Fig. 3
Sketch of axisymmetric liquid droplet (blue shading) on a viscoelastic substrate (gray shading) with contact line (black dot) and surrounding air phase (white) on a rigid wafer (stripe pattern) and capillary interfaces (black lines). The left side shows the reference domain (Lagrangian) \(\Omega ^0\) and the right side shows the deformed configuration (Eulerian) \(\Omega\) and all referential and deformed interfaces \(\Gamma _{ij}(t)=\varvec{\chi }(t,\Gamma ^0_{ij})\) for \(i,j\in \{\textrm{a},\ell , \textrm{s}, \textrm{w}\}\). The (deformed) droplet radius R is indicated by a white dashed line. We denote the solid contact angle between \(\Gamma _\textrm{as}\) and \(\Gamma _{\ell \textrm{s}}\) by \(\vartheta _\textrm{s}\) and the liquid contact angle between \(\Gamma _{\ell \textrm{s}}\) and \(\Gamma _\mathrm{a\ell }\) by \(\vartheta _\ell\). The substrate is initially flat \(\Omega ^0_\textrm{s}=\{\varvec{x}\in \mathbb {R}^3:0\le z\le 1\}\) and the liquid droplet is the half of an ellipsoid \(\Omega ^0_\ell =\{\varvec{x}\in \mathbb {R}^3:\nicefrac {r^2}{r_x^2} + \nicefrac {(z-H)^2}{r_z^2}\le 1 \text { and }z\ge H\}\) with \(\varvec{x}=(x,y,z)\) and \(r^2=x^2+y^2\). The substrate is supported by a rigid wafer \(\Omega ^0_\textrm{w}=\{\varvec{x}\in \mathbb {R}^3:z\le 0\}\) surrounded by an ambient air domain \(\Omega ^0_\textrm{a}=\mathbb {R}^3\setminus (\Omega _\textrm{s}\cup \Omega _\textrm{w}\cup \Omega _\ell )\).
