Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Series

The no-slip condition — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The air a wing carries along, and how little of it there is. The Blasius profile, in the wing's frame, with the free stream at one. No slip says the air at the surface is at rest relative to the surface, which in the ground's frame means it is moving with the wing — but only exactly at the wall. The deficit, integrated across the layer, is the displacement thickness: at a Reynolds number of 1e+6 and a metre of chord it is 1.72 millimetres of air moving at flight speed, which is the whole of what is 'carried'. The step drawn on the axis is that same deficit as a solid slab. A wing does not drag a blanket of air with it; it leaves a boundary layer behind it, and the layer is made of air that keeps being replaced.

    The air a wing does not carry

    No slip says the air touching a surface moves with it, and the usual reading is that a wing drags a blanket of air along. The blanket is 1.7 millimetres thick per metre of chord, it is different air every instant, and the drag it costs falls as it gets thicker.

    part 1 · misconceptions
  2. A force that depends on the molecular scale only through its logarithm. The force per unit length needed to move a 30° contact line of water at 1 mm/s, out to 1 mm, against the slip length on a logarithmic axis, from a picometre to a tenth of a millimetre. Each tenfold change in the slip length moves the force by the same fixed amount, so eight decades of the most uncertain length in the problem change the answer by a factor of about twenty — and at zero slip length the line keeps rising without end. The dashed curve takes the exact wedge's angle factor with a sharp cutoff; the solid one the thin-film wedge with Navier slip.

    The drop a no-slip wall would never let spread

    Liquid touching a solid moves with it, and nearly everywhere that is as close to exact as anything in fluid mechanics. At the edge of a spreading drop it cannot be: the stress in the corner rises as one over the distance from the edge, and the force needed to move the edge is infinite. Something slips over a nanometre, and because the answer depends on that length only through its logarithm, a drop spreads at almost the same rate whatever the something is.

    part 2 · misconceptions

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