compared with previous studies as a validation of the theoretical model and numerical code. Finally, we simulate the retraction of an extended nematic drop in a Newtonian matrix as a method for measuring interfacial tension.

Type
Papers
Copyright
© 2004 Cambridge University Press

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