The solutions of Navier–Stokes equations in squeezing flow between parallel plates

The velocity profile in a layer of viscous Newtonian fluid between two parallel plates, where one plate is immobile and other is either moving away or moving to the first one, is studied. The distance between plates changes in time according to a power-law: h∼|t|sh∼|t|s. Precise solutions of the Navier–Stokes equations are constructed as series in powers of Reynolds number. The cases of uniform motion (s=1s=1) of the plates and uniformly accelerated motion (s=2s=2) are studied in detail. For the case h∼t the series is convergent, in other cases the series is asymptotic. The critical Reynolds number corresponding to the appearance of counterflow is also determined.

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