Journal of Applied Mathematics and Physics, 2014, 2, 349-358 Published Online May 2014 in SciRes. http://www.scirp.org/journal/jamp http://dx.doi.org/10.4236/jamp.2014.26042 How to cite this paper: Ponnuswamy, V. and Govindaraj, S. (2014) Behaviour of Couple Stress Fluids in Porous Annular Squeeze Films. Journal of Applied Mathematics and Physics, 2, 349-358. http://dx.doi.org/10.4236/jamp.2014.26042 Behaviour of Couple Stress Fluids in Porous Annular Squeeze Films Vimala Ponnuswamy 1 , Sumathi Govindaraj 2 1 Department of Mathematics, Anna University, Chennai-600025, Tamil Nadu, India 2 Department of Mathematics, Adhiparasakthi Engineering College, Melmaruvathur-603319, Tamil Nadu, India Email: vimalap@annauniv.edu Received March 2014 Abstract The laminar squeeze flow of an incompressible couple stress fluid between porous annular disks is studied using hydrodynamic lubrication theory. The modified Reynolds’ equation is derived us- ing Stokes microcontinuum theory and is solved analytically. Analytical expressions for the squeeze film pressure and the load carrying capacity are obtained in terms of Fourier-Bessel se- ries. Numerical results are obtained for the sinusoidal motion of the upper disk. The effect of cou- ple stresses and that of porous facing on the squeeze film behaviour are analysed through the squeeze film pressure and the load carrying capacity. Further, the equation for the gap width be- tween the disks is obtained from the inverse problem. Keywords Squeeze Films, Hydrodynamic Lubrication, Couple Stresses, Non-Newtonian Fluid 1. Introduction Squeeze film technology is widely applied in many areas of Engineering and Applied Sciences such as clutch plates in automotive transmission, impact film in bio-lubricated joints and turbo-machinery. The classical con- tinuum theory focuses on the use of a Newtonian lubricant in various squeeze film mechanisms [1-4]. The non- Newtonian characteristics of lubricants become important, when the lubricants contain additives with large quantity of high molecular weight polymers as the viscosity index improvers. Grease, emulsion, liquid crystals and body fluids like blood and synovial are examples of such lubricants. As the classical continuum theory of fluids neglects the size effects of particles, a microcontinuum theory has been developed by Stokes [5] to take into account the particle size effects of such non-Newtonian fluids. Many researchers have applied the micro- continuum theory of couple stress fluids in various squeeze film investigations [6-8]. Self lubricating porous bearings have been widely used in industry for a long time due to their special feature of self contained oil reservoir apart from low cost and other aspects of lubrication mechanism. In such bearings, as two surfaces approach each other, a part of the fluid will be squeezed out and the remaining part will flow through the porous media. This will reduce the time required for the oil to reach a prescribed thickness and will change the nature of the flow pattern. There have been numerous studies on various types of such porous bear- ings with a Newtonian or a non-Newtonian lubricant [9]-[12].