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Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduli

  • L. FUSI (a1) and F. ROSSO (a1)
Abstract

We model the axisymmetric unidirectional flow of a Herschel–Bulkley fluid with rheological parameters that depend linearly on pressure. Adopting an appropriate scaling, we formulate the mathematical problem in cylindrical geometry exploiting an integral formulation for the momentum equation in the unyielded part. We prove that, under suitable assumptions on the data of the problem, explicit solutions can be determined. In particular, we determine the position of the yield surface together with the pressure and velocity profiles. With the aid of some plots, we finally discuss the dependence of the solution on the physical parameters of the problem.

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[1] E. N. Andrade (1930) The viscosity of liquids. Nature 125, 309310.

[6] L. Fusi , A. Farina & F. Rosso (2014) On the mathematical paradoxes for the flow of a viscoplastic film down an inclined surface. Int. J. Non-Linear Mech. 58, 139150.

[7] L. Fusi , A. Farina , Rosso F. & S. Roscani (2015) Pressure driven lubrication flow of a Bingham fluid in a channel: A novel approach. J. Non-Newtonian Fluid Mech. 221, 6675.

[9] L. Fusi , A. Farina & F. Rosso (2015) Planar squeeze flow of a bingham fluid. J. Non-Newtonian Fluid Mech. 225, 19.

[10] L. Fusi (2017) Non-isothermal flow of a Bingham fluid with pressure and temperature dependent viscosity. Meccanica, DOI: 10.1007/s11012-017-0655-8.

[14] M. Paluch , Z. Dendzik & S. J. Rzoska (1999) Scaling of high-pressure viscosity data in low-molecular-weight glass-forming liquids. Phys. Rev. B 60 (5), 2979.

[19] K. R. Rajagopal (2015) Remarks on the notion of “pressure”. Int. J. Non-Linear Mech. 71, 165172.

[22] M. Vasudevaiah & K. R. Rajagopal (2005) On fully developed flows of fluids with a pressure dependent viscosity in a pipe. Appl. Math. 50 (4), 341353.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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