Concept

Elasticity — where it appears

A solid's give under load, which it returns when the load is removed. Under a squeezed liquid film it stores energy and gives it back late, so it adds a spring to the film's force before it takes anything from the damping.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Elasticity adds a spring at first order and a slip only at second. The damping's deficit, one minus the damping ratio, and the in-phase force against Λ on logarithmic axes. The in-phase force rises in proportion to Λ — a fitted slope of 1.0000 — and the damping's deficit as its square, 2.0000. A slip length changes the damping at first order and adds no spring at all, so a soft wall and a slipping one are distinct in kind: the soft wall announces itself first in the phase of the force.

A soft wall is read as slip only at second order

A drainage force smaller than Taylor's has been read as the liquid slipping at the wall. A wall that gives under the drainage pressure lowers the force too, and it can be mistaken for slip. Solved together, the flow and the elastic wall say how: the softness first adds a spring to the force, in phase with the motion, and only at second order takes anything from the damping a slip length is read from. When it does, the slip it imitates grows as the square of the frequency and falls as the square of the gap.

misconceptions · The no-slip condition

A mica sheet shields the glue's false slip only where the pressed region is narrower than the sheet bends. The slip length, in nanometres, that a dynamic drainage measurement at 100 Hz would read from a wall that does not slip, against the gap: a 3 mm sphere in water over bare glue of plane-strain modulus 1 GPa, and over mica sheets 1, 3 and 5 µm thick on the same glue. At 3 nm the bare glue reads 9.48 nm and the sheets 8.75, 2.68 and 1.06; at 30 nm, 0.1 against 0.099, 0.067 and 0.043.

A mica sheet hides its glue only at the smallest gaps, and changes how the false slip falls

A drainage measurement against a soft wall reads a slip that is not there, falling as the square of the gap. The wall in a surface-force apparatus is not a soft half-space but a stiff mica sheet on a soft glue, and the sheet spreads the drainage pressure over its own bending length before the glue feels it. Where the pressed region is wider than that length the sheet changes nothing; where it is narrower the sheet sinks as one piece, a spring in series with the liquid. That cuts the false slip only by the square of the bending length over the pressed width — threefold at three nanometres for three micrometres of mica — and it turns the slip's fall with the gap from the inverse square towards the inverse, which is the test an experimenter would have used to see it.

misconceptions · The no-slip condition

Named alongside it

The objects these essays reach for when they reach for this one.

Inverse problem Lubrication Measurement Model limit The no-slip condition Reynolds equation Slip Squeeze film Boundary condition

All concepts