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# Yield stress fluid flows

A Virtual Special Issue of the *Journal of Non-Newtonian Fluid Mechanics *devoted to **yield stress fluid flows** has just been released. With this first Virtual Special Issue of the journal we inaugurate a practice, which we plan to make regular, of highlighting developments on a particular subject of relevance in order to guide and encourage research in the field. Each virtual special issue will be built around a recent invited review paper by a leading expert and consist of links to recent, and some not-so-recent, JNNFM papers in the field of the review. These papers, which we select with advice from the author of the review, will showcase a wide range of high-quality contributions to illustrate the wealth and vigor of the topic.

We are delighted that **Philippe Coussot** was willing to write the first review article in this new series, on the topic of experimental studies of yield stress fluids. We have chosen 15 papers to complement this review, beginning with the experimental work of **Jossic et al.** (2013). This study of creeping flow around a perpendicular disc, is a good illustration of the interesting flow physics that remain to be investigated with complex fluids in classical flows. The next several papers address the technologically-important topic of two-phase flows of yield-stress fluids: the experiments of Sikorski et al. (2009) on bubbles rising on yield stress fluids, the interesting and original experiments on droplets of yield stress fluids by **German and Bertola** (2010) and finally a theoretical analysis of droplet formation, together with some experiments, by Balmforth et al. (2010). **Taghavi et al**. (2012) is next, experimentally characterizing fluid displacement of a buoyant miscible yield stress fluid by a denser Newtonian fluid, a very important problem in drilling.

While the opening review paper deals only with laminar flows, yield stress fluid flows are also important under transitional and turbulent flow conditions, as in the pipe flow experiments of **Peixinho et al.** (2005), another case of relevance to drilling. We close the showcase of experiments with the contribution of **Rensing et al**. (2011) on ice slurries in water-in-oil emulsions showing that yield stress fluids can be found with unusual combinations of components.

Numerical investigations of yield stress fluid flows are increasingly useful and popular. The numerical methods have to deal with the yield condition and there are two approaches to doing so: regularization facilitates the governing equations by introducing a high viscosity fluid at low shear rates, thus transforming the yield stress material into a fluid, but it is an approximation and the location of the yield surface becomes ill-defined. This is well shown by Mitsoulis (2007) in his work on extrudate swell, a very relevant problem for polymer processing. Lagrangian tracking methods explicitly compute the yield surface and do not approximate the material as a fluid, but are computationally more complex. This is illustrated by **Huilgol and You** (2005) in their application to pipe flow of various yield stress fluid models. The last paper in this section, by Dimakopoulos et al. (2013), compares both approaches in their numerical computations of steady bubble rise in a yield stress fluid.

To illustrate the diversity of applications where yield stress fluids are of relevance three works were selected. Two-phase flows with a solid phase are here represented by the computations of Liu et al. (2003) on the interactions between moving rigid spheres in a Bingham material. The restart of pipeline flows of waxy crude oils by **Vinay et al**. (2006) is relevant for flow assurance in the oil industry and the detailed investigation of **Turan et al**. (2010) on free convection of Bingham fluids in a 2D square enclosure with differentially heated walls presents useful heat transfer correlations.

Analytical approaches to a problem provide the most complete and elegant picture of its solution, if it exists. A good example is the analysis of the squeeze flow of a cylindrical sample of a yield stress paste between parallel plates by Sherwood (2002). Last, but not least, the modeling of yield stress fluids can be actually rather complex because the yield stress is often combined with such characteristics as thixotropy. The development of adequate rheological constitutive equations for such materials is well shown by **Souza Mendes** (2009).

We hope you enjoy reading or revisiting these contributions and that doing so will lead to new research ideas and insights. Several further invited reviews and their corresponding virtual special issues are in progress and we look forward to presenting these in the near future.

*Editors of the Journal of Non-Newtonian Fluid Mechanics*Fernando Pinho, University of Porto, Portugal

Mike Graham, University of Wisconsin-Madison, USA

*Executive Publisher, Elsevier*Keith Lambert

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