Turkish Journal of Science & Technology Volume 9(1), 97-103, 2014 Effects of piezo-viscous dependency on squeeze film between circular plates: Couple Stress fluid model U. P. SINGH Ansal Technical Campus, Faculty of Applied Science, Department of Mathematics, Lucknow; India; * journals4phd@gmail.com (Received:04.11.2013; Accepted:08.03.2014) Abstract In high pressure fluid flows applications such as fluid film lubrication, microfluidics and geophysics, the piezo- viscous effect i.e. viscosity-pressure dependence plays an important role. In the present theoretical investigation, the combined effects of piezo-viscous dependency and non-Newtonian couple stresses on the performance of circular plate squeeze film bearings have been investigated using Stokes Micro-continuum theory of couple stress fluids together with the exponential variation of viscosity with pressure. Analytic solution for film pressure is obtained using small perturbation analysis. The numerical results for pressure and load capacity with different values of viscosity-pressure parameter are calculated and compared with iso-viscous couple stress and Newtonian lubricants. Due to piezo-viscous effect, enhanced pressure, increased load capacity and longer response time is observed in the analysis. Key words: Couple stress Fluids, Load-carrying capacity, Piezo-viscous effect, Squeeze-film lubrication, Viscosity-pressure 1. Introduction The squeeze film lubrication plays very important role in various applications of engineering and technology. Ball bearings, matching gears, machine tools, rolling elements and automotive engines are some common examples of squeeze film lubrication. The squeeze film phenomenon is also observed during approach of faces of disc clutches under lubricated condition. The mechanical action (squeezing, shearing etc.) changes the lubricants’ temperature as well as viscosity and density which account for the variation of bearings performance characteristics. Many researchers such as Dowson [1], Wada and Hayashi [2] and Kapur [3] emphasized the variation of viscosity and density with temperature and pressure and reported a significant variation in the pressure, load capacity etc. In high pressure applications, the viscosity of lubricants depends much on pressure than the temperature [4]. In such mechanism, the variation of viscosity is also more significantly over the density variation [4, 5]. Denn [6] emphasized that under a pressure of about 5 MPa, the dependence of viscosity on pressure become important even if the flow is incompressible. Bair et al. [7] shown that the viscosity of bis(phenoxyphenoxy)benzene varies from 0.0251 Pa.s to 72 Pa.s under pressure variation 0.1–300 MPa, and the viscosity of dipentaerythritol hexaisostearate varies from 0.0251 Pa.s to 66.2 Pa.s under pressure variation 0.1-942 MPa under isothermal condition. Therefore, it is reasonable to analyze the bearing performance with a pressure dependent viscosity [8] considering the isothermal, incompressible flow of lubricants of the form p o e     (1) where  is the viscosity, P is the pressure, o  is the viscosity at atmospheric pressure, and  is the pressure-viscosity coefficient. Kottke [9] reported the range of  between 10 to 70 MPa –1 for lubricants. Venner and Lubrecht [10] reported that  may range between 10 –8 to 2×10 –8 Pa –1 for mineral oils. The investigation of squeeze film characteristics between rectangular, porous rectangular, curved circular plates etc. has been analyzed from time to time by various researchers such as Burbidge and Colin [11] Sanni [12], Abell and Ames [13], Gupta and Vora [14], Gupta and Gupta [15], Murti [16] and Wu [17] using classical Newtonian model. After Stokes [18] proposed micro-continuum theory for couple stresses in fluids accounting the particle size effects of micro- structures in