Erratum to: Modeling of complex interfaces for pendant drop experiments

Abstract

The original version of this article unfortunately contained mistakes. Theo A. Tervoort was not listed among the authors. The correct information is given above. In Balemans et al. (2016), an axisymmetric finite element model is presented to study the behaviour of complex interfaces in pendant drop experiments. While the bulk fluid of the pendant drop is modeled as a Newtonian fluid, the interface behaviour is described using a quasi-linear Kelvin-Voigt constitutive model. To study the influence of the five model parameters of this constitutive model, a parameter study is performed. Furthermore, small amplitude oscillatory measurements are simulated to demonstrate the applicability of the numerical model. The quasi-linear two-dimensional Kelvin-Voigt viscoelastic constitutive equation as proposed by Verwijlen et al. (2014) and used in Balemans et al. (2016) is not material frame indifferent, because the Cauchy-Green deformation tensor Cs is directly coupled to the surface stress tensor ς. Instead the Finger tensor Bs should be used to construct a material frame indifferent constitutive equation. The correct formulation of the quasi-linear twodimensional Kelvin-Voigt constitutive equation becomes (Formula presented.) where J = det(Bs). The constitutive equation has both viscous and elastic properties, and all simulations for Balemans et al. (2016) have been repeated after implementation of Eq. 1 into the numerical model. The results show minor differences for small deformations and small values of the surface elasticity parameters. However, the results presented in Figure 18 (only K = 100 μN/mm) and Figure 21 are significantly different. These deviating results are summarized in Fig. 1, where the apex length in time for G = 1, 10, 50, 100 μN/mm is shown at a surface tension γ = 50 μN/mm, surface dilatational viscosity κ = 1 μNs/mm, surface shear viscosity μ = 1 μNs/mm, and surface dilatational elasticityK = 100 μN/mmas presented before using the Cauchy-Green tensor Cs (dotted lines) and with the use of the Finger tensor Bs (solid lines). Using the new results, Figures 18 and 21 of the article by Balemans et al. (2016) should be replaced with Figs. 2 and 3, respectively. The conclusions of the article do not change. (Figure presented.).