Determination of Pseudo-viscosity Coefficients for Visco-elastic Lubricants

In this paper we assume determination of pseudo-viscosity coefficients of visco-elastic non-Newtonian fluid flow directly near the cooperating micro-bearing surface. We show the constitutive stress-strain dependencies of nonNewtonian visco-elastic media with regard to the content of addition of nano-particles. The greater content of nano-particles and influences of superficial layer of cooperating surfaces on the dynamic oil viscosity, the more distinct non-Newtonian properties. The non-Newtonian properties create non-linear dependencies between strain and stress. Moreover the dynamic viscosity or apparent dynamic viscosity of oil often decreases along with shear rate increasing during motion. Dynamic viscosity of oil inside very thin boundary layers depends on Young’s modulus of the cell body being in contact with the oil. Considered visco-elastic oils with nano-particles have non-Newtonian pseudo-plastic properties, described in the beginning by means of Rivlin-Ericksen constitutive relations. Hence their stress-strain dependencies presented in this paper have the modified Rivlin-Ericksen form. Scientific efforts brought into this elaboration represent an impact to the considered domain by providing for some data on comparisons between boundary conditions for lubrication flow in super thin boundary layer lying on the external surface of biological cells of joint cartilage and boundary conditions for lubrication of micro-bearing of shaft diameter smaller than 2 mm.