 Load-controlled breakdown of weak squeeze-flow compliance

For weakly compliant sphere-plane squeeze flow, the dimensionless upward force is $F=6\pi [-{\dot{H}}_0/H_0+\epsilon ({\ddot{H}}_0/H_0^3-12{\dot{H}}_0^2/(5H_0^4))+\cdots ]$. Under fixed positive load, the leading motion is ${\dot{H}}_0=-A{H}_0$. Its elastic force correction is negative, $-(7/5)\epsilon A^2/H_0^2$, 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 $\epsilon A/H_0^2$ 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.