1 Correction to: Meccanica (2017) 52:3481–3487 https://doi.org/10.1007/s11012-017-0618-0

We have found two mistakes in Eqs. (13) and (14) of Ref. [1], which we wish to correct. We note that these errors did not produce significant effects on the subsequent numerical analysis, because the corrective term only introduces a negligible contribution to the solution in the region of interest of the parameters.

The error in Eq. (13) is simply a misprint and does not affect the rest of the paper. The correct version of Eq. (13) is

$$\begin{aligned} \left( {w_{f}} - {w_{a}} - \frac{{\partial }w_{f}}{{\partial }{\theta ^{\prime}}} {\theta ^{\prime}} \right) \delta {\bar{S}}= 0. \end{aligned}$$
(1)

Since this equation is requested to vanish for any \(\delta {\bar{S}}\), with the use of Eqs. (5) of Ref. [1], we obtain

$$\begin{aligned}&- k [{\theta ^{\prime}}(\bar{S})]^2 + b[({\lambda ^{-}} -{1})^2 - ({\lambda ^{+}} -{1})^2] \nonumber \\&\quad + 2 \mu ({\lambda ^{+}} - {\lambda ^{-}}) + 2 w {\lambda ^{+}} = 0 \end{aligned}$$
(2)

where \({\lambda ^{-}} = 1 + \mu /b\) and \({\lambda ^{+}} = \bar{\lambda }\). Furthermore, Eq. (12) of Ref. [1] leads to \(\mu = b (\bar{\lambda }- 1) - w\), which inserted into (2) yields the correct version of Eq. (14)

$$\begin{aligned} - k [\theta '({\bar{S}})]^2 + 2 {\bar{\lambda }}w - \frac{w^{2}}{b}= 0. \end{aligned}$$
(3)

This can be further simplified using the elasto-capillary length \(\ell _{ec}\) so that (3) rewrites as

$$\begin{aligned} - k [\theta '({\bar{S}})]^{2} + 2 {\bar{\lambda }}w - w \frac{\ell ^{2}}{\ell _{ec}^{2}}= 0. \end{aligned}$$
(4)

In §3 of Ref. [1] we studied the case \({\ell ^{2}}/{\ell _{ec}^{2}} \simeq 1.37 \times 10^{-5}\), so that the corrective term contribution is negligible. We are grateful to Jun Zhong for his remarks.