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A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index
Academy of Romanian Scientists, 3 Ilfov, Bucharest 050044, Romania
*whom correspondence should be addressed. E-mail: c_fetecau@yahoo.com
Received: 18 January 2026, Revised: 22 February 2026, Accepted: 28 February 2026, Published Online: 7 March 2026
(This article belongs to the Section Fluids and Plasma Physics (FPP))
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APA Style
Fetecau, C. (2026). A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index. Journal of Engineering Research and Sciences, 5(3), 14–20. https://doi.org/10.55708/js0503002
Fetecau, C. (2026). A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index. Journal of Engineering Research and Sciences, 5(3), 14–20. https://doi.org/10.55708/js0503002
Chicago/Turabian Style
Constantin Fetecau. "A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index." Journal of Engineering Research and Sciences 5, no. 3 (March 2026): 14–20. https://doi.org/10.55708/js0503002
Constantin Fetecau. "A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index." Journal of Engineering Research and Sciences 5, no. 3 (March 2026): 14–20. https://doi.org/10.55708/js0503002
IEEE Style
C. Fetecau, "A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index," Journal of Engineering Research and Sciences, vol. 5, no. 3, pp. 14–20, Mar. 2026, doi: 10.55708/js0503002.
C. Fetecau, "A Note on Modified Stokes’ Problems for Fluids with Power-Law Dependence of Viscosity on Pressure with 3/2 index," Journal of Engineering Research and Sciences, vol. 5, no. 3, pp. 14–20, Mar. 2026, doi: 10.55708/js0503002.
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Abstract
The modified Stokes’ problems for incompressible Newtonian fluids with power-law dependence of viscosity on the pressure of 3/2 index are analytically investigated. The influence of the gravitational acceleration is taken into account. Exact expressions are derived for permanent dimensionless velocity and shear stress fields in terms of standard Bessel functions. They satisfy the governing equations and boundary conditions. Similar solutions corresponding to same problems for ordinary fluids are recovered as limiting cases of previous solutions. Some characteristics of the fluid behavior are graphically underlined. It is shown that the fluids with pressure-dependent viscosity flow faster than ordinary fluids and the shear stress of the first problem of Stokes is constant on entire flow domain although the corresponding velocity is function of the spatial variable. Obtained solutions, which are new in the literature, have been used to find the required time to touch the steady state. This time is important for experimental researchers who want to know the transition moment of the motion to steady state.
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- M.M. Denn, Polymer Melt Processing, Cambridge University Press, Cambridge, U.K., 2008.
- K.R. Rajagopal, G. Saccomandi, L. Vergori, “Flow of fluids with pressure and shear-dependent viscosity down an inclined plane,” Journal of Fluid Mechanics, vol. 706, pp. 173–189, 2012, doi:10.1017/jfm.2012.244.
- G.G. Stokes, “On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids,” Transactions of the Cambridge Philosophical Society, vol. 8, pp. 287–305, 1845.
- P.W. Bridgman, The Physics of High Pressure, MacMillan Company, New York, 1931.
- E.M. Griest, W. Webb, R.W. Schiessler, “Effect of pressure on viscosity of high hydrocarbons and their mixture,” Journal of Chemical Physics, vol. 29, pp. 711–720, 1958.
- K.L. Johnson, R. Cameron, “Shear behavior of elastohydrodynamic oil films at high rolling contact pressures,” Proceedings of the Institution of Mechanical Engineers, vol. 182, pp. 307–319, 1967.
- K.L. Johnson, J.L. Tevaarwerk, “Shear behavior of elastohydrodynamic oil films.” Proceedings of the Royal Society of London, Series A, vol. 356, pp. 215–236, 1977.
- S. Bair, W.O. Winer, “The high-pressure high shear stress rheology of liquid lubricants,” Journal of Tribology, vol. 114, pp. 1–13, 1992, doi:10.1115/1.2920862.
- S. Bair, P, Kottke, “Pressure-viscosity relationship for elastohydrodynamic,” Tribology Transactions, vol. 46(3), pp. 289–295, 2003, doi:10.1080/10402000308982628.
- V. Prusa, S. Srinivasan, K.R. Rajagopal, “Role of pressure dependent viscosity in measurements with falling cylinder viscometer,” International Journal of Non-Linear Mechanics, vol. 47(7), pp. 743–750, 2012, doi:10.1016/j.ijnonlinmec.2012.02.001.
- K.R. Rajagopal, G. Saccomandi, L. Vergori, “Flow of fluids with pressure and shear-dependent viscosity down an inclined plane,” Journal of Fluid Mechanics, vol. 706, pp. 173–189, 2012, doi: 10.1017/jfm.2012.244.
- F.J. Martinez-Boza, M.J. Martin-Alfonso, C. Gallegos, M. Fernandez, “High-pressure behavior of intermediate fuel oils,” Energy & Fuels 25(11), pp. 5138–5144, 2011, doi:10.1021/ef200958v.
- J.M. Dealy, J. Wang, Melt Rheology and Its Applications in the Plastics Industry, 2nd ed., Springer, Dordrecht, The Netherlands, 2013.
- M. Asif, M. Sajid, M.N. Sadiq, “Investigation of blade coating with pressure-dependent viscosity in couple stress fluid flow,” Journal of Plastic Film & Sheeting 42(1), pp. 51–70, 2025, doi:10.1177/87560879251358512.
- X. Chen, Z. Xie, Y. Jian, “Streaming potential of viscoelastic fluids with the pressure-dependent viscosity in nanochannel,” Physics of Fluids, vol. 36, Issue 3, 032025, 2024, doi:10.1063/5.0197157.
- A.Z. Szeri, Fluid Film Lubrication, Cambridge University, Cambridge, 1998.
- C. Barus, “Note on the dependence of viscosity on pressure and temperature,” Proceedings of the American Academy of Arts and Sciences, vol. 27, pp. 13–18, 1891, doi:10.2307/20020462.
- C. Barus, “Isothermals, isopiestics and isometrics relative to viscosity,” American Journal of Science, vol. s3-45, Issue 266, pp. 87–96, 1893, doi:10.2475/ajs.s3-45.266.87.
- K.R. Rajagopal, “Couette flows of fluids with pressure dependent viscosity,” International Journal of Applied Mechanics and Engineering, vol. 9, no.3, pp. 573–585, 2004.
- F.T. Akyildiz, D. Siginer, “A note on the steady flow of Newtonian fluids with pressure dependent viscosity in a rectangular duct,” International Journal of Engineering Science, vol. 104, pp. 1–4, 2016, doi:10.1016/j.ijengsci.2016.04.004.
- K.D. Housiadas, G.C. Georgiou, “Analytical solution of the flow of a Newtonian fluid with pressure-dependent viscosity in a rectangular duct,” Applied Mathematics and Computation, vol. 322, pp. 123–128, 2018, doi:10.1016/j.amc.2017.11.029.
- B. Calusi, L.I. Palade, “Modeling of a fluid with pressure-dependent viscosity in Hele-Shaw flow,” Modelling, vol. 5(4), pp. 1490–1504, 2024, doi:10.3390/modelling5040077.
- R.S. Herbst, C. Harley, K.R. Rajagopal, “Flow of fluids with pressure-dependent viscosity in intersecting planes,” Fluids, vol. 10(2), 33, 2025, doi:10.3390/fluids10020033.
- C. Fetecau, Hanifa Hanif, “Long-time solutions of the modified MHD Stokes’ problems for a class of Maxwell fluids with pressure-dependent viscosity. Applications,” Discrete and Continuous Dynamical Systems – Series S, Published online: December 15, 2025, doi: 10.3934/dcdss.2026021.
- C. Fetecau, “Permanent solutions for MHD modified Stokes’ problems of some Maxwell fluids with power-law dependence of viscosity on pressure,” accepted for publication in journal Annals of Academy Romanian Sciences. Series of Applied Mathematics in 2026.
- C. Sin, E.S. Baranovskii, Regularity Theory for Generalized Navier-Stokes Equations: Non-Newtonian Fluids with Variable Power-Law, Vol. 10, De Gruyter Series in Applied and Numerical Mathematics, Walter de Gruyter GmbH & Co.KG, 2025.
- K.R. Rajagopal, G. Saccomandi, L. Vergori, “Unsteady flows of fluids with pressure dependent viscosity,” Journal of Mathematical Analysis and Applications, vol. 404, Issue 2, pp. 362–372, 2013, doi:10.1016/j.jmaa.2013.03.025.
- D.G. Zill, Free Course in Differential Equations with Modelling Applications, Ninth. ed., BROOKS/COLE, CENGAGE Learning, Australia, United Kingdom, United States, 2009.
- K.R. Rajagopal, “A note on unsteady unidirectional flows of a non-Newtonian fluid,” International Journal of Non-Linear Mechanics, vol. 17, Issues 5-6, pp. 369–373, 1982, doi:10.1016/0020-7462(82)90006-3.
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