Diffusive–stochastic–viscoelastic model for specific adhesion of viscoelastic solids via molecular bonds

A diffusive–stochastic–viscoelastic model is proposed for the specific adhesion of viscoelastic solids via stochastically formed molecular bonds. In this model, it is assumed that molecular-level behaviors, including the diffusion of mobile adhesion molecules and stochastic reaction between adhesion molecules and binding sites, are Markovian stochastic processes, while the mesoscopic deformation of the viscoelastic media is governed by continuum mechanics. Systematic Monte Carlo simulations of this model are used to investigate how competition between the time scales of molecular diffusion, reaction, and deformation creep of the solids may influence the lifetime and dynamic strength of their adhesion. The results reveal that there exists an optimal characteristic time for molecular diffusion corresponding to the longest lifetime and greatest adhesion strength, which is in good agreement with experimentally observed characteristic time scales of molecular diffusion in cell membranes. In addition, the results show that the viscosity of the media can significantly increase the lifetime and dynamic strength, since deformation creep and stress relaxation can effectively reduce the concentration of interfacial stress and increase the rebinding probability of molecular bonds.