A simple model of the adhesive failure of a layer: Cohesive effects

Abstract

A fine-scale model is developed for the removal of an adhesive layer by a uniform stress. The initial motivation of this modeling project was a description of the removal of a layer of filter cake from cylindrical filters by backpulse cleaning. The model includes the bonding forces of adhesion between the layer and a substrate, as well as the forces of cohesion between imaginary “gridblocks’’ within the layer. For stresses greater than a threshold value, some of the layer is removed, with the fraction removed depending upon the stress, the average adhesive and cohesive forces, and the distribution of these forces about their average. The cohesive forces reduce the threshold well below the average strength of the adhesive force, because they increase the stress near broken adhesive bonds. The cohesive forces also sharpen the threshold in the cleaning pressure significantly, so that the threshold is very much sharper than the distribution of adhesive strengths. For moderate filter cake thickness (moderately strong cohesive forces), the threshold becomes steplike, with no cleaning just below the threshold and complete cleaning at the threshold and above. The model also provides the pressure dependence of the size and shape distributions for the fragments of the filter cake layer removed from the filter, enabling the model to address questions of cleaning efficiency, “patchy cleaning,’’ re-entrainment, and trapping of large cake-fragments in the filter vessel.