The tearing of an adhesive layer between flexible tapes pulled apart

Abstract

The tearing of a pressure-sensitive (‘tacky’) adhesive is examined. Two flexible strips bonded by a layer of adhesive are passed between adjacent cylindrical guides and peeled apart, causing the adhesive layer to separate into two about a surface tension membrane. Treating the adhesive as a Newtonian viscous fluid, the slow-flow problem is solved by an iterative numerical scheme in which the surface tension membrane boundary in the vicinity of the region of separation is approximated by a shear-free boundary given by a sixth-degree polynomial expression. The energy dissipation rate, a measure of the ‘strength’ of the adhesive, is obtained from the flow.The solution method is also used to determine the similar flow induced by two counter-rotating rollers partially immersed in a large bath of fluid. The results are in fairly good agreement with available experimental data. The symmetrical eddies observed under the lowest point of the surface tension membrane in the stable flow between the rollers are reproduced in the solution, proving that fluid inertia effects are not essential for their existence.

Interfacial Shape and Evolution Equations for Liquid Films and Other Viscocapillary Flows

“…The interrelationships of these approaches were examined recently (Higgins et al, (1977). Some other areas where essentially the same strategy can be identified are studies of viscous peeling (Williamson, 1972), partially submerged bearings (Coyne and Elrod, 1970), thin-film flows (Wilkes and Nedderman, 1962;Ruschak, 1978) stability of falling liquid films (Kapitza, 1948; Massot et al, 1966;Krantz and Goren, 1971), motion of bubbles in tubes and channels (Bretherton, 1961; Gardner and Adebiyi, 1974), dynamics of viscous sheets (Brown, 1960;Yeow, 1974). These are summarized in Table I, a guide to the previous work.…”

“…Table I lists upstream end point conditions used by various authors. Excepting Williamson (1972), all have in effect supposed that viscous stresses on the meniscus in the upstream zone are negligible, for all have supposed that the meniscus shape there satisfies the Young-Laplace equation of interfacial statics (3.7) or a linearization of it. When there is strong recirculation in the upstream region, as in the viscous peeling flow analyzed by Williamson (1972), or when there is a moving contact line, as in the capillary displacement flow analyzed by Huh and Mason (1977) and Silliman and Scriven (1979), it appears that more careful treatment is required.…”

“…Excepting Williamson (1972), all have in effect supposed that viscous stresses on the meniscus in the upstream zone are negligible, for all have supposed that the meniscus shape there satisfies the Young-Laplace equation of interfacial statics (3.7) or a linearization of it. When there is strong recirculation in the upstream region, as in the viscous peeling flow analyzed by Williamson (1972), or when there is a moving contact line, as in the capillary displacement flow analyzed by Huh and Mason (1977) and Silliman and Scriven (1979), it appears that more careful treatment is required. This Williamson (1972) accomplished by patching a fully two-dimensional numerical solution of the creeping flow equation system for the recirculation region to his approximate equation of interfacial shape; he matched meniscus location, slope, and curvature where the two representations overlap.…”

Theory of Meniscus Shape in Film Flows. A Synthesis

“…Examples are given in Table II. The original derivations by Landau and Levich (1942), White and Tallmadge (1965), Williamson (1972), Spiers et al (1974), and Lee and Tallmadge (1975,1976) were circuitous and incorporated assumptions along the way. In some cases the resulting formula is inconsistent because it retains terms of the same order as others that are omitted.…”

“…In some cases the resulting formula is inconsistent because it retains terms of the same order as others that are omitted. The inconsistency of Williamson (1972) and Spiers et al (1974) in replacing (9) by dp/dy = 0 while retaining dU/dy in (12) was first pointed out by Esmail and Hummel (1975a), who attempted to rectify the matter by using an integral approach (see next section) to include further terms.…”