We experimentally study the impacts of viscous, immiscible oil drops into a deep pool of water.

We report the results of a numerical and theoretical study of buckling in elastic columns containing a line of holes. Buckling is a common failure mode of elastic columns under compression, found over scales ranging from metres in buildings and aircraft to tens of nanometers in DNA. This failure usually occurs through lateral buckling, described for slender columns by Euler’s theory. When the column is perforated with a regular line of holes, a new buckling mode arises, in which adjacent holes collapse in orthogonal directions. In this paper, we firstly elucidate how this alternate hole buckling mode coexists and interacts with classical Euler buckling modes, using finite-element numerical calculations with bifurcation tracking. We show how the preferred buckling mode is selected by the geometry, and discuss the roles of localized (hole-scale) and global (column-scale) buckling. Secondly, we develop a novel predictive model for the buckling of columns perforated with large holes. This model is derived without arbitrary fitting parameters, and quantitatively predicts the critical strain for buckling. We extend the model to sheets perforated with a regular array of circular holes and use it to provide quantitative predictions of their buckling.

The presence of ambient air in liquid-slamming events plays a crucial role in influencing the shape of the liquid surface prior to the impact, and the distribution of loads created upon impact. We study the effect of trapped air on impact loads in a simplified geometry, by slamming a horizontal flat disc onto a stationary water bath at a well-controlled velocity. We show how air trapping influences pressure peaks at different radial locations on the disc, how the pressure impulses are affected and how local pressure impulses differ from those obtained from area-integrated (force) impulses at impact. More specifically, we find that the air layer causes a gradual buildup of the load before the peak value is reached, and show that this buildup follows inertial scaling. Further, the same localised pressure impulse at the disc centre is found to be lower than the corresponding (area-integrated) force impulse on the entire disc. While the (area-integrated) force impulses are close to the classical result of Batchelor (An Introduction to Fluid Dynamics, Cambridge University Press, 1967, § 6.10) and Glasheen & McMahon (Phys. Fluids, vol. 8, issue 8, 1996, pp. 2078–2083), the localised pressure impulses at the disc centre, where the trapped air layer is at its thickest, lie closer to the theoretical estimation by Peters et al. (J. Fluid Mech., vol. 724, 2013, pp. 553–580) for an air-cushioned impact.

Nederlandse titel: De inslag van vloeistoffen en de invloed van de omringende lucht