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Abstract

The present theoretical study is concerned with the analysis of surface roughness effects on the steady-state performance of stepped circular hydrostatic thrust bearings lubricated with non-Newtonian fluids: Rabinowitsch fluid model. To take the effects of surface roughness into account, Christensen’s theory for rough surfaces has been adopted. The expression for pressure gradient has been derived in stochastic form employing the energy integral approach. Results for stochastic film pressure and load-carrying capacity have been plotted and analyzed based on numerical results. Due to surface roughness, significant variations in the theoretical results of these properties have been observed.
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Bibliography

[1] U.P. Singh, R.S. Gupta, and V.K. Kapur. On the steady performance of hydrostatic thrust bearing: Rabinowitsch fluid model. Tribology Transactions, 54(5):723-729, 2011. doi: 10.1080/10402004.2011.597541.
[2] U.P. Singh, R.S. Gupta, and V.K. Kapur. On the application of Rabinowitsch fluid model on an annular ring hydrostatic thrust bearing. Tribology International, 58:65-70, 2013. doi: 10.1016/j.triboint.2012.09.014.
[3] U.P. Singh, R.S. Gupta, and V.K. Kapur. On the steady performance of annular hydrostatic thrust bearing: Rabinowitsch fluid model. Journal of Tribology, 134(4):044502, 2012. doi: 10.1115/1.4007350.
[4] B.J. Hamrock, S.R. Schmid, and B.O. Jacobson. Fundamentals of Fluid Film Lubrication. CRC Press, 2004. doi: 10.1201/9780203021187.
[5] R. Bassani and P. Piccigallo. Hydrostatic Lubrication, Elsevier, 1992.
[6] J.A. Coombs and D. Dowson. An experimental investigation of the effects of lubricant inertia in a hydrostatic thrust bearing. Proceedings of the Institution of Mechanical Engineers, Conference Proceedings, 179(10):96-114, 1964. doi: 10.1243/PIME_CONF_1964_179_270_02.
[7] J. Peterson, W.E. Finn, and D.W. Dareing. Non-Newtonian temperature and pressure effects of a lubricant slurry in rotating hydrostatic step bearing. Tribology Transactions, 37(4):857-863, 1994. doi: 10.1080/10402009408983369.
[8] V.K. Kapur and K. Verma. The simultaneous effects of inertia and temperature on the performance of a hydrostatic thrust bearing. Wear, 54(1):113-122, 1979. doi: 10.1016/0043-1648(79)90050-4.
[9] P. Singh, B.D. Gupta, and V.K. Kapur. Design criteria for stepped thrust bearings. Wear, 89(1):41-55, 1983. doi: 10.1016/0043-1648(83)90213-2.
[10] S.C. Sharma, S.C. Jain, and D.K. Bharuka. Influence of recess shape on the performance of a capillary compensated circular thrust pad hydrostatic bearing. Tribology International, 35(6):347-356, 2002. doi: 10.1016/S0301-679X(02)00013-0.
[11] Z. Tian, H. Cao, and Y. Huang. Static characteristics of hydrostatic thrust bearing considering the inertia effect on the region of supply hole. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 233(1):188-193, 2019. doi: 10.1177/1350650118773944.
[12] Y.K. Younes. A revised design of circular hydrostatic bearings for optimal pumping power. Tribology International, 26(3):195-200, 1993. doi: 10.1016/0301-679X(93)90093-G.
[13] O.J. Bakker and R.A.J. van Ostayen. Recess depth optimization for rotating, annular, and circular recess hydrostatic thrust bearings. Journal of Tribology, 132(1):011103, 2010. doi: 10.1115/1.4000545.
[14] H. Sawano, Y. Nakamura, H. Yoshioka, and H. Shinno. High performance hydrostatic bearing using a variable inherent restrictor with a thin metal plate. Precision Engineering, 41:78-85, 2015. doi: 10.1016/j.precisioneng.2015.02.001.
[15] J.S. Yadav and V.K. Kapur. On the viscosity variation with temperature and pressure in thrust bearing. International Journal of Engineering Science, 19(2):269-77, 1981. doi: 10.1016/0020-7225(81)90027-6.
[16] P. Zhicheng, S. Jingwu, Z. Wenjie, L. Qingming, and C. Wei. The dynamic characteristics of hydrostatic bearings. Wear, 166(2):215-220, 1993. doi: 10.1016/0043-1648(93)90264-M.
[17] J.R. Lin. Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids. Tribology International, 32(4):207-216, 1999. doi: 10.1016/S0301-679X(99)00034-1.
[18] H. Christensen. Stochastic models for hydrodynamic lubrication of rough surfaces. Proceedings of the Institution of Mechanical Engineers, 184(1):1013-1026, 1969. doi: 10.1243/PIME_ PROC_1969_184_074_02.
[19] J. Prakash and K. Tiwari. Effect of surface roughness on the squeeze film between rotating porous annular discs with arbitrary porous wall thickness. International Journal of Mechanical Sciences, 27(3):135-144, 1985. doi: 10.1016/0020-7403(85)90054-2.
[20] P. Singh, B.D. Gupta, and V.K. Kapur. Optimization of corrugated thrust bearing characteristics. Wear, 167(2):109-120, 1993. doi: 10.1016/0043-1648(93)90315-D.
[21] J.R. Lin. Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings. International Journal of Machine Tools and Manufacture, 40(11):1671-1689, 2000. doi: 10.1016/S0890-6955(00)00012-2.
[22] A.W. Yacout. The surfacse roughness effect on the hydrostatic thrust spherical bearings performance: Part 3 of 5 - Recessed clearance type of bearings. In Proceedings of the ASME International Mechanical Enginering Congress and Exposition, Volume 9: Mechanical Systems and Control, Parts A, B, and C, pages 431-447, Seattle, Washington, USA, November 11-15, 2007. doi: 10.1115/IMECE2007-41013.
[23] Y. Xuebing, X. Wanli, L. Lang, and H. Zhiquan. Analysis of the combined effect of the surface roughness and inertia on the performance of high-speed hydrostatic thrust bearing. In: Luo J., Meng Y., Shao T., Zhao Q. (eds): Advanced Tribology, 197-201, Springer, 2009. doi: 10.1007/978-3-642-03653-8_66.
[24] A. Walicka, E. Walicki, P. Jurczak, and J. Falicki. Thrust bearing with rough surfaces lubricated by an Ellis fluid. International Journal of Applied Mechanics and Engineering, 19(4):809-822, 2014. doi: 10.2478/ijame-2014-0056.
[25] V.K. Stokes. Couple stress in fluids. The Physics of Fluids, 9(9):1709-1715, 1966. doi: 10.1063/1.1761925.
[26] S. Wada and H. Hayashi. Hydrodynamic lubrication of journal bearings by pseudo-plastic lubricants: Part 2, Experimental studies. Bulletin of JSME, 14(69):279-286, 1971. doi: 10.1299/jsme1958.14.279.
[27] H.A. Spikes. The behaviour of lubricants in contacts: current understanding and future possibilities. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 208(1):3-15, 1994. doi: 10.1243/PIME_PROC_1994_208_345_02.
[28] P. Bourging and B. Gay. Determination of the load capacity of finite width journal bearing by finite element method in the case of a non-Newtonian lubricant. Journal of Tribology, 106(2):285-290, 1984. doi: 10.1115/1.3260906.
[29] H. Hayashi and S. Wada. Hydrodynamic lubrication of journal bearings by pseudo-plastic lubricants: Part 3, Theoretical analysis considering effects of correlation. Bulletin of JSME, 17(109):967-974, 1974. doi: 10.1299/jsme1958.17.967.
[30] H. Hashimoto and S. Wada. The effects of fluid inertia forces in parallel circular squeeze film bearings lubricated with pseudo-plastic fluids. Journal of Tribology, 108(2):282-287, 1986. doi: 10.1115/1.3261177.
[31] J.-R. Lin. Non-Newtonian effects on the dynamic characteristics of one dimensional slider bearings: Rabinowitsch fluid model. Tribology Letters, 10:237-243, 2001. doi: 10.1023/A:1016678208150.
[32] U.P. Singh, R.S. Gupta, and V.K. Kapur. Effects of inertia in the steady state pressurised flow of a non-Newtonian fluid between two curvilinear surfaces of revolution: Rabinowitsch fluid model. Chemical and Process Engineering, 32(4):333-349, 2011. doi: 10.2478/v10176-011-0027-1.
[33] J.R. Lin. Non-Newtonian squeeze film characteristics between parallel annular disks: Rabinowitsch fluid model. Tribology International, 52:190-194, 2012. doi: 10.1016/j.triboint. 2012.02.017.
[34] U.P. Singh. Application of Rabinowitsch fluid model to pivoted curved slider bearings. Archive of Mechanical Engineering, 60(2):247-266, 2013. doi: 10.2478/meceng-2013-0016.
[35] U.P. Singh and R.S. Gupta. Dynamic performance characteristics of a curved slider bearing operating with ferrofluids. Advances in Tribology, 2012:1-6, 2012. doi: 10.1155/2012/278723.
[36] U.P. Singh, R.S. Gupta, and V.K. Kapur. On the squeeze film characteristics between a long cylinder and a flat plate: Rabinowitsch model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 227(1):34-42, 2013. doi: 10.1177/1350650112458742.
[37] S.C. Sharma and S.K. Yadav. Performance of hydrostatic circular thrust pad bearing operating with Rabinowitsch fluid model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 227(11):1272-1284, 2013. doi: 10.1177/1350650113490147.
[38] Y. Huang and Z. Tian. A new derivation to study the steady performance of hydrostatic thrust bearing: Rabinowitch fluid model. Journal of Non-Newtonian Fluid Mechanics, 246:31-35, 2017. doi: 10.1016/j.jnnfm.2017.04.012.
[39] U.P. Singh, P. Sinha, and M. Kumar. Analysis of hydrostatic rough thrust bearing lubricated with Rabinowitsch fluid considering fluid inertia in supply region. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tibology, 235(2):386-395, 2021. doi: 10.1177/1350650120945887.
[40] A. Cameron. Basic Lubrication Theory, 3rd edition. E. Horwood, 1981.
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Authors and Affiliations

Udaya P. Singh
1
ORCID: ORCID

  1. Rajkiya Engineering College, Sonbhadra, Uttar Pradesh, India
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Abstract

The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy’s equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel’s and Kuwabara’s cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.
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Bibliography

[1] D.A. Nield and A. Bejan. Convection in Porous Media. Springer, New York, 2006.
[2] H.P.G. Darcy. Les Fontaines Publiques de la Ville de Dijon. Victor Delmont, Paris, 1856.
[3] H.C. Brinkman. A calculation of viscous force exerted by flowing fluid on dense swarm of particles. Applied Science Research, 1:27-34, 1949. doi: 10.1007/BF02120313.
[4] D.D. Joseph and L.N. Tao. The effect of permeability on the slow motion of a porous sphere. Journal of Applied Mathematics and Mechanics, 44(8-9):361-364, 1964. doi: 10.1002/zamm.19640440804.
[5] D.N. Sutherland and C.T. Tan. Sedimentation of a porous sphere. Chemical Engineering Science, 25(12):1948-1950, 1970. doi: 10.1016/0009-2509(70)87013-0.
[6] M.P. Singh and J.L. Gupta. The effect of permeability on the drag of a porous sphere in a uniform stream. Journal of Applied Mathematics and Mechanics, 51(1):27-32, 1971. doi: zamm.19710510103.
[7] I.P. Jones. Low Reynolds number flow past a porous spherical shell. Mathematical Proceedings of the Cambridge Philosophical Society, 73(1):231-238, 1973. doi: 10.1017/S0305004100047642.
[8] G. Neale, N. Epstein, and W. Nader. Creeping flow relative to permeable spheres. Chemical Engineering Science, 28(10):1865-1874, 1973. doi: 10.1016/0009-2509(73)85070-5.
[9] V.M. Shapovalov. Viscous fluid flow around a semipermeable particle. Journal of Applied Mechanics and Technical Physics, 50(4):584-588, 2009. doi: 10.1007/s10808-009-0079-x.
[10] G.S. Beavers and D.D. Joseph. Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics, 30(1):197-207, 1967. doi: 10.1017/S0022112067001375.
[11] P.G. Saffman. On the boundary condition at the surface of a porous medium. Studies in Applied Mathematics, 50(2):93-101, 1971. doi: 10.1002/sapm197150293.
[12] S. Khabthani, A. Sellier, and F. Feuillebois. Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition. Journal of Fluid Mechanics, 867:949-968, 2019. doi: 10.1017/jfm.2019.169.
[13] M.C. Lai, M.C. Shiue, and K.C. Ong. A simple projection method for the coupled Navier-Stokes and Darcy flows. Computational Geosciences, 23:21-33, 2019. doi: 10.1007/s10596-018-9781-1.
[14] J. Happel and H. Brenner. Low Reynolds Number Hydrodynamics. Englewood Cliffs New Jork, Prentice-Hall, 1965.
[15] J. Happel. Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. American Institute of Chemical Engineers Journal, 4(2):197-201, 1958. doi: 10.1002/aic.690040214.
[16] S. Kuwabara. The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. Journal of the Physical Society of Japan, 14(4):527-532,1959. doi: 10.1143/JPSJ.14.527.
[17] S.B. Chen and X. Ye. Boundary effect on slow motion of a composite sphere perpendicular to two parallel impermeable plates. Chemical Engineering Science, 55(13):2441-2453, 2000. doi: 10.1016/S0009-2509(99)00509-6.
[18] D. Srinivasacharya. Motion of a porous sphere in a spherical container. Comptes Rendus Mecanique, 333(8):612-616, 2005. doi: 10.1016/j.crme.2005.07.017.
[19] S.I. Vasin, A.N. Fillipov, and V.M. Starov. Hydrodynamic permeability of membranes built up by particles covered by porous shells: Cell models. Advances in Colloid Interface Science, 139(1-2):83-96, 2008. doi: 10.1016/j.cis.2008.01.005.
[20] P.K. Yadav, A. Tiwari, S. Deo, A. Filippov, and S. Vasin. Hydrodynamic permeability of membranes built up by spherical particles covered by porous shells: effect of stress jump condition. Acta Mechanica, 215:193-209, 2010. doi: 10.1007/s00707-010-0331-8.
[21] J. Prakash, G.P. Raja Sekhar, and M. Kohr. Stokes flow of an assemblage of porous particles: stress jump condition. Zeitschrift für angewandte Mathematik und Physik, 62:1027-1046, 2011. doi: 10.1007/s00033-011-0123-6.
[22] E.I. Saad. Stokes flow past an assemblage of axisymmetric porous spherical shell-in-cell models: effect of stress jump condition. Meccanica, 48:1747-1759, 2013. doi: 10.1007/s11012-013-9706-y.
[23] J. Prakash and G.P. Raja Sekhar. Estimation of the dynamic permeability of an assembly of permeable spherical porous particle using cell model. Journal of Engineering Mathematics, 80:63-73, 2013. doi: 10.1007/s10665-012-9580-y.
[24] M.K. Prasad and T. Bucha. Creeping flow of fluid sphere contained in a spherical envelope: magnetic effect. SN Applied Science, 1(12):1594, 2019. doi: 10.1007/s42452-019-1622-x.
[25] M.K. Prasad and T. Bucha. Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models. Pramana - Journal of Physics, 94(1):1-10, 2020. doi: 10.1007/s12043-019-1892-2.
[26] M.K. Prasad and T. Bucha. MHD viscous flow past a weakly permeable cylinder using Happel and Kuwabara cell models. Iranian Journal of Science and Technology Transaction A: Science, 44:1063-1073, 2020. doi: 10.1007/s40995-020-00894-4.
[27] D. Khanukaeva. Filtration of micropolar liquid through a membrane composed of spherical cells with porous layer. Theoretical and Computational Fluid Dynamics, 34(3):215-229, 2020. doi: 10.1007/s00162-020-00527-x.
[28] M.K. Prasad. Boundary effects of a nonconcentric semipermeable sphere using Happel and Kuwabara cell models. Applied and Computational Mechanics, 15:1-12, 2021. doi: 10.24132/acm.2021.620.
[29] G.G. Stokes. On the effect of the internal friction of fluids on the motion of pendulums. Proceedings of Cambridge Philosophical Society, 9:8-106, 1851.
[30] C.R. Reddy and N. Kishore. Momentum and heat transfer phenomena of confined spheroid particles in power-law liquids, Industrial and Engineering Chemical Research, 53(2):989-998, 2014. doi: 10.1021/ie4032428.
[31] A. Acrivos and T.D. Taylor. The Stokes flow past an arbitrary particle: the slightly deformed sphere. Chemical Engineering Science, 19(7):445-451, 1964. doi: 10.1016/0009-2509(64)85071-5.
[32] H. Ramkissoon. Stokes flow past a slightly deformed fluid sphere, Journal of Applied Mathematics and Physics, 37:859-866, 1986. doi: 10.1007/BF00953677.
[33] D. Palaniappan. Creeping flow about a slightly deformed sphere. Zeitschrift für angewandte Mathematik und Physik, 45:832-838, 1994. doi: 10.1007/BF00942756.
[34] G. Dassios, M. Hadjinicolaou, F.A. Coutelieris, and A.C. Payatakes. Stokes flow in spheroidal particle-in-cell models with Happel and Kuwabara boundary conditions. International Journal of Engineering Science, 33(10):1465-1490, 1995. doi: 10.1016/0020-7225(95)00010-U.
[35] H. Ramkissoon. Slip flow past an approximate spheroid. Acta Mechanica, 123:227-233, 1997. doi: 10.1007/BF01178412.
[36] T. Zlatanovski. Axi-symmetric creeping flow past a porous prolate spheroidal particle using the Brinkman model. The Quarterly Journal of Mechanics and Applied Mathematics, 52(1):111-126, 1999. doi: 10.1093/qjmam/52.1.111.
[37] S. Deo and S. Datta. Slip flow past a prolate spheroid. Indian Journal of Pure and Applied Mathematics, 33(6):903-909, 2002.
[38] P. Vainshtein, M. Shapiro, and C. Gutfinger. Creeping flow past and within a permeable spheroid. International Journal of Multiphase Flow, 28(12):1945-1963, 2002. doi: 10.1016/S0301-9322(02)00106-4.
[39] H. Ramkissoon and K. Rahaman. Wall effects on a spherical particle. International Journal of Engineering Science, 41(3-5), 283-290, 2003. doi: 10.1016/S0020-7225(02)00209-4.
[40] S. Senchenko and H.J. Keh. Slipping Stokes flow around a slightly deformed sphere. Physics of Fluids, 18(8):088104, 2006. doi: 10.1063/1.2337666.
[41] D. Srinivasacharya. Flow past a porous approximate spherical shell, Zeitschrift für angewandte Mathematik und Physik, 58, 646-658, 2007. doi: 10.1007/s00033-006-6003-9.
[42] Y.C. Chang and H.J. Keh. Translation and rotation of slightly deformed colloidal spheres experiencing slip. Journal of Colloid and Interface Science, 330:201-210, 2009. doi: 10.1016/j.jcis.2008.10.055.
[43] E.I. Saad. Translation and rotation of a porous spheroid in a spheroidal container. Canadian Journal of Physics, 88(9):689-700, 2010. doi: 10.1139/P10-040.
[44] E.I. Saad. Stokes flow past an assemblage of axisymmetric porous spheroidal particle in cell models. Journal of Porous Media, 15(9):849-866, 2012. doi: /10.1615/JPorMedia.v15.i9.40.
[45] D. Srinivasacharya and M.K. Prasad. Axisymmetric creeping motion of a porous approximate sphere with an impermeable core. The European Physics Journal Plus, 128(1):9, 2013. doi: 10.1140/epjp/i2013-13009-1.
[46] D. Srinivasacharya and M.K. Prasad. Creeping motion of a porous approximate sphere with an impermeable core in a spherical container. European Journal of Mechanics - B/Fluids, 36:104-114, 2012. doi: 10.1016/j.euromechflu.2012.04.001.
[47] D. Srinivasacharya and M.K. Prasad. Axisymmetric motion of a porous approximate sphere in an approximate spherical container. Archive of Mechanics, 65(6):485-509, 2013.
[48] K.P. Chen. Fluid extraction from porous media by a slender permeable prolate-spheroid. Extreme Mechanics Letter, 4:124-130, 2015. doi: 10.1016/j.eml.2015.06.001.
[49] M. Rasoulzadeh and F.J. Kuchuk. Effective permeability of a porous medium with spherical and spheroidal vug and fracture inclusions. Transport in Porous Media, 116:613-644, 2017. doi: 10.1007/s11242-016-0792-x.
[50] P.K. Yadav, A. Tiwari, and P. Singh. Hydrodynamic permeability of a membrane built up by spheroidal particles covered by porous layer. Acta Mechanica, 229:1869-1892, 2018. doi: 10.1007/s00707-017-2054-6.
[51] M.K. Prasad and T. Bucha. Steady viscous flow around a permeable spheroidal particle. International Journal of Applied and Computational Mathematics, 5:109, 2019. doi: 10.1007/s00707-017-2054-6.
[52] M.K. Prasad and T. Bucha. Effect of magnetic field on the slow motion of a porous spheroid: Brinkman's model. Archive of Applied Mechanics, 91:1739-1755, 2021. doi: 10.1007/s00419-020-01852-7.
[53] J.D. Sherwood. Cell models for suspension viscosity. Chemical Engineering Science, 61(10):6727-6731, 2006. doi: 10.1016/j.ces.2006.07.016.
[54] A. Tiwari, P.K. Yadav, and P. Singh. Stokes flow through assemblage of non homogeneous porous cylindrical particle using cell model technique. National Academy of Science Letters, 41(1):53-57, 2018. doi: 10.1007/s40009-017-0605-y.
[55] H.H. Sherief, M.S. Faltas, and E.I. Saad. Slip at the surface of an oscillating spheroidal particle in a micropolar fluid. ANZIAM Journal, 55(E):E1-E50, 2013. doi: 10.21914/anziamj.v55i0.6813.
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Authors and Affiliations

Tina Bucha
1
ORCID: ORCID
Madasu Krishna Prasad
2
ORCID: ORCID

  1. Department of Mathematics, National Institute of Technology, Raipur, Chhattisgarh, India
  2. Department of Mathematics, National Institute of Technology, Raipur-492010, Chhattisgarh, India

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