Potential “ways of thinking” about the shear-banding phenomenon
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McKinley_Potential ways.pdf
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Author(s)
Fardin, Marc-Antoine
Gay, C.
Lerouge, S.
Ober, Thomas Joseph
Gregoire, G.
McKinley, Gareth H.
Date Issued
November 2011
Journal
Soft Matter
Citation
Fardin, M. A., T. J. Ober, C. Gay, G. Grégoire, G. H. McKinley, and S. Lerouge. Potential "Ways of Thinking” About the Shear-banding Phenomenon. Soft Matter 8, no. 4 (2012): 910.
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Author's final manuscript
Abstract
Shear-banding is a curious but ubiquitous phenomenon occurring in soft matter. The phenomenological similarities between the shear-banding transition and phase transitions has pushed some researchers to adopt a ‘thermodynamical’ approach, in opposition to the more classical ‘mechanical’ approach to fluid flows. In this heuristic review, we describe why the apparent dichotomy between those approaches has slowly faded away over the years. To support our discussion, we give an overview of different interpretations of a single equation, the diffusive Johnson–Segalman (dJS) equation, in the context of shear-banding. We restrict ourselves to dJS, but we show that the equation can be written in various equivalent forms usually associated with opposite approaches. We first review briefly the origin of the dJS model and its initial rheological interpretation in the context of shear-banding. Then we describe the analogy between dJS and reaction–diffusion equations. In the case of anisotropic diffusion, we show how the dJS governing equations for steady shear flow are analogous to the equations of the dynamics of a particle in a quartic potential. Going beyond the existing literature, we then draw on the Lagrangian formalism to describe how the boundary conditions can have a key impact on the banding state. Finally, we reinterpret the dJS equation again and we show that a rigorous effective free energy can be constructed, in the spirit of early thermodynamic interpretations or in terms of more recent approaches exploiting the language of irreversible thermodynamics.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1039/c1sm06165h
