arXiv subjects

Dominic Vella

Publications and source records attributed to Dominic Vella.

At least 37 records · Page 2Linked to original sources

arXiv2022

Substrate Curvature Curbs the Coffee Ring Effect

"When the liquid phase of a particle-laden droplet evaporates, a ring of solute is typically formed - what has become known as the "coffee ring effect". A key focus of recent work has been the suppression of the coffee-ring effect to leave behind more spatially-uniform particle coatings instead. Efforts to suppress the coffee ring effect often focus on physical effects such as Marangoni flows. Here we focus on a purely geometric effect - the effect of substrate curvature - by evaporating suspension droplets on spherical surfaces of different radius of curvature. We find that stains formed on more highly curved substrates are more uniform. To understand this, we propose a model of the evaporation-induced flow, combined with a detailed calculation of how curvature modifies the local evaporation rate. This model shows that evaporation in the centre of the droplet is enhanced, leading to increased concentration of solute there and a reduction in the propensity for ring-formation.

physics.flu-dyn↗

arXiv2022

Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat 'skirt' region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

cond-mat.soft↗

arXiv2022

Bendocapillary Instability of Liquid in a Flexible-Walled Channel

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a `weaving' pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods, and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are always unstable to perturbations of sufficiently small wavenumber, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

physics.flu-dyn↗

arXiv2022

Delamination from an adhesive sphere: Curvature-induced dewetting versus buckling

Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates -- what is a petty frustration when placing a sticky bandage onto an elbow or knee is a more serious matter in the coating and painting industries. Irrespective of their resistance to bending, a key driver of such phenomena is Gauss' \textit{Theorema Egregium}, which implies that naturally flat sheets cannot conform to doubly-curved surfaces without developing a strain whose magnitude grows sharply with the curved area. Previous attempts to characterize the onset of curvature-induced delamination, and the complex patterns it gives rise to, assumed a dewetting-like mechanism in which the propensity of two materials to form contact through interfacial energy is modified by an elastic energy penalty. We show that this approach may characterize moderately bendable adhesive sheets, but fails qualitatively to describe the curvature-induced delamination of ultrathin films, whose mechanics is governed by their propensity to buckle under minute levels of compression. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination that accounts for two elementary buckling motifs, shallow "rucks" and localized "folds". We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experimental observations. Beyond gaining control on the use of ultrathin adhesives in cutting edge technologies such as stretchable electronics, our analysis is a significant step towards quantifying the multiscale morphological complexity that emerges upon imposing geometrical and mechanical constraints on highly bendable solid objects.

cond-mat.soft↗

arXiv2022

Shape-morphing structures based on perforated kirigami

Shape-morphing structures, which are able to change their shapes from one state to another, are important in a wide range of engineering applications. A popular scenario is morphing from an initial two-dimensional (2D) shape that is flat to a three-dimensional (3D) target shape. One of the exciting manufacturing paradigms is transforming flat 2D sheets with prescribed cuts (i.e. kirigami) into 3D structures. By employing the formalism of the 'tapered elastica' equation, we develop an inverse design framework to predict the shape of the 2D cut pattern that would generate a desired axisymmetric 3D shape. Our previous work has shown that tessellated 3D structures can be achieved by designing both the width and thickness of the cut 2D sheet to have particular tapered designs. However, the fabrication of a sample with variable thickness is quite challenging. Here we propose a new strategy -- perforating the cut sheet with tapered width but uniform thickness to introduce a distribution of porosity. We refer to this strategy as perforated kirigami and show how the porosity function can be calculated from our theoretical model. The porosity distribution can easily be realized by laser cutting and modifies the bending stiffness of the sheet to yield a desired elastic deformation upon buckling. To verify our theoretical approach, we conduct finite element simulations and physical experiments. We also examine the loading-bearing capacity of morphed structures via indentation tests in both FEM simulations and experiments. As an example, the relationship between the measured geometric rigidity of morphed half-ellipsoids and their aspect ratio is investigated in details.

cond-mat.soft↗

arXiv2022

Droplets on Lubricated Surfaces: The slow dynamics of skirt formation

A key question in the interaction of droplets with lubricated and liquid-infused surfaces is what determines the apparent contact angle of droplets. Previous work has determined this using measured values of the geometry of the `skirt' -- the meniscus-like deformation that forms around the base of the deposited droplet. Here, we consider theoretically the equilibrium of a droplet on a smooth, impermeable lubricant-coated surface, and argue that the small effect of gravity within the skirt and the size of the substrate are important for determining the final equilibrium. However, we also show that the evolution of the skirt towards this ultimate equilibrium is extremely slow (on the order of days for typical experimental parameter values). We therefore suggest that previous experiments on smooth lubricated surfaces may have observed only slowly-evolving transients, rather than `true' equilibria, potentially explaining why a wide range of skirt sizes have been reported.

cond-mat.soft↗

arXiv2022

Effect of Macroscopic Surface Heterogeneities on an Advancing Contact Line

The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular defects introduced as arrays of cocoa butter patches or small circular holes. These heterogeneous surfaces were submerged into aqueous ethanol solutions, while measuring the additional force arising from the deformation of the advancing contact line and characterising the interface shape and its pinning on the defects. Initially, the submersion force is linear with submerged depth, suggesting a constant defect-induced stiffness. This regime ends when the contact line de pins from the defects. A simple scaling is proposed to describe the depinning force and the depinning energy. We find that, as the defect separation increases, the interface stiffness increases too, with a weak dependency on the defect radius. This interaction between defects cannot be captured by the simple scaling, but can be well predicted by a theory considering the interface deformation in presence of periodic arrays of holes. Creating a 4-phase contact line, by including solid defects (cocoa butter) reduced pinning forces. The radius of the defect had a nonlinear effect on the depinning depth. The 4-phase contact line resulted in depinning before the defects are fully submerged. These experimental results and the associated theory help understanding quantitatively the extent to which surface heterogeneities can slow down wetting. This in turn paves the way to tailor the design of heterogeneous surfaces, towards desired wetting performances.

cond-mat.mtrl-sci↗

arXiv2022

Compression of a pressurized spherical shell by a spherical or flat probe

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere, or compression between two plates. Previously, different theoretical approaches have been developed to retrieve material parameters (e.g. elastic modulus) or state variables (e.g. pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

physics.bio-ph↗

arXiv2022

Droplet trapping in bendotaxis caused by contact angle hysteresis

Passive droplet transport mechanisms, in which continuous external energy input is not required for motion, have received significant attention in recent years. Experimental studies of such mechanisms often ignore, or use careful treatments to minimize, contact angle hysteresis, which can impede droplet motion, or even arrest it completely. Here, we consider the effect of contact angle hysteresis on bendotaxis, a mechanism in which droplets spontaneously deform an elastic channel via capillary pressure and thereby move. Here, we seek to understand when contact angle hysteresis prevents bendotaxis. We supplement a previous mathematical model of the dynamics of bendotaxis with a simple model of contact angle hysteresis, and show that this model predicts droplet trapping when hysteresis is sufficiently strong. By identifying the equilibrium configurations adopted by these trapped droplets and assessing their linear stability, we uncover a sensitive dependence of bendotaxis on contact angle hysteresis and develop criteria to describe when droplets will be trapped.

physics.flu-dyn↗

arXiv2021

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis

We consider the effect of droplet geometry on the early-stages of coffee ring formation during the evaporation of a thin droplet with an arbitrary simple, smooth, pinned contact line. We perform a systematic matched asymptotic analysis of the small-capillary number, large-solutal Peclet number limit for two evaporative models: a kinetic model, in which the evaporative flux is constant across the droplet, and a diffusive model, in which the evaporative flux is singular at the contact line. For both evaporative models, solute is transported to the contact line by a capillary flow while, local to the contact line, solute diffusion counters advection. The resulting interplay leads to the formation of the nascent coffee ring. By exploiting a coordinate system embedded in the contact line, we solve explicitly the local leading-order problem, deriving a similarity profile (in the form of a gamma distribution) that describes the coffee ring profile in its early stages. Notably, the ring characteristics change due to the concomitant asymmetry in the shape of the droplet free surface, the evaporative flux (in the diffusive evaporative regime) and the mass flux into the contact line. We utilize the asymptotic model to determine the effects of geometry on the growth of the coffee ring for a droplet with an elliptical contact set. Our results offer mechanistic insight into the effect of contact-line curvature on the development of the coffee-ring from deposition up to jamming of the solute; moreover our model predicts when finite concentration effects become relevant.

physics.flu-dyn↗

arXiv2021

Liquid bridge splitting enhances normal capillary adhesion and resistance to shear on rough surfaces

The effect of 'bridge splitting' is considered in the case of capillary adhesion: for a fixed total volume of liquid, does having more capillary bridges increase the total adhesion force? Previous studies have shown that the capillary-induced adhesion force between two planar surfaces is only substantially enhanced by bridge splitting in specific circumstances. Here this previous result is reconsidered, and it is shown that bridge splitting may significantly increase the adhesion forces when one of the surfaces is rough. The resistance to shear is also examined, and it is shown that bridge splitting on a rough surface can lead to a steady capillary-induced shear force that scales linearly with translation velocity, even in the absence of contact-line pinning.

physics.flu-dyn↗

arXiv2021

The nascent coffee ring: how solute diffusion counters advection

We study the initial evolution of the coffee ring that is formed by the evaporation of a thin, axisymmetric, surface tension-dominated droplet containing a dilute solute. When the solutal Péclet number is large, we show that diffusion close to the droplet contact line controls the coffee-ring structure in the initial stages of evaporation. We perform a systematic matched asymptotic analysis for two evaporation models -- a simple, non-equilibrium, one-sided model (in which the evaporative flux is taken to be constant across the droplet surface) and a vapour-diffusion limited model (in which the evaporative flux is singular at the contact line) -- valid during the early stages in which the solute remains dilute. We call this the `nascent coffee ring' and describe the evolution of its features, including the size and location of the peak concentration and a measure of the width of the ring. Moreover, we use the asymptotic results to investigate when the assumption of a dilute solute breaks down and the effects of finite particle size and jamming are expected to become important. In particular, we illustrate the limited validity of this model in the diffusive evaporative flux regime.

physics.flu-dyn↗

arXiv2021

Deformable and robust core-shell protein microcapsules templated by liquid-liquid phase separated microdroplets

Microcapsules are a key class of microscale materials with applications in areas ranging from personal care to biomedicine, and with increasing potential to act as extracellular matrix (ECM) models of hollow organs or tissues. Such capsules are conventionally generated from non-ECM materials including synthetic polymers. Here, we fabricated robust microcapsules with controllable shell thickness from physically- and enzymatically-crosslinked gelatin and achieved a core-shell architecture by exploiting a liquid-liquid phase separated aqueous dispersed phase system in a one-step microfluidic process. Microfluidic mechanical testing revealed that the mechanical robustness of thicker-shell capsules could be controlled through modulation of the shell thickness. Furthermore, the microcapsules demonstrated environmentally-responsive deformation, including buckling by osmosis and external mechanical forces. A sequential release of cargo species was obtained through the degradation of the capsules. Stability measurements showed the capsules were stable at 37 °C for more than two weeks. Finally, all-aqueous liquid-liquid phase separated and multiphase liquid-liquid phase separated systems were generated with the gel-sol transition of microgel precursors. These smart capsules are promising models of hollow biostructures, microscale drug carriers, and building blocks or compartments for active soft materials and robots.

cond-mat.soft↗

arXiv2020

Validity of Winkler's mattress model for thin elastomeric layers: Beyond Poisson's ratio

Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness that depends on the problem under consideration.

cond-mat.soft↗

arXiv2020

Delayed bifurcation in elastic snap-through instabilities

We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. We study when and how the arch transitions between states and show that the end-shortening at which the fast 'snap' happens depends on the rate at which the end-shortening is reduced. This lag in snap-through is a consequence of delayed bifurcation and occurs even in the perfectly elastic case when viscous (and viscoelastic) effects are negligible. We present the results of numerical simulations to determine the magnitude of this lag as the loading rate and the importance of external viscous damping vary. We also present an asymptotic analysis of the geometrically-nonlinear problem that reduces the salient dynamics to that of an ordinary differential equation; the form of this reduced equation is generic for snap-through instabilities in which the relevant control parameter is ramped linearly in time. Moreover, this asymptotic reduction allows us to derive analytical results for the observed lag in snap-through that are in good agreement with the numerical results of our simulations. Finally, we discuss scaling laws for the lag that should be expected in other examples of delayed bifurcation in elastic instabilities.

cond-mat.soft↗

arXiv2020

Indentation of two-dimensional solids: The signatures of geometrical and material nonlinearity

The material characterization of ultra-thin solid sheets, including two-dimensional materials like graphene, is often performed through indentation tests on a flake suspended over a hole in a substrate. While this `suspended indentation' is a convenient means of measuring properties such as the stretching (two-dimensional) modulus of such materials, experiments on ostensibly similar systems have reported very different material properties. In this paper, we present a modelling study of this indentation process assuming elastic behaviour. In particular, we investigate the possibility that the reported differences may arise from different geometrical parameters and/or non-Hookean deformations, which lead to the system exploring nonlinearities with geometrical or material origins.

cond-mat.mtrl-sci↗

arXiv2020

The compression of a heavy floating elastic film

We study the effect of film density on the uniaxial compression of thin elastic films at a liquid--fluid interface. Using a combination of experiments and theory, we show that dense films first wrinkle and then fold as the compression is increased, similarly to what has been reported when the film density is neglected. However, we highlight the changes in the shape of the fold induced by the film's own weight and extend the model of Diamant and Witten [Phys.Rev.Lett. 2011, 107, 164302, arXiv:1107.5505] to understand these changes. In particular, we suggest that it is the weight of the film that breaks the up-down symmetry apparent from previous models, but elusive experimentally. We then compress the film beyond the point of self-contact and observe a new behaviour dependent on the film density: the single fold that forms after wrinkling transitions into a closed loop after self-contact, encapsulating a cylindrical droplet of the upper fluid. The encapsulated drop either causes the loop to bend upward or to sink deeper as compression is increased, depending on the relative buoyancy of the drop-film combination. We propose a model to qualitatively explain this behaviour. Finally, we discuss the relevance of the different buckling modes predicted in previous theoretical studies and highlight the important role of surface tension in the shape of the fold that is observed from the side -- an aspect that is usually neglected in theoretical analyses.

cond-mat.soft↗

arXiv2020

Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses

Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal pressure have emerged as a theoretical and experimental paradigm for the study of dynamic buckling with controlled loads. Experimentally, an elastic ring is placed within a soap film. When the film outside the ring is removed, surface tension pulls the ring inward, mimicking an external pressurization. Here we present a theoretical analysis of this process by performing a post-bifurcation analysis of an elastic ring under pressure. This analysis allows us to understand how inertia, material properties, and loading affect the observed shape. In particular, we combine direct numerical solutions with a post-bifurcation asymptotic analysis to show that inertia drives the system towards higher modes that cannot be selected in static buckling. Our theoretical results explain experimental observations that cannot be captured by a standard linear stability analysis.

cond-mat.soft↗