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According to the Stokes microcontinuum theorem and Christensen's stochastic model, the main objective of this paper is to theoretically predict the combined influences of couple stresses and surface roughness on the lubrication performance of journal‐bearing systems. To take account of the presence of both the surface roughness of bearings and the couple stress effect due to the lubricant containing the polar suspensions, the generalized stochastic non‐Newtonian Reynolds‐type equation is derived. Compared to the Newtonian‐lubricant smooth‐bearing case, the couple stress effects and the longitudinal roughness improve the load carrying capacity, and thus decrease the attitude angle and friction parameter, while the effect of transverse roughness is opposite to that of the longitudinal one in the journal‐bearing system.

This paper aims to investigate analytically the air bearing pressure and film spacing of the linear head/tape interface by numerical iterations between the one‐dimensional compressible Reynolds and Bernoulli tape equations.

In order to account for the molecular rarefaction effect of the ultra‐thin gas lubrication, the pressure flow rate with three optimal adjustable coefficients was implemented into the steady state Reynolds equation. Using the central finite difference approach, the two coupled nonlinear equations can be discretized and numerically solved. To speed up the convergence of the tape position to be obtained, a fictitious stiffness was implied during the process.

By comparison with the Talke's first order model, the differences are significant and cannot be neglected. A smaller film spacing of head/tape can be acquired by a lower tape speed or a higher tape tension, while the slot edge defect and stain will effectively lower the built‐up pressure, thus decreasing the recording density and data access efficiency.

Incorporating the high‐order slip‐flow model into the modified Reynolds equation and coupled with the Bernoulli tape deflection equation, this study proposes a feasible approach to the analysis of molecular rarefaction effect on head/tape interface in a linear tape drive.

According to the Christensen stochastic roughness model, the purpose of this study is to developing a modified Reynolds equation to investigate the effects of surface roughness and molecular rarefaction on ultra‐thin compressible and isothermal gas lubrication.

Basing upon the average film thickness method with three adjustable coefficients, the higher order slip‐flow velocity distribution was accommodated.

Compared to the smooth case, the longitudinal roughness improves the pressure distribution and load carrying capacity, while the effect of transverse roughness is opposite to that of longitudinal one. The molecular rarefaction effect may diminish the built‐up air bearing pressure and reduce the roughness effect on load carrying capacity. The squeeze number has evident effect in depression of maximum pressure of slider rail with transverse roughness.

Combing the high‐order slip‐flow model and Christensen roughness model, this research paper proposed a feasible study of the analysis of molecular rarefaction effect on slider air‐bearing system.