Skip to main content Accessibility help

Derivation of Non-Newtonian Magnetic Fluid Lubricated Rough Centrosymmetric Squeeze Film Reynolds Equation and its Application

  • J. R. Lin (a1), L. M. Chu (a2), H. L. Chiang (a1) and Y. K. Chiu (a1)


Based upon the Shliomis ferromagnetic fluid model and the Stokes microcontinuum theory incorporating with the Christensen stochastic model, a modified Reynolds equation of centrosymmetric squeeze films has been derived in this paper. The Reynolds equation includes the combined effects of non-Newtonian rheology, magnetic fluids with applied magnetic fields, rotational inertia forces, and surface roughness. To guide the use of the derived equation, the squeeze film of rotational rough-surface circular disks lubricated with non-Newtonian magnetic fluids is illustrated. According to the results obtained, the effects of rotation inertia decrease the load capacity and the squeeze film time of smooth circular disks. By the use of non-Newtonian magnetic fluids with applied magnetic fields, the rotational circular disks predict better squeeze film performances. When the influences of circumferential roughness patterns are considered, the non-Newtonian magnetic-fluid lubricated rotational rough disks with applied magnetic fields provide further higher values of the load capacity and the squeeze film time as compared to those of the smooth case.


Corresponding author

*Corresponding author (


Hide All
1. Shliomis, M. I., “Effective Viscosity of Magnetic Suspensions,” Soviet Physics - JETP, 34, pp. 12911294 (1972).
2. Shliomis, M. I., “Magnetic Fluids,” Soviet Physics Uspekhi, 17, pp. 153169 (1974).
3. Rosensweig, R. E., Ferrohydrodynamics, Cambridge University Press, New York (1985).
4. Gitter, K. and Odenbach, S., “Experimental Investigations on a Branched Tube Model in Magnetic Drug Ttargeting,” Journal of Magnetism and Magnetic Materials, 323, pp. 14131416 (2011).
5. Shafii, M. B., Daneshvar, F., Jahani, N. and Mobini, K., “Effect of Ferrofluid on the Performance and Emission Patterns of a Four-Stroke Engine,” Advances in Mechanical Engineering, 2011, pp. 115 (2011).
6. Zhang, B. and Nakajima, A., “Dynamics of the Magnetic Fluid Support Grinding of Si3N4 Ceramic Balls for Ultraprecision Bearings and Importance in Spherical Surface Generation,” Precision Engineering, 27, pp. 18 (2003).
7. Tu, Y. O., “Mathematical Modeling and Computer Simulation for Spin Coating of Ferrofluid,” IEEE Transations on Magnetics, 24, pp. 31293131 (1988).
8. Chandra, P., Sinha, P. and Kumar, D., “Ferrofluids Lubrication of a Journal Bearing Considering Cavitation,” Tribology Transactions, 35, pp. 163169 (1992).
9. Lin, J. R., “Dynamic Characteristics of Magnetic Fluid Based Sliding Bearings,” Mechanika, 19, pp. 554558 (2013).
10. Lin, J. R., Hung, T. C. and Hu, S. T., “Effects of Fluid Inertia Forces in Ferrofluid Lubricated Circular Stepped Squeeze Films – Shliomis Model,” Industrial Lubrication and Tribology, 68, pp. 712717 (2016).
11. Oliver, D. R., “Load Enhancement Effects Due to Polymer Thickening in a Short Model Journal Bearing,” Journal of Non-Newtonian Fluid Mechanics, 30, pp. 185189 (1988).
12. Stokes, V. K., “Couple Stresses in Fluids,” Physics of Fluids, 9, pp. 17091715 (1966).
13. Walicki, E. and Walicka, A., “Inertia Effecting the Squeeze Film of a Couple-Stress Fluid in Biological Bearings,” International Journal of Applied Mechanics and Engineering, 4, pp. 363373 (1999).
14. Srivastava, V. P., “Particle-Fluid Suspension Model of Blood Flow through Stenotic Vessels with Applications,” International Journal of Bio-Medical Computing, 38, pp. 141154 (1995).
15. Mekheimer, K. S., “Peristaltic Transport of a Couple Stress Fluid in a Uniform and Non-Uniform Channels,” Biorheology, 39, pp. 755765 (2002).
16. Lin, J. R., Lu, R. F., Lin, M. C. and Wang, P. Y., “Squeeze Film Characteristics of Parallel Circular Disks Lubricated by Ferrofluids with Non-Newtonian Couple Stresses,” Tribology International, 61, pp. 5661 (2013).
17. Christensen, H., “Stochastic Model for Hydrodynamic Lubrication of Rough Surfaces,” Proceedings of the Institution of Mechanical Engineers, 184, pp. 10131025 (1969-1970).
18. Andharia, P. I., Gupta, J. L. and Deheri, G. M., “Effect of Transverse Roughness on the Behavior of Squeeze Film in a Spherical Bearing,” International Journal of Applied Mechanics and Engineering, 4, pp. 1924 (1999).
19. Prakash, J. and Tiwari, K., “Roughness Effects in Porous Circular Squeeze-Plates with Arbitrary Wall Thickness,” Journal of Lubrication Technology, 105, pp. 9095 (1983).
20. Hsu, C. H., Lai, C., Lu, R. F. and Lin, J. R., “Combined Effects of Surface Roughness and Rotating Inertia on the Squeeze Film Characteristics of Parallel Circular Disks,” Journal of Marine Science and Technology, 17, pp. 6066 (2009).
21. Lin, J. R., Liang, L. J., Lin, M. C. and Hu, S. T., “Effects of Circumferential and Radial Rough Surfaces in a Non-Newtonian Magnetic Fluid Lubricated Squeeze Film,” Applied Mathematical Modelling, 39, pp. 67436750 (2015).
22. Batchelor, G. K., “The Effect of Brownian Motion on the Bulk Stress in a Suspension of Spherical Particles,” Journal of Fluid Mechanics, 83, pp. 97117 (1977).



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed