The present study is concerned with estimating the inertial effects on the draining of thin fluid layer between two parallel plane boundaries. In particular, we consider the case in which an initially stationary object with a circular plane lower surface begins suddenly moving under the action of a constant applied force toward a parallel plane wall when the inertia of the object and that of the intervening fluid in the gap are not negligible. The method of solution is a matched asymptotic expansion involving characterization of the solution by different characteristic time scales in different parts of the solution domain in the limit of small but finite Reynolds number based on the gap height. The asymptotic solution is presented for the time-dependent motion of the object and the fluid in the thin film including a proper description of the effects of both the inertia of the object and the inertia of the fluid.

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