= Cusp flow between touching cylinders
{title2=$\mathcal A=w^3/(3a),\quad\kappa=2a/w^2$}
On one side of two touching cylinders of radius $a$, the leading gap is $d(x)=x^2/a$. A completely wetting semicircular meniscus at $x=w\ll a$ has radius $w^2/(2a)$ and suction $p=-2\gamma a/w^2$. The area is $\mathcal A=\int_0^wd(x)dx=w^3/(3a)$ to leading order. Integrating the local slit <Poiseuille flow> gives $Q=-w^7p_z/(84\mu a^3)=-\gamma w^4w_z/(21\mu a^2)$. Thus $(w^3)_t=\gamma(w^4w_z)_z/(7\mu a)$.
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