Stability of Equilibrium States of a Liquid

Capillary surfaces in and around exotic cylinders with application to stability analysis

“…The function is monotonically increasing (Myshkis et al. 1987). The eigenvalue varies monotonically with for fixed mode and this relation between and is called modal monotonicity by Bostwick & Steen (2015).…”

“…In this work, stability is examined by the direct computation method proposed in Myshkis et al. (1987).…”

“…According to the approach of Myshkis et al. (1987), the perturbations are given by It is known that axisymmetric perturbations without a fixed volume constraint are more dangerous than non-axisymmetric ones (Myshkis et al. 1987; Slobozhanin & Alexander 2003).…”

“…(1987), the perturbations are given by It is known that axisymmetric perturbations without a fixed volume constraint are more dangerous than non-axisymmetric ones (Myshkis et al. 1987; Slobozhanin & Alexander 2003). Because the perturbations for the exotic cylinders are unconstrained, only the axisymmetric perturbation needs to be analysed in the study of stability, which leads to an eigenvalue problem (Myshkis et al.…”

“…Because the perturbations for the exotic cylinders are unconstrained, only the axisymmetric perturbation needs to be analysed in the study of stability, which leads to an eigenvalue problem (Myshkis et al. 1987) with where the prime refers to the derivative with respect to and is the dimensionless curvature of the generatrix of the exotic cylinder at the contact point ( if the solid is convex to the liquid). Here, is the arc length of the profile where the meniscus meets the solid.…”