Pattern Formation during Deformation of a Confined Viscoelastic Layer: From a Viscous Liquid to a Soft Elastic Solid

We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system [poly(dimethylsiloxane) with different degrees of cross-linking] allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called “elastic” with interfacial crack propagation, where the fingering wavelength scales only with the film thickness, and a bulk regime called “viscoelastic,” where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and present a reduced parameter describing the transition between the two regimes and allowing us to predict the observed patterns over the whole range of viscoelastic properties.

Figure 1

The storage and loss moduli $G^{\prime }$ (solid symbols) and $G^{\prime \prime }$ (open symbols) as a function of the frequency $\omega$ for different amounts of curing agent.

Figure 2

Left side: Schematic view of the “probe tack” experiment. Right side: Interfacial crack propagation and bulk deformation mechanisms.

Figure 3

Formation of air fingers in the elastic and viscoelastic cases: (a) interfacial crack propagation and (b) bulk deformation.

Figure 4

Left side, viscoelastic case: $\lambda$ depends on $b$ and $v$. $\square =350\mu \mathrm{m}$, $\blacksquare =230\mu \mathrm{m}$, $◯=120\mu \mathrm{m}$, and $▴=60\mu \mathrm{m}$. Right side, elastic case: $\lambda$ depends only on $b$. $\square =300\mu \mathrm{m}$, $◯=130\mu \mathrm{m}$, and $▴=70\mu \mathrm{m}$. The black lines are a guide for the eye.

Figure 5

In the viscoelastic case, the wavelength scales linearly with the thickness and is inversely proportional to the square root of the capillary number.

Figure 6

In the case of interfacial crack propagation, the wavelength scales only with the thickness $b$. The solid line is a straight line fit to the data yielding $\lambda =2.3b$.

Figure 7

Open symbols represent bulk deformation and black solid symbols interfacial crack propagation. Experiments right at the transition can show both mechanisms due to fluctuations in the sample preparation.