Plane flow of thixotropic elasto-viscoplastic materials through a 1:4 sudden expansion Fernanda B. Link a , Sérgio Frey a,1 , Roney L. Thompson b , Mônica F. Naccache c , Paulo R. de Souza Mendes c,⇑ a Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Rua Sarmento Leite 425, Porto Alegre, RS 90050-170, Brazil b LMTA-PGMEC, Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, RJ 24210-240, Brazil c Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ 22453-900, Brazil article info Article history: Received 28 May 2014 Received in revised form 3 February 2015 Accepted 18 February 2015 Available online xxxx Keywords: Thixotropy Elasto-viscoplasticity Oldroyd-B model Sudden expansion Galerkin least-squares method abstract A numerical investigation of an elasto-viscoplastic thixotropic fluid flowing through a 1:4 plane expan- sion is performed, using a recently proposed constitutive equation. The conservation equations are solved using a four-field Galerkin least-squares formulation in terms of the extra stress, pressure, velocity, and structure parameter—a scalar quantity that represents the structuring level of the material microstruc- ture. The focus is on determining the effect of thixotropy, elasticity and viscoplasticity on the topology of yielded and unyielded regions of the expansion, on the field of structuring level, and on the field of elastic strain. Relevant ranges of the relaxation time, yield stress, and thixotropy characteristic time are investigated. The numerical results reveal significant effects of these parameters. The trends observed are physically sound and in accordance with the related literature. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction Thixotropic materials can be found both in nature and in indus- trial applications, and are present in a large number of our daily activities. Emulsions, gels, paints, drilling fluids, food products, and mineral slurries are some examples of possibly thixotropic materials. Typically these materials consist of dispersions possess- ing a microstructure that governs their macroscopic behavior in response to applied stresses. These structured materials exhibit a complex non-Newtonian behavior, usually including viscoelastic- ity, yield stress and thixotropy. Thixotropic materials present a time delay between a change in the applied stress and the response of the microstructure (breakdown or buildup). Many thixotropic constitutive models have been proposed over the last decades, but testing and validation information is rather scarce. Mujumdar et al. [1] developed a model to describe the rheologi- cal behavior of thixotropic fluids with yield stress and elasticity, based on the kinetic process responsible for structure changes in the fluid. A structure parameter k that indicates the level of struc- ture of the material was defined. The rheological response is a function of the material structure, and time effects are taken into account in the evolution equation for the structure parameter. In the constitutive equation proposed, the total stress is an arithmetic mean of an elastic and a viscous term, weighted by the structure parameter k. When the material structure breaks down, a viscous behavior occurs, and elasticity decreases. The results obtained were in fair agreement with frequency sweep experiments. The thixotropic behavior of fluids was thoroughly reviewed by Barnes [2] and Mewis and Wagner [3,4]. In these articles, typical experiments and fluid responses are presented and analyzed, and the relation between thixotropy and viscoelasticity, reversibility and modeling are also discussed. It is observed that elasticity can be present in thixotropic fluids, especially in the gel phase. Mewis and Wagner [4] observed that different approaches have been used for modeling thixotropy. In this paper we analyze the performance of the constitutive equation for elasto-viscoplastic thixotropic fluids proposed by de Souza Mendes [5] in the flow through a plane expansion. This geometry has been studied numerically and experimentally by several authors and using some of the well known models for purely viscous or viscoelastic fluids, e.g. Papanastasiou, Power- law and Oldroyd-B models (e.g. [6–12]). In these studies, the effect of different parameters (such as the Reynolds number, Yield http://dx.doi.org/10.1016/j.jnnfm.2015.02.009 0377-0257/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail addresses: feulink@mecanica.ufrgs.br (F.B. Link), frey@mecanica.ufrgs.br (S. Frey), rthompson@id.uff.br (R.L. Thompson), naccache@puc-rio.br (M.F. Nac cache), pmendes@puc-rio.br (P.R. de Souza Mendes). 1 Visiting Professor in Department of Chemical and Biomolecular Engineering, Rice 6100 Main St., Houston, TX 77005, United States. Journal of Non-Newtonian Fluid Mechanics xxx (2015) xxx–xxx Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm Please cite this article in press as: F.B. Link et al., Plane flow of thixotropic elasto-viscoplastic materials through a 1:4 sudden expansion, J. Non-Newtonian Fluid Mech. (2015), http://dx.doi.org/10.1016/j.jnnfm.2015.02.009