No abstract

When rollers, placed horizontally and side by side so that each is half immersed in a tank of liquid, rotate in opposite directions, liquid is carried through the gap between them and divides to form a sheet over each roller. At low speeds the sheets are of uniform thickness across the width of the rollers, but at higher speeds they are regularly ridged owing to alternate increase and decrease in thickness. Preliminary observations led to the development of an approximate theoretical treatment of the even-flow régime and the critical conditions when the ribbed flow is about to begin. Results of this work are in full agreement with detailed experimental results.

The nature of photogenerated cross-links in solid poly(vinyl cinnamate) is investigated. Hydrolysis of irradiated films and subsequent chromatography of the hydrolysis products show that the principal matrix reaction is cycloaddition between polymer-bound cinnamoyl groups. The overall quantum yield of the cross-linking reaction decreases during irradiation and the reaction virtually stops while half of the potentially reactive chromophores are still intact. Since all cinnamoyl groups are identical in structure, the lack of reactivity of some must be attributed to their environment. This suggests a description of the matrix in terms of chromophore sites, where the reactive groups are considered together with their immediate surroundings. Sites are characterized by their reaction probability and by geometry. The distribution of site reactivities in the ensemble may be derived from the dependence of the quantum yield of the photoreaction on chromophore conversion. The distribution of chromophore configurations at the sites is inferred from the distribution of cyclic isomers in the final products. Product analysis after cycloaddition may thus be used as a probe into the micromorphology of the polymer matrix.

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

We consider a drop of liquid hanging from a horizontal support and sandwiched between two vertical plates separated by a very narrow gap. Equilibrium profiles of such ‘two-dimensional’ drops were calculated by Neumann (1894) for the case when the angle of contact between the liquid and the horizontal support is zero. This paper gives the equilibrium profiles for other contact angles and the criterion for their stability. Neumann showed that, as the drop height increases, its cross-sectional area increases until a maximum is reached. Thereafter, as the height increases, the equilibrium area decreases. This behaviour is shown to be typical of all contact angles. When the maximum area is reached, the total energy is a minimum. It is shown that the drops are stable as long as the height and the area increase together.