arXiv subjects

Dominic Vella

Publications and source records attributed to Dominic Vella.

At least 55 records · Page 3Linked to original sources

arXiv2020

Dynamic buckling of elastic rings in a soap film

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 non-trivial 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.

cond-mat.soft↗

arXiv2020

Dynamics of wrinkling in ultrathin elastic sheets

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 ultra-thin polymer sheet floating on water. The vertical deflection of the sheet's centre induced by impact draws material radially inwards, 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 quasi-static 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 new controls of wrinkle wavelength.

cond-mat.soft↗

arXiv2020

Impact on floating thin elastic sheets: A mathematical model

We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time $t$ after impact, the transverse wave is located at a radial distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim t^{2/3}$ scaling observed for capillary--inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor, but subsequently addressing a finite-radius spherical impactor, contrasting this case with the classic Wagner theory of impact. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the geometrically-imposed compression without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments, and we compare our predictions with experimental data.

cond-mat.soft↗

arXiv2019

Limitations of curvature--induced rigidity: How a curved strip buckles under gravity

The preference of thin flat sheets to bend rather than stretch, combined with results from Geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal direction inhibits bending in the other: so-called curvature-induced rigidity. Here, we study the buckling behaviour of a rectangular strip of finite thickness held horizontally in a gravitational field, but with a transverse curvature imposed at one end. The finite thickness of the sheet limits the efficacy of curvature-induced rigidity in two ways: (i) finite bending stiffness acts to `uncurve' the sheet, even if this costs some stretching energy, and (ii) for sufficiently long strips, finite weight deforms the strip downwards, releasing some of its gravitational potential energy. We find the critical imposed curvature required to prevent buckling (or, equivalently, to rigidify the strip), determining the dependence on geometrical and constitutive parameters, as well as describing the buckled shape of the strip well beyond the threshold for buckling. In doing so, we quantify the intuitive understanding of curvature-induced rigidity that we gain from curving the crust of a slice of pizza to prevent it from drooping downwards as we eat.

cond-mat.soft↗

arXiv2019

Wettability-independent droplet transport by \emph{Bendotaxis}

We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful means of transporting droplets in technological applications, for example in developing self-cleaning surfaces, and discuss the implications of our results for such applications.

cond-mat.soft↗

arXiv2019

Elasto-capillary adhesion: The effect of deformability on adhesion strength and detachment

We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the equilibrium adhesive force for this elastocapillary adhesive is significantly enhanced in comparison to the capillary adhesion between rigid plates. In particular, the equilibrium adhesion force is orders of magnitude greater when the membrane is sufficiently deformed to contact the substrate. From a dynamic perspective, however, the formation of a fluid-filled dimple slows this approach to contact and means that stable attachment is only achieved if adhesion is maintained for a minimum time. The inclusion of a variable membrane tension (as a means of modifying the deformability) gives additional control over the system, allowing new detachment strategies to be explored.

physics.flu-dyn↗

arXiv2018

Dynamics of viscoelastic snap-through

We study the dynamics of snap-through when viscoelastic effects are present. To gain analytical insight we analyse a modified form of the Mises truss, a single-degree-of-freedom structure, which features an `inverted' shape that snaps to a `natural' shape. Motivated by the anomalously slow snap-through shown by spherical elastic caps, we consider a thought experiment in which the truss is first indented to an inverted state and allowed to relax while a specified displacement is maintained; the constraint of an imposed displacement is then removed. Focussing on the dynamics for the limit in which the timescale of viscous relaxation is much larger than the characteristic elastic timescale, we show that two types of snap-through are possible: the truss either immediately snaps back over the elastic timescale or it displays `pseudo-bistability', in which it undergoes a slow creeping motion before rapidly accelerating. In particular, we demonstrate that accurately determining when pseudo-bistability occurs requires the consideration of inertial effects immediately after the indentation force is removed. Our analysis also explains many basic features of pseudo-bistability that have been observed previously in experiments and numerical simulations; for example, we show that pseudo-bistability occurs in a narrow parameter range at the bifurcation between bistability and monostability, so that the dynamics is naturally susceptible to critical slowing down. We then study an analogous thought experiment performed on a continuous arch, showing that the qualitative features of the snap-through dynamics are well captured by the truss model. In addition, we analyse experimental and numerical data of viscoelastic snap-through times reported in the literature. Combining these approaches suggests that our conclusions may also extend to more complex viscoelastic structures used in morphing applications.

cond-mat.soft↗

arXiv2018

Pull-in dynamics of overdamped microbeams

We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down considerably. This slowing down is highly sensitive to external forces, and so has widespread potential for applications that use pull-in time as a sensing mechanism, including high-resolution accelerometers and pressure sensors. Previously, the bottleneck phenomenon has only been understood using lumped mass-spring models that do not account for effects such as variable residual stress and different boundary conditions. We extend these studies to incorporate the beam geometry, developing an asymptotic method to analyse the pull-in dynamics. We attribute bottleneck behaviour to critical slowing down near the pull-in transition, and we obtain a simple expression for the pull-in time in terms of the beam parameters and external damping coefficient. This expression is found to agree well with previous experiments and numerical simulations that incorporate more realistic models of squeeze film damping, and so provides a useful design rule for sensing applications. We also consider the accuracy of a single-mode approximation of the microbeam equations --- an approach that is commonly used to make analytical progress, without systematic investigation of its accuracy. By comparing to our bottleneck analysis, we identify the factors that control the error of this approach, and we demonstrate that this error can indeed be very small.

physics.app-ph↗

arXiv2018

Regimes of wrinkling in an indented floating elastic sheet

A thin, elastic sheet floating on the surface of a liquid bath wrinkles when poked at its centre. We study the onset of wrinkling as well as the evolution of the pattern as indentation progresses far beyond the wrinkling threshold. We use tension field theory to describe the macroscopic properties of the deformed film and show that the system passes through a host of different regimes, even while the deflections and strains remain small. We show that the effect of the finite size of the sheet ultimately plays a key role in determining the location of the wrinkle pattern, and obtain scaling relations that characterize the number of wrinkles at threshold and its variation as the indentation progresses. Some of our predictions are confirmed by recent experiments of Ripp \emph{et al.} [arxiv: 1804.02421].

cond-mat.soft↗

arXiv2018

Static bistability of spherical caps

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two `self-equilibrated' states, one natural and the other inside out (or `everted'). Though this is familiar from everyday life -- an umbrella is remarkably stable, yet a contact lens can be easily turned inside out -- the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more `robust' to snap-through. Our work sheds new light on the robustness of the `mirror buckling' symmetry of spherical shell caps.

cond-mat.soft↗

arXiv2018

Partial wetting of thin solid sheets under tension

We consider the equilibrium of liquid droplets sitting on thin elastic sheets that are subject to a boundary tension and/or are clamped at their edge. We use scaling arguments, together with a detailed analysis based on the Föppl-von-Kármán equations, to show that the presence of the droplet may significantly alter the stress locally if the tension in the dry sheet is weak compared to an intrinsic elasto-capillary tension scale $γ^{2/3}(Et)^{1/3}$ (with $γ$ the droplet surface tension, $t$ the sheet thickness and $E$ its Young modulus). Our detailed analysis suggests that some recent experiments may lie in just such a "non-perturbative" regime. As a result, measurements of the tension in the sheet at the contact line (inferred from the contact angles of the sheet with the liquid--vapour interface) do not necessarily reflect the true tension within the sheet prior to wetting. We discuss various characteristics of this non-perturbative regime.

cond-mat.soft↗

arXiv2017

The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling'

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by `mirror buckling' --- a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformation is then localized in a ridge in which the deformed and undeformed portions of the shell join together, commonly referred to as Pogorelov's ridge. Rather than using an energy formulation, we revisit this problem from the point of view of the shallow shell equations and perform an asymptotic analysis that exploits the largeness of the indentation depth. This reveals first that the stress profile associated with mirror buckling is singular as the indenter is approached. This consequence of point indentation means that mirror buckling must be modified to incorporate the shell's bending stiffness close to the indenter and gives rise to an intricate asymptotic structure with seven different spatial regions. This is in contrast with the three regions (mirror-buckled, ridge and undeformed) that are usually assumed and yields new insight into the large compressive hoop stress that ultimately causes the shell to buckle azimuthally.

cond-mat.soft↗

arXiv2017

Using evaporation to control capillary instabilities in micro-systems

The instabilities of fluid interfaces represent both a limitation and an opportunity for the fabrication of small-scale devices. Just as non-uniform capillary pressures can destroy micro-electrical mechanical systems (MEMS), so they can guide the assembly of novel solid and fluid structures. In many such applications the interface appears during an evaporation process and is therefore only present temporarily. It is commonly assumed that this evaporation simply guides the interface through a sequence of equilibrium configurations, and that the rate of evaporation only sets the timescale of this sequence. Here, we use Lattice-Boltzmann simulations and a theoretical analysis to show that, in fact, the rate of evaporation can be a factor in determining the onset and form of dynamical capillary instabilities. Our results shed light on the role of evaporation in previous experiments, and open the possibility of exploiting diffusive mass transfer to directly control capillary flows in MEMS applications.

cond-mat.soft↗

arXiv2017

Delayed pull-in transitions in overdamped MEMS devices

We consider the dynamics of overdamped MEMS devices undergoing the pull-in instability. Numerous previous experiments and numerical simulations have shown a significant increase in the pull-in time under DC voltages close to the pull-in voltage. Here the transient dynamics slow down as the device passes through a meta-stable or bottleneck phase, but this slowing down is not well understood quantitatively. Using a lumped parallel-plate model, we perform a detailed analysis of the pull-in dynamics in this regime. We show that the bottleneck phenomenon is a type of critical slowing down arising from the pull-in transition. This allows us to show that the pull-in time obeys an inverse square-root scaling law as the transition is approached; moreover we determine an analytical expression for this pull-in time. We then compare our prediction to a wide range of pull-in time data reported in the literature, showing that the observed slowing down is well captured by our scaling law, which appears to be generic for overdamped pull-in under DC loads. This realization provides a useful design rule with which to tune dynamic response in applications, including state-of-the-art accelerometers and pressure sensors that use pull-in time as a sensing mechanism. We also propose a method to estimate the pull-in voltage based only on data of the pull-in times.

physics.app-ph↗

arXiv2017

Critical slowing down in purely elastic `snap-through' instabilities

Many elastic structures have two possible equilibrium states: from umbrellas that become inverted in a sudden gust of wind, to nano-electromechanical switches, origami patterns and the hopper popper, which jumps after being turned inside-out. These systems typically transition from one state to the other via a rapid `snap-through'. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions, as in the Venus flytrap. Similarly, the beak of the hummingbird snaps through to catch insects mid-flight, while technological applications are increasingly exploiting snap-through instabilities. In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. Here, we study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena, and provides a handheld demonstration of such phenomena, as well as a new tool for tuning dynamic responses in applications of elastic bistability.

cond-mat.soft↗

arXiv2017

Passive control of viscous flow via elastic snap-through

We demonstrate the passive control of viscous flow in a channel by using an elastic arch embedded in the flow. Depending on the fluid flux, the arch may `snap' between two states --- constricting and unconstricting --- that differ in hydraulic conductivity by up to an order of magnitude. We use a combination of experiments at a macroscopic scale and theory to study the constricting and unconstricting states, and determine the critical flux required to transition between them. We show that such a device may be precisely tuned for use in a range of applications, and in particular has potential as a passive microfluidic fuse to prevent excessive fluxes in rigid-walled channels.

cond-mat.soft↗

arXiv2017

Indentation of a floating elastic sheet: Geometry versus applied tension

The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth. For small indentation depths, we find that the force--indentation curve is linear with a stiffness that we characterize in terms of the applied tension and bending stiffness of the sheet. At larger indentations the force--indentation curve becomes nonlinear and the sheet is subject to a wrinkling instability. We study this wrinkling instability close to the buckling threshold and calculate both the number of wrinkles at onset and the indentation depth at onset, comparing our theoretical results with experiments. Finally, we contrast our results with those previously reported for very thin, highly bendable membranes.

cond-mat.soft↗

arXiv2017

Non-wetting drops at liquid interfaces: From liquid marbles to Leidenfrost drops

We consider the flotation of deformable, non-wetting drops on a liquid interface. We consider the deflection of both the liquid interface and the droplet itself in response to the buoyancy forces, density difference and the various surface tensions within the system. Our results suggest new insight into a range of phenomena in which such drops occur, including Leidenfrost droplets and floating liquid marbles. In particular, we show that the floating state of liquid marbles is very sensitive to the tension of the particle-covered interface and suggest that this sensitivity may make such experiments a useful assay of the properties of these complex interfaces.

cond-mat.soft↗