Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

In this paper, the effects of an air bubble on the Newtonian squeeze film characteristics between two circular parallel plates with sinusoidal relative motion are theoretically investigated by considering the fluid film inertia effects. In the derivation of the lubrication equation, a single central air bubble of a cylindrical shape is considered. Approximating the momentum equation governing the squeeze film flow by the mean value averaged across the film thickness and assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained. The nonlinear differential equation is solved by the Runge-Kutta-Gill method, and then the squeeze film force is determined. Moreover, the analytical solutions for the air bubble radius and pressure distribution are derived based on the perturbation method for a small amplitude of sinusoidal motion, and the analytical results are compared with the numerical results. From the calculated results, the combined effects of air bubble and fluid film inertia on the squeeze film force are clarified.