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Saffman-Taylor instability in yield stress fluids

Maleki Jirsaraei, N ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1088/0953-8984/17/14/010
  3. Publisher: Institute of Physics Publishing , 2005
  4. Abstract:
  5. Pushing a fluid with a less viscous one gives rise to the well known Saffman-Taylor instability. This instability is important in a wide variety of applications involving strongly non-Newtonian fluids that often exhibit a yield stress. Here we investigate the Saffmann-Taylor instability in this type of fluid, in longitudinal flows in Hele-Shaw cells. In particular, we study Darcy's law for yield stress fluids. The dispersion equation for the flow is similar to the equations obtained for ordinary viscous fluids but the viscous terms in the dimensionless numbers conditioning the instability now contain the yield stress. This also has repercussions on the wavelength of the instability as it follows from a linear stability analysis. As a consequence of the presence of yield stress, the wavelength of maximum growth is finite even at vanishing velocities. We study Darcy's law and the fingering patterns experimentally for a yield stress fluid in a linear Hele-Shaw cell. The results are in rather good agreement with the theoretical predictions. In addition we observe different regimes that lead to different morphologies of the fingering patterns, in both rectangular and circular Hele-Shaw cells. © 2005 IOP Publishing Ltd
  6. Keywords:
  7. Cells ; Dispersions ; Flow of fluids ; Gels ; Newtonian liquids ; Rheology ; Stability ; Stress analysis ; Viscosity of liquids ; Darcy's law ; Dispersion equations ; Non-Newtonian fluids ; Saffman-Taylor instability ; Fluid dynamics
  8. Source: Journal of Physics Condensed Matter ; Volume 17, Issue 14 , 2005 , Pages S1209-S1218 ; 09538984 (ISSN)
  9. URL: https://iopscience.iop.org/article/10.1088/0953-8984/17/14/011