Topographic de-adhesion in the viscoelastic limit

Abstract

The superiority of many natural surfaces at resisting soft, sticky biofoulants have inspired the integration of dynamic topography with mechanical instability to promote self-cleaning artificial surfaces. The physics behind this novel mechanism is currently limited to elastic biofoulants where surface energy, bending stiffness and topographical wavelength are key factors. However, the viscoelastic nature of many biofoulants causes a complex interplay between these factors with time-dependent characteristics such as material softening and loading rate. Here, we enrich the current elastic theory of topographic de-adhesion using analytical and finite-element models to elucidate the nonlinear, time-dependent interaction of three physical, dimensionless parameters: biofoulant's stiffness reduction, the product of relaxation time and loading rate, and the critical strain for short-term elastic de-adhesion. Theoretical predictions, in good agreement with numerical simulations, provide insight into tuning these control parameters to optimize surface renewal via topographic de-adhesion in the viscoelastic regime.

Keywords: biofoulants; de-adhesion; finite-element simulations; topography; viscoelastic; wrinkle.

Figure 1.

Topography-driven delamination motivated by dynamically actuated wrinkled surface in artery. (a) A three-dimensional view of biofoulants attached to the arterial luminal wrinkles. The SEM images show that the arterial wrinkle surface is covered with platelets and thromboses at an early stage. The schematic drawing of the artery provides a continuum model for their interaction that has been proposed in previous works [–10] at the stage where biofoulants grow and expand over multiple wrinkle wavelengths. (b) Cross-sectional views of the postulated detachment process of biofoulants from the wrinkled topography at different levels of actuated pulse pressure through the cardiac cycle illustrated in black on the right. During systole (top), the high pressure distends the artery and flattens the luminal wrinkling. As the cardiac cycle progresses, the arterial pressure drops gradually until the diastolic pressure (bottom) is reached. As the pressure decreases, the artery contracts and the amplitude of the wrinkles grows. The cardiac cycle then repeats when the left ventricle again contracts pumping blood into the arterial system. Current attempts with experiment and computational modelling focus on elastic behaviours of the biofoulant and show a scaling dependence of the critical surface curvature on the surface energy, bending stiffness and topographic geometrical wavelength [8].

Figure 2.

Delamination processes under increasing applied strain $ϵ$ of a slowly relaxing viscoelastic foulant layer (a–c) when compared with a fast relaxing viscoelastic foulant layer (d–f). The latter conforms more stably to the wrinkled topography and requires a higher strain $ϵ=0.12$ (f) than the former $ϵ=0.05$ (b) to cause its detachment.

Figure 3.

Compression of a viscoelastic foulant layer attached to a bilayer for studying wrinkle-induced delamination. (a) Schematics of a thin viscoelastic foulant layer attached to a bilayer system composed of a thin film on top of a substrate subjected to increasing compression. The bilayer wrinkles, which induces a wrinkle pattern on the foulant layer. As the wrinkle curvature increases κ = A/λ², the foulant layer starts to de-adhere from the bilayer. Here, A and λ are the wrinkle amplitude and wavelength. (b) Energy balance approach shows the dependence of the critical strain on three controlling dimensionless parameters. Two representative values of ${ϵ}_{\mathrm{de}}$ and three representative values of E_∞/E₀ are selected for plotting here. Note that when E_∞/E₀ = 1.0, the result of the elastic foulant layer [8] is reproduced as shown by the horizontal, flat curves. In these cases, the critical strain is equal to ${ϵ}_{\mathrm{de}}$ and is independent of $\dot{ϵ}{\tau }_R$.

Figure 4.

Normalized ratio (or the slope/pre-factor a in the scaling law: ${ϵ}_c-{ϵ}_w=a{\lambda }^{2}G/B_p$) versus L_pz. Various values of E_p are examined. The flat line is a fit showing the linear scaling as predicted from scaling analysis which results in a slope of the same order as the one computed for the elastic foulant layer [8] (a ≈ 0.025, see electronic supplementary material, appendix 3).

Figure 5.

Finite-element results show how the three controlling dimensionless parameters affect the critical strain (a) and general fits to collapse numerical and analytical data (b). Four marker types (downward pointing triangle, square, diamond and circle) correspond to four loading rates $\dot{ϵ}/{\dot{ϵ}}_{\mathrm{el}}=0.75,1,1.5,2$, respectively, used in FE simulations, where ${\dot{ϵ}}_{\mathrm{el}}$ is the loading rate adopted from the FE simulations in the previous study for elastic foulant layer [8] (see electronic supplementary material, appendix 3). Open and closed markers are for E_∞/E₀ = 0.5 and E_∞/E₀ = 0.25, respectively. Increasing levels of grey colour of the markers for the numerical data correspond to increasing values of ${ϵ}_{\mathrm{de}}$; however, the colour code and line styles in (b) for the analytical results are consistent with figure 3b.