= Slip length
{title2=$b=\ell_s$}
The <slip length> measures tangential wall mobility in the <Navier slip boundary condition>. Where the wall <shear rate> is nonzero,
$$
b=\frac{u_{\mathrm{rel}}}{\partial_nu}.
$$
The numerator is a <velocity> and the denominator has units $\mathrm{s^{-1}}$, so $b$ has units of length. Geometrically, take a local inward normal coordinate $s$, with the wall at $s=0$. The tangent line to the relative <velocity> profile is
$$
u_{\mathrm{rel,lin}}(s)=u_{\mathrm{rel}}(0)+s\partial_nu(0)
=(b+s)\partial_nu(0).
$$
It reaches zero at $s=-b$, a fictitious distance $b$ inside the solid. This extrapolation does not assert that <fluid> exists there. At a moving wall, extrapolate to the wall's <velocity>, rather than to zero laboratory <velocity>. If both the wall <shear rate> and relative <velocity> vanish, their ratio cannot determine $b$.
The useful comparison is $b/H$, where $H$ is the channel gap. A small absolute <slip length> can noticeably change <volumetric flow rate> in a micrometre-scale channel. Measured effective <slip length> may summarize unresolved interfacial structure; it need not mean literal molecular sliding at every point. The review distinguishes intrinsic, apparent and effective slip and discusses how surface conditions affect measurements. https://arxiv.org/pdf/cond-mat/0501557[Lauga, Brenner and Stone (2005), §§2.2 and 3.1: slip terminology and measurement]{ref}
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