Molecular model for wall slip: role of convective constraint release

Abstract

A tube model is proposed for predicting wall slip phenomenon driven by the interfacial "disentanglement" mechanism. We model the dynamics of tethered chains, which are grafted on a high-energy wall and are entangled with the bulk chains flowing past them. The starting point of our model is the contour variable model (Mead; et al. Macromolecules 1998, 31, 7895), from which we develop a constitutive equation for tethered chains. We show that while the bulk chains are able to relax their orientation in the intermediate shear rate regime by the convective constraint release (CCR) mechanism, the tethered chains experience a highly restricted CCR that is unable to randomize its flow-induced orientation above a critical shear rate or stress. This decreases the resistance to flow for the bulk chains, which suddenly slip past the oriented tethered chains. The model correctly predicts the molecular weight dependence of the slip length, critical slip velocity and critical wall shear stress. It also quantitatively predicts the slip length and the critical slip velocity for a PDMS melt for which valuable molecular level experimental data are available in the literature.