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Edge fracture instability in sheared complex fluids: Onset criterion and possible mitigation strategy

Hemingway, Ewan J.; Fielding, Suzanne M.

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Authors

Ewan J. Hemingway



Abstract

We perform a detailed theoretical study of the edge fracture instability, which commonly destabilizes the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson–Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on the shear rate of the shear and normal stresses. The threshold for the onset of edge fracture is shown to be relatively robust against variations in the wetting angle where the fluid-air interface meets the hard walls of the flow cell, whereas the nonlinear dynamics depend strongly on the wetting angle. We perform a linear stability calculation to derive an exact analytical expression for the onset of edge fracture, expressed in terms of the shear-rate derivative of the second normal stress difference, the shear-rate derivative of the shear stress (sometimes called the tangent viscosity), the jump in the shear stress across the interface between the fluid and the outside air, the surface tension of that interface, and the rheometer gap size. (The shear stress to which we refer is σ xy σxy with x ̂ x^ being the flow direction and y ̂ y^ being the flow-gradient direction. The interface normal is in the vorticity direction z ̂ z^ .) Full agreement between our analytical calculation and nonlinear simulations is demonstrated. We also elucidate in detail the mechanism of edge fracture and finally suggest a new way in which it might be mitigated in experimental practice. We also suggest that, by containing the second normal stress difference, our criterion for the onset of edge fracture may be used as a means to determine that quantity experimentally. Some of the results in this paper were first announced in an earlier letter [E. J. Hemingway, H. Kusumaatmaja, and S. M. Fielding, Phys. Rev. Lett. 119, 028006 (2017)]. The present paper provides additional simulation results, calculational details of the linear stability analysis, and more detailed discussion of the significance and limitations of our findings.

Citation

Hemingway, E. J., & Fielding, S. M. (2019). Edge fracture instability in sheared complex fluids: Onset criterion and possible mitigation strategy. Journal of Rheology, 63(5), https://doi.org/10.1122/1.5095717

Journal Article Type Article
Acceptance Date Jun 30, 2019
Online Publication Date Jul 22, 2019
Publication Date Jul 22, 2019
Deposit Date Aug 1, 2019
Publicly Available Date Mar 28, 2024
Journal Journal of Rheology
Print ISSN 0148-6055
Electronic ISSN 1520-8516
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 63
Issue 5
DOI https://doi.org/10.1122/1.5095717

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