Drops on soft solids: Free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $\gamma/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $\gamma/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $\gamma/ER \gg 1$. The elastic deformations are worked out in the simplifying case where the solid surface energy is assumed constant. The total free energy turns out lower on softer substrates, consistent with recent experiments

Symmetric and Asymmetric Coalescence of Drops on a Substrate

The coalescence of viscous drops on a substrate is studied experimentally and theoretically. We consider cases where the drops can have different contact angles, leading to a very asymmetric coalescence process. Side view experiments reveal that the "bridge" connecting the drops evolves with self-similar dynamics, providing a new perspective on the coalescence of sessile drops. We show that the universal shape of the bridge is accurately described by similarity solutions of the one-dimensional lubrication equation. Our theory predicts a bridge that grows linearly in time and stresses the strong dependence on the contact angles. Without any adjustable parameters, we find quantitative agreement with all experimental observations.Comment: 5 pages, 4 figure

Організація взаємодії слідчих та оперативних служб ОВС при розкритті й розслідуванні злочинів, пов’язаних із викраденням людей

Досліджується проблема організації взаємодії слідчих та оперативних служб при розкритті та розслідуванні злочинів, пов’язаних з викраденням людей.Исследуется проблема организации взаимодействия следователей и оперативных служб при раскрытии и расследовании преступлений, связанных с похищением людей.The problem of the organization of interoperability of inspectors and operative services at disclosing and investigation of the crimes connected with kidnapping

Werkgelegenheid en gespreide verantwoordelijkheid

Gesprek met als thema: Wat moet de inzet van het CDA zijn op sociaal-economisch terrein bij de komende verkiezingen voor de Tweede Kame