Tear-off versus global existence for a structured model of adhesion mediated by transient elastic linkages

TL;DR

This paper analyzes a microscopic model of friction involving transient elastic linkages, proving conditions for both finite and infinite existence of solutions, which correspond to tear-off or sustained adhesion.

Contribution

It establishes existence and uniqueness of solutions under weaker hypotheses, including cases with unbounded off-rate functions, and identifies conditions for global adhesion.

Findings

Finite existence time corresponds to tear-off.

Under certain conditions, solutions exist globally, indicating sustained adhesion.

The model accommodates unbounded off-rate functions.

Abstract

We consider a microscopic model for friction mediated by transient elastic linkages introduced in [V. Milisic and D. Oelz. SIAM J. on Math. Anal. (2015). V. Milisic and D. Oelz. J. Math. Pures Appl. (2011)]. In the present study we prove existence and uniqueness of a solution to the coupled system under weaker hypotheses. The theory we present covers the case where the off-rate of linkages is unbounded but increasing at most linearly with respect to the mechanical load. The time of existence is typically bounded and corresponds to tear-off where the moving binding site does not have any bonds with the substrate. However, under additional assumptions on the external force we prove global in time existence of a solution that consequently stays attached to the substrate.