Improved Muller approximate solution of the pull-off of a sphere from a viscoelastic substrate

TL;DR

This paper improves Muller's approximate solution for the sphere detachment problem from viscoelastic substrates, providing a more accurate model that aligns well with numerical results across various withdrawal speeds.

Contribution

The authors revise Muller's solution, offering a more precise fitting method that accurately predicts contact radius and pull-off behavior over a wide range of speeds.

Findings

Improved fit of the contact radius at pull-off across speeds

Accurate convergence to JKR value at low speeds

Enhanced agreement with numerical simulations

Abstract

The detachment of a sphere from a viscoelastic substrate is clearly a fundamental problem. In the case viscoelastic dissipation is concentrated at the contact edge, and the work of adhesion follows a quite popular simplified model, Muller has suggested an approximate solution, which however is based on an empirical observation. We revisit Muller's solution and show it leads to very poor fitting of the actual full numerical results, particularly for the radius of contact at pull-off, and we suggest an improved fitting of the pull-off which works extremely well over a very wide range of withdrawing speeds, and correctly converges to the JKR value at very low speeds.