Many electrorheological fluids (ERFs) as fluids with microstructure demonstrate viscoplastic behaviours. Rheometric measurements indicate that some flows of these fluids may be modelled as the flows of a Herschel-Bulkley fluid. In this paper, the flow of a Herschel-Bulkley ER fluid—with a fractional power-law exponent—in a narrow clearance between two fixed surfaces of revolution with common axis of symmetry is considered. The flow is externally pressurized, and it is considered with inertia effect. In order to solve this problem, the boundary layer equations are used. The influence of inertia forces on the pressure distribution is examined by using the method of averaged inertia terms of the momentum equation. Numerical examples of externally pressurized ERFs flows in the clearance between parallel disks and concentric spherical surfaces are presented. 1. Introduction In recent years, the study of fluids with microstructures has gained much importance because of its numerous applications in various engineering disciplines such as chemical engineering, polymer processing, plastic forming foundry engineering, and engineering of lubrication [1–14]. In machines and mechanisms systems of many industrial processes, the phenomena of a flow of viscoplastic fluids are used. One of these phenomena is a slide bearing lubrication [9, 10, 13]. Advances in technology and severe operational requirements of machines necessitated the development of improved lubricants to ensure a smooth and safe operation. Generally, viscosity of lubricants decreases with temperature. For operations under high speeds and heavy loads, oils containing high molecular weight polymers as viscosity index improvers are used to increase a load carrying capacity of the modified lubricants [9, 13]. Most substances used in the lubrication technology are polymer solutions, thus, the characteristics of the bearings change when such rheological substances, known as non-Newtonian fluids, are used as lubricants. Several constitutive relations applied were used to model the non-Newtonian characteristics exhibited by some lubricants [7, 11, 13, 15, 16]. Another ones of these phenomena are processes of vibration control and torque transmission. In the last years, the electrorheological fluids (abbreviated to ERFs) have acquired a great relevance for supporting vibration control and torque transmission devices, based on the characteristic dependence of their viscosity on applied electric field strength. Since their initial discovery by Winslow [17], many particle-dispersion electrorheological fluids,
References
[1]
H. A. Barnes, J. F. Hutton, and K. Walters, An Introduction to Rheology, Elsevier, Amsterdam, The Netherlands, 1989.
[2]
J. S. Basavaraja, S. C. Sharma, and S. C. Jain, “A study of misaligned electrorheological fluid lubricated hole-entry hybrid journal bearing,” Tribology International, vol. 43, no. 5-6, pp. 1059–1064, 2010.
[3]
R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamic of Polymeric Liquids, vol. 1, John Wiley, New York, NY, USA, 1977.
[4]
R. B. Bird, C. F. Curtis, R. C. Armstrong, and O. Hassager, Dynamic of Polymeric Liquids, vol. 2, John Wiley, New York, NY, USA, 1987.
[5]
N. Casson, Rheology of Dispersed Systems, C.C. Mills, New York, NY, USA, 1959.
[6]
C. D. Han, Rheology and Processing of Polymeric Materials, Oxford University Press, 2009.
[7]
R. P. Chhabra and J. F. Richardson, Non-Newtonian Flow and Applied Rheology, Butterworth-Heinemann, Oxford, UK, 2008.
[8]
J. Falicki, The influence viscoplastic lubricants on the pressure distributions in the thrust slide bearings [Ph.D. thesis], University Press, Zielona Góra, Poland, 2007.
[9]
J. Falicki and A. Walicka, “Effect of the choice of oil additives on rheological properties of engine oils,” International Journal Applied Mechanics and Engineering, vol. 10, pp. 309–315, 2005.
[10]
N. Heinrichson, On the design of tilting-pad thrusts bearings [Ph.D. thesis], Lyngby, Denmark, 2006.
[11]
R. I. Tanner, Engineering Rheology, Oxford University Press, 2000.
[12]
N. Roussel, Analyse des écoulements des fluides homogènes complexes et plastiques diphasiques: application à l’essai de compression simple [Ph.D. thesis], Rennes, France, 2001.
[13]
E. Walicki, Rheodynamics of Slide Bearings Lubrication, University Press, Zielona Góra, Poland, 2005 (in Polish).
[14]
A. Walicka, “Pressure distribution in a squeeze film of a Shulman fluid between surfaces of revolution,” International Journal of Engineering Science, vol. 69, pp. 33–48, 2013.
[15]
A. Walicka, Rheodynamics of Non-Newtonian Fluids Flow in Straight and Curved Channels, University Press, Zielona Góra, Poland, 2002 (in Polish).
[16]
A. Walicka, Rotational Flows of the Rheologically Complex Media in Thin Annular Channels, University Press, Zielona Góra, Poland, 2002 (in Russian).
[17]
W. M. Winslow, “Induced fibration of suspensions,” Journal of Applied Physics, vol. 20, no. 12, pp. 1137–1140, 1949.
[18]
S. Y. Jung and S.-B. Choi, “Analysis of a short squeeze-film damper operating with electrorheological fluids,” Tribology Transactions, vol. 38, no. 4, pp. 857–862, 1995.
[19]
K. Kobayashi, K. Okamura, T. Sakai, and M. Sato, “Evaluation of the flow rate of an electro-rheological fluid (Corn Starch-Kerosene) flowing through a narrow channel formed by a pair of electrodes,” Canadian Journal of Chemical Engineering, vol. 74, no. 3, pp. 394–398, 1996.
[20]
M. V. Korobko, Electrostructured (Electrorheological) Fluids: Dynamics Singularities and Possibility of Aplication, BAS Press, Minsk, Russia, 1996.
[21]
Z. P. Shulman, R. G. Gorodkin, E. V. Korobko, and V. K. Gleb, “The electrorheological effect and its possible uses,” Journal of Non-Newtonian Fluid Mechanics, vol. 8, no. 1-2, pp. 29–41, 1981.
[22]
Z. P. Shulman and V. Nosov, “Rotation of the axisimmetric dielectric bodies (DEB) in electrorheological suspensions (ERS),” International Journal of Modern Physics B, vol. 10, no. 23-24, pp. 2903–2915, 1996.
[23]
D.-Y. Lee and N. M. Wereley, “Quasi-steady Herschel-Bulkley analysis of electro- and magneto-rheological flow mode dampers,” Journal of Intelligent Material Systems and Structures, vol. 10, no. 10, pp. 761–769, 1999.
[24]
Y. T. Choi, J. U. Cho, S. B. Choi, and N. M. Wereley, “Constitutive models of electrorheological and magnetorheological fluids using viscometers,” Smart Materials and Structures, vol. 14, no. 5, pp. 1025–1036, 2005.
[25]
A. Walicka, J. Falicki, and E. Walicki, “Flows of electro- and magneto-rheological fluids in curved clearances,” in Rheology—Theory and Application, M. Dziubiński and K. Antosik, Eds., pp. 369–398, Warsaw, Poland, 2011.
[26]
A. D. Dimarogonas and A. Kollias, “Electrorheological fluid-controlled “smart” journal bearings,” Tribology Transactions, vol. 35, no. 4, pp. 611–618, 1992.
[27]
J. Peng and K.-Q. Zhu, “Effects of electric field on hydrodynamic characteristics of finite-length ER journal bearings,” Tribology International, vol. 39, no. 6, pp. 533–540, 2006.
[28]
A. K. El Wahed, J. L. Sproston, R. Stanway, and E. W. Williams, “An improved model of ER fluids in squeeze-flow through model updating of the estimated yield stress,” Journal of Sound and Vibration, vol. 268, no. 3, pp. 581–599, 2003.
[29]
S. Lim, S.-M. Park, and K.-I. Kim, “AI vibration control of high-speed rotor systems using electrorheological fluid,” Journal of Sound and Vibration, vol. 284, no. 3–5, pp. 685–703, 2005.
[30]
Z. P. Shulman, Convective Heat Transfer of Rheologically Complex Fluids, Energy, Moscow, Russia, 1975 (in Russian).
[31]
W. H. Herschel, “Viscosity and friction,” SAE Journal, vol. 10, pp. 31–38, 1922.
[32]
E. Walicki, A. Walicka, and J. Falicki, “Inertia effects of viscoplastic lubricant in curved squeeze film,” Applied Mechanics and Engineering, vol. 4, pp. 99–108, 1999.
[33]
K. P. Vishwanath and A. Kandasamy, “Inertia effects in circular squeeze film bearing using Herschel-Bulkley lubricants,” Applied Mathematical Modelling, vol. 34, no. 1, pp. 219–227, 2010.
[34]
T. C. Jordan and M. T. Shaw, “Electrorheology,” IEEE Transactions on Electrical Insulation, vol. 24, no. 5, pp. 849–878, 1989.
[35]
Y. Otsubo, “Electrorheological properties of silica suspensions,” Journal of Rheology, vol. 36, no. 3, pp. 479–496, 1992.
[36]
M. Whittle, R. Firoozian, D. J. Peel, and W. A. Bullough, “Decomposition of the pressure response in an ER valve control system,” Journal of Intelligent Material Systems and Structures, vol. 5, no. 1, pp. 105–111, 1994.
[37]
A. Walicka, “Analysis of polymers flow through dies of forming devices,” Applied Mechanics and Engineering, vol. 4, no. 2, pp. 341–361, 1999.
[38]
A. Walicka and J. Falicki, “Pressure distributions in a curvilinear thrust hydrostatic bearing lubricated by a Herschel-Bulkley fluid,” International Journal of Applied Mechanics and Engineering, vol. 13, no. 2, pp. 543–552, 2008.
[39]
E. Walicki and A. Walicka, “Reynolds number effects in the flow of an electrorheological fluid between fixed surfaces of revolution,” Journal of Intelligent Material Systems and Structures, vol. 9, no. 8, pp. 662–666, 1998.
[40]
G. H. Covey and B. R. Stanmore, “Use of the parallel-plate plastometer for the characterisation of viscous fluids with a yield stress,” Journal of Non-Newtonian Fluid Mechanics, vol. 8, no. 3-4, pp. 249–260, 1981.
