Viscoelastic and Poroelastic Relaxations of Soft Solid Surfaces

Understanding surface mechanics of soft solids, such as soft polymeric gels, is crucial in many engineering processes, such as dynamic wetting and adhesive failure. In these situations, a combination of capillary and elastic forces drives the motion, which is balanced by dissipative mechanisms to determine the rate. While shear rheology (i.e., viscoelasticity) has long been assumed to dominate the dissipation, recent works have suggested that compressibility effects (i.e., poroelasticity) could play roles in swollen networks. We use fast interferometric imaging to quantify the relaxation of surface deformations due to a displaced contact line. By systematically measuring the profiles at different time and length scales, we experimentally observe a crossover from viscoelastic to poroelastic surface relaxations.

Figure 1

Interferometric imaging. (a) Schematic showing major components of the imaging system, including a monochromatic LED light source ($\lambda \pm \mathrm{\Delta }\lambda =643\pm 22\mathrm{nm}$), the sample stage ($S$) with a capillary tube ($C$) to deposit the liquid, a reference mirror ($M$), two focusing lenses ($L1$ and $L2$), and a beam splitter ($B$). (b)–(e) Series of unprocessed interference images from the gel surface after forced dewetting at $t=0$. Scale bar: $100\mu \mathrm{m}$. (f) Surface profile just before dewetting ($t<0$) obtained by confocal microscopy (black dots) and surface profiles after dewetting ($t=0.2$, 0.4, 1.0, 3.0, and 10.0 s) reconstructed from interferograms (colored dots). Inset: Enlarged $t>0$ data.

Figure 2

Variation of relaxation dynamics with waiting time and deformation sizes. (a) Relaxation plots of the ridge height and dimple depth measured in experiments for a 1.1 mm radius droplet. Inset: Interference image showing the “dimple.” Scale bar: $100\mu \mathrm{m}$. (b) Theoretical calculation results of the ridge and dimple relaxations based on power-law rheology. (c) Measured $h(t)/h_0$ for different wetting liquids (water and fluorinated oil). (d) Measured ridge height $h$ versus time $t$ for various water droplet radii $R$.

Figure 3

Quantifying poroelastic response. (a) Relaxation of normal force after indentation. Measured normalized force $\mathrm{\Delta }\overline{F}$ versus time $t$ for different indentation depths $h_p$ on soft gels (solid dots) and solvent-extracted (“dry”) networks (hollow dots). (b) Force relaxation data of the gels from (a) collapsed by normalizing time with $R_p{h}_p$. Inset: Schematic of the indentation experiments. (c) Surface profile data from Fig. 1 collapsed by normalizing the height by $h_0$ and time by $R{h}_0$.

Figure 4

Dominance of viscoelasticity at small length scales and short times. (a)–(c) Series of raw interference images showing the relaxation of the substrate after a $21\mu \mathrm{m}$ radius glycerol droplet has been removed by flooding. We define $L$ as the maximum deformation of the fringes due to the presence of liquid droplets, and the initial deformation is indicated by $L_0$. Scale bar: $50\mu \mathrm{m}$. (d) Plots of $L/L_0$ versus $t$ for different sizes of droplets on soft gels. The error bars indicate the uncertainty in determining $L$ from the image analysis.