The lubrication approximation in analysing flow fields makes use of the geometrical properties of the flow field that it is long in the flow direction and narrow in a direction transverse to it. This “slenderness” of the flow field has as a consequence that the orders of magnitude of the velocities and their spatial derivatives in the two coordinate directions are very different. A narrow flow field allows both effects of the inertia of the fluid and derivatives of viscous stress in the main flow direction to be neglected in the momentum balance, so that the flow is dominated by an equilibrium of pressure and viscous forces. What is essentially solved, therefore, are the Stokes equations. We first derive the lubrication approximation and then discuss some flows of this kind with technical relevance.
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