As pointed out by recent works [14], the velocity appearing in the Boussinesq-Scriven constitutive equation [5] for the viscous interfacial stress is the three-dimensional fluid velocity evaluated on the interface, including both the tangential and normal components to that surface. Previous studies (see, e.g., Refs. [68]) have erroneously interpreted this velocity as the two-dimensional velocity resulting from the projection of the fluid velocity onto the interface, which can lead to significant errors for high interface curvatures. Besides, there are works in which it is not clear whether the velocity in the Boussinesq-Scriven equation was misinterpreted as explained above, or the authors were implicitly assuming that the surface was always flat when that equation was invoked (see, e.g., Refs. [9] and [10]).

The above consideration implies that in Eq. (28) of the review, $vS$ should be the fluid velocity $v$ evaluated on the free surface, including both the tangential and normal components. In addition, Eqs. (29) and (30) should read [1,4]
$τnS=OhsSκ¯[−F(vtF)s+κ¯vn]+OhdSκ[(Fvt)sF+κvn]$
(1)
$τt1S=[(OhsS+OhdS)((Fvt)sF+κvn)]s+2(OhsSK¯−(OhsS)sFsF)vt−2κ1(OhsSvn)s$
(2)

where $κ¯=κ1−κ2, K¯=κ1κ2$, and vn and vt are the normal and tangential components of the velocity on the free surface, respectively.

The error described above affects Fig. 38 of the review. We have recalculated the evolution of the liquid bridge according to Eqs. (1) and (2). The results are plotted in Fig. 1. The major qualitative conclusion obtained from this figure still holds. As stated in the review, surface viscosities enhance the accumulation of surfactant in the central part of the liquid bridge.

Fig. 1
Fig. 1

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