Viscous Control of Peeling an Elastic Sheet by Bending and Pulling

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.

Figure 1

Schematic of the model and experimental setup.

Figure 2

Asymptotic, numerical and experimental profiles of the elastic blister at $t/\tau =1$. (a) Asymptotic and numerical solutions for $ϵ\equiv h_0/L_h=0.001$. Inset shows the peeling-by-bending traveling-wave solution $F$ to (4). (b) Experimental profiles for $ϵ=0.035$, 0.054, 0.151, and 0.175, with other experimental parameters detailed in Ref. 17, and numerical solutions for $ϵ=0.5,\dots ,0.001$. Inset shows the scaled experimental profiles at the blister edge for $ϵ=0.035$ and 0.054 with numerical solutions for $ϵ=0.03$ and 0.1.

Figure 3

Numerical and experimental results, with similarity solutions (6, 7) for $ϵ=0.001$. (a) Dimensionless radius with time. (b) Dimensionless height at the origin with time.

Figure 4

Collapse of experimental data from a Hele-Shaw cell with an elastic wall [5]. The raw data are the same as in their Fig. 2a, and is replotted with approximately corresponding symbols for a range of flow rates $Q$ [${\mathrm{cm}}^3{\min }^{-1}$], sheet thickness $d$ (their $h$), and prewetting film thickness $h_0$; $h_0/d$ varies from 0.57 to 1.7. See Ref. 5 for details. An average value $1/\delta \simeq 30$ was used when evaluating the line $0.748t^{3/8}$ from (18).