Dynamic buckling may occur when a load is rapidly applied to, or removed from, an elastic object at rest. In contrast to its static counterpart, dynamic buckling offers a wide range of accessible patterns depending on the parameters of the system and the dynamics of the load. To study these effects, we consider experimentally the dynamics of an elastic ring in a soap film when part of the film is suddenly removed. The resulting change in tension applied to the ring creates a range of interesting patterns that cannot be easily accessed in static experiments. Depending on the aspect ratio of the ring's cross section, high-mode buckling patterns are found in the plane of the remaining soap film or out of the plane. Paradoxically, while inertia is required to observe these nontrivial modes, the selected pattern does not depend on inertia itself. The evolution of this pattern beyond the initial instability is studied experimentally and explained through theoretical arguments linking dynamics to pattern selection and mode growth. We also explore the influence of dynamic loading and show numerically that, by imposing a rate of loading that competes with the growth rate of instability, the observed pattern can be selected and controlled.

The wrinkling of thin elastic objects provides a means of generating regular patterning at small scales in applications ranging from photovoltaics to microfluidic devices. Static wrinkle patterns are known to be governed by an energetic balance between the object’s bending stiffness and an effective substrate stiffness, which may originate from a true substrate stiffness or from tension and curvature along the wrinkles. Here, we investigate dynamic wrinkling induced by the impact of a solid sphere onto an ultrathin polymer sheet floating on water. The vertical deflection of the sheet’s center induced by impact draws material radially inward, resulting in an azimuthal compression that is relieved by the wrinkling of the entire sheet. We show that this wrinkling is truly dynamic, exhibiting features that are qualitatively different to those seen in quasistatic wrinkling experiments. Moreover, we show that the wrinkles coarsen dynamically because of the inhibiting effect of the fluid inertia. This dynamic coarsening can be understood heuristically as the result of a dynamic stiffness, which dominates the static stiffnesses reported thus far, and allows control of wrinkle wavelength.

Thin glass sheets may be manufactured using a two-part process in which a sheet is first cast and then subsequently reheated and drawn to a required thickness. The latter redrawing process typically results in a sheet with non-uniform thickness and with smaller width than the cast glass block. Experiments suggest that the loss of width can be minimized and the non-uniformities can be essentially confined to thickening at the sheet edges if the heater zone through which the glass is drawn is made very short. We present a three-dimensional mathematical model for the redraw process and consider the limits in which (i) the heater zone is short compared with the sheet width, and (ii) the sheet thickness is small compared with both of these length scales. We show that, in the majority of the sheet, the properties vary only in the direction of drawing and the sheet motion is one-dimensional, with two-dimensional behaviour and the corresponding thick edges confined to boundary layers at the sheet extremities. We present numerical solutions to this boundary-layer problem and demonstrate good agreement with experiment, as well as with numerical solutions to the full three-dimensional problem. We show that the final thickness at the sheet edge scales with the inverse square root of the draw ratio, and explore the effect of tapering of the ends to identify a shape for the initial preform that results in a uniform rectangular final product.

Abstract. When a hazardous chemical agent has soaked into a porous medium, such as concrete, 4it can be difficult to neutralise. One removal method is chemical decontamination, where a cleanser 5 is applied to react with and neutralise the agent, forming less harmful reaction products. There are 6 often several cleansers that could be used to neutralise the same agent, so it is important to identify 7 the cleanser features associated with fast and effective decontamination. As many cleansers are 8 aqueous solutions while many agents are immiscible with water, the decontamination reaction often 9 takes place at the interface between two phases. In this paper, we develop and analyse a mathematical 10 model of a decontamination reaction between a neat agent and an immiscible cleanser solution. We 11 assume that the reaction product is soluble in both the cleanser phase and the agent phase. At the 12 moving boundary between the two phases, we obtain coupling conditions from mass conservation 13 arguments and the oil-water partition coefficient of the product. We analyse our model using both 14 asymptotic and numerical methods, and investigate how different features of a cleanser affect the time 15 taken to remove the agent. Our results reveal the existence of two regimes characterised by different 16 rate-limiting transport processes, and we identify the key parameters that control the removal time 17 in each regime. In particular, we find that the oil-water partition coefficient of the reaction product 18 is significantly more important in determining the removal time than the effective reaction rate. 19