Viscous Control of Peeling an Elastic Sheet by Bending and Pulling

Abstract

Propagation of a viscous fluid beneath an elastic sheet is controlled by local dynamics at the peeling front, in close analogy with the capillary-driven spreading of drops over a precursor film. Here we identify propagation laws for a generic elastic peeling problem in the distinct limits of peeling by bending and peeling by pulling, and apply our results to the radial spread of a fluid blister over a thin prewetting film. For the case of small deformations relative to the sheet thickness, peeling is driven by bending, leading to radial growth as t(7/22). Experimental results reproduce both the spreading behavior and the bending wave at the front. For large deformations relative to the sheet thickness, stretching of the blister cap and the consequent tension can drive peeling either by bending or by pulling at the front, both leading to radial growth as t(3/8). In this regime, detailed predictions give excellent agreement and explanation of previous experimental measurements of spread in the pulling regime in an elastic Hele-Shaw cell.

Analogies between elastic and capillary interfaces

“…1. Similarly, the spreading of droplets under elastic membranes gives rise to interesting dynamics reminiscent of capillary drop spreading [53], and many other examples could be given. A particularly nice example is found for the Cheerios effect [54], i.e., the interaction of particles at a fluid interface, for which elastic counterparts were proposed recently.…”

The speed of an inclined ruck

“…By analogy with fracture mechanics, we demand that the latter is equal to the effective work of adhesion, w. In §4, we determine w by considering the detailed mechanics of how contact and adhesion is actually achieved in three different models. We write the result formally in terms of functions W ± (U) that are yet to be defined 1 2 Bκ 10) so that (2.9) becomes…”

“…The count for the number of far-field boundary conditions that must be imposed for η → ∞ leaves us requiring a single condition for η → −∞, which we take to be g ηηη → 0. Thus, the solution to this peeling problem determines a value for 10) to which the bulk of the ruck must match. For the peeling layer at the back of the ruck, the farfield behaviours are switched around.…”

“…[8,9]) and a number of other fluid mechanical 'peeling' problems (e.g. [10,11]). It demands consideration of a local 'microscopic' model for the two peeling regions, which constitutes the bulk of our analysis.…”

Pursing of planar elastic pockets

“…More recently, Hewitt et al (2015) developed an elastohydrodynamic lubrification theory that characterise deflection of elastic sheets under different conditions. Lister et al (2013) applied an optical method to measure deflection with high resolution along a line when peeling sheets are bent or stretched. The same method was applied by Pihler-Puzović et al (2015) to measure the shape of a circular elastic pocket in the stretching regime as a method of calibration.…”