= Load-controlled breakdown of weak squeeze-flow compliance
{title2=$H_0^*\sim\sqrt{\varepsilon A},\quad A=F/(6\pi)$}
For <weakly compliant sphere-plane squeeze flow>, the dimensionless upward <force> is $F=6\pi[-\dot H_0/H_0+\varepsilon(\ddot H_0/H_0^3-12\dot H_0^2/(5H_0^4))+\cdots]$. Under fixed positive load, the leading motion is $\dot H_0=-AH_0$. Its elastic force correction is negative, $-(7/5)\varepsilon A^2/H_0^2$, so weak compliance initially increases the approach speed. Pressure indents the wall and widens the gap, reducing squeeze resistance. The perturbation loses uniform validity when $\varepsilon A/H_0^2$ becomes order one. This is also when the elastic deflection becomes comparable to the nominal gap; it does not by itself prove contact or breakdown of the slender-gap approximation.
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