Surface Elasticity Research Articles

A new model for spatial rods incorporating surface energy effects

A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.

Influence of Surface Roughness on Interfacial Properties of Particle Networks

The behavior of colloidal particles near fluid interfaces has attracted significant scientific interest, as particles minimize the contact area between the two fluid phases, stabilizing interfacial systems. This study explores the influence of surface roughness on the properties of particle monolayers at the air–water interface, focusing on colloidal silica particles and fumed silica particles of similar hydrodynamic diameter. This research involves comparing low-surface-area (LSA) and medium-surface-area (MSA) fumed silica particles with spherical colloidal silica particles (250 nm in diameter). Utilizing a Langmuir trough, the interfacial particle networks are compressed and expanded. Analysis of surface pressure isotherms reveals that fumed silica particle monolayers form networks at a lower particle surface coverage compared to spherical particles. The spherical particle monolayer exhibits a higher apparent surface elasticity, indicating greater resistance to the applied compression compared to fumed silica networks. Additionally, monolayers formed by fumed silica particles display hysteresis even after successive compressions and expansions due to irreversible particle interlocking and the formation of multilayered aggregates. These findings provide insights into the impact of surface roughness on the behavior of particle monolayers at fluid interfaces, offering valuable information for designing and optimizing mechanisms involved in emulsion and foam stabilization.

Sensing touch location on an elastic surface by monitoring structural vibrations

In recent years, touchscreens have become ubiquitous, and projected capacitance (p-cap) has arisen as the dominant touch-sensing technology. Though powerful, p-cap has some characteristics that make it less suited for certain applications. Active acoustic sensing (AAS) systems work by sensing the vibration response of an elastic surface to a system-generated excitation and associating specific response characteristics with touch locations on the surface. These systems have the potential to offer advantages over p-cap in terms of scalability, cost, and performance in harsh environments. AAS systems may also offer the ability to sense touch pressure as an additional input parameter. We developed an empirical model of surface vibrational response as a function of the location of an applied force and then used this model to inform the signal processing and machine learning approaches employed in a prototype AAS system. In this presentation, we provide results from our empirical model as well as details of the prototype system, including its construction and performance.

Plastic deformation effect on contact behaviour in granular materials

Contact tests on machined and natural granite showed that extensive plastic deformation which extends to the core shape is happening before the cross-over from the behaviour of an elastic rough surface to the Hertzian behaviour of an elastic smooth contact when all asperities have yielded in the surface. The plastic deformation, which was found to take place when the estimated maximum stresses at the contact reaches about 0.6 of the material hardness, affects the behaviour during normal loading as the material will start to deform at constant stiffness after reaching these stresses. The plastic deformation during lateral loading also affects the applicability of lateral loading models. The data yielded a much lower lateral stiffness which is around one order of magnitude less than that predicted by the available contact models.

Odd elasticity and topological waves in active surfaces.

Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.

Bending edge wave on a functionally graded fluid‐saturated porous magneto‐electro‐elastic plate

AbstractThis study investigates the localized wave propagation at the free edge of a thin semi‐infinite Magneto‐Electro‐Elastic (MEE) plate. The plate is supported by a two‐parameters elastic foundation. Biot's porosity theory is considered to formulate the porosity in the model, and the pore structure is saturated with an incompressible fluid. The Kirchhoff–Love plate theory determines the plate displacement field. A non‐homogeneity in the material parameters is considered, which varies with the spatial coordinate along the thickness direction of the plate. In order to illustrate the impacts of the surface elements on bending wave propagation, the model incorporates the surface elasticity theory. The short circuit boundary conditions are implemented to derive the general form of the potential function connected with the electric and magnetic fields, respectively. The dispersion relation for bending edge wave on a MEE fluid‐saturated porous plate is obtained by considering a sinusoidal waveform, which propagates along the free edge of the plate. A numerical method named Finite Difference (FD) scheme is employed to analyze the stability of the numerical scheme and also extract the expression of the velocity profiles of the bending edge wave in the absence of the pore structure. The impacts of the various parameters included in the considered model are examined using a numerical example, from which conclusions regarding their sensitivity are derived.

On the incremental equations in surface elasticity

We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau–Rayleigh and Wilkes instabilities in a solid cylinder.

Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity

Boundary Value Problems in a Theory of Bending of Thin Micropolar Plates with Surface Elasticity

Flow and irreversible mechanism of pure and hybridized non-Newtonian nanofluids through elastic surfaces with melting effects

Abstract The significance of nanofluid research in nanotechnology, pharmaceutical, drug delivery, food preparation, and chemotherapy employing single- and two-phase nanofluid models has drawn the attention of researchers. The Tiwari–Das model does not capture the diffusion and random movement of nanoparticles (NPs) when they are injected into complex functional fluids. In order to fix the peculiar behavior of NPs, more complex models like the Buongiorno model are coupled with the single-phase model. To examine the heat-mass transfer attributes of nanofluids, a single- and two-phase mixture model is coupled for the first time. The effect of hybrid NPs on the hemodynamic properties of the blood flow through a stretched surface with interface slip in the neighborhood of the stagnation point is examined. Due to their significance in medicinal uses and nominal toxicity, blood is loaded with zinc–iron ( ZnO − F e 2 O 3 ) {\rm{ZnO}}\left-{\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) NPs. However, blood is speculated to have the hematocrit viscosity of the Powell–Eyring fluid. The single-phase model predicts an improvement in heat transport due to an increased volumetric friction of NPs, while the two-phase models provide closer estimates of heat-mass transfer due to Brownian and thermophoretic phenomena. Entropy evaluation predicts the details of irreversibility. The mathematical structures are effectively solved with a Runge–Kutta fourth-order algorithm along with a shooting mechanism. The Eyring–Powell parameters decrease the drag coefficient and mass/thermal transport rate. A higher estimation of the slip, material, and magnetic parameters decreases the flow behavior. The Bejan number increases with the diffusion parameter and decreases as the magnetic and Brinkman numbers increase. The effect of iron oxide ( F e 2 O 3 ) \left({\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) is observed to be dominant.

Interplay of surface and bulk elasticity in morphological stability of ultra-thin film coatings

Interplay of surface and bulk elasticity in morphological stability of ultra-thin film coatings

Associations between Surface Deformation and Groundwater Storage in Different Landscape Areas of the Loess Plateau, China

The Loess Plateau is an important grain-producing area and energy base in China and is an area featuring dramatic changes in both surface and underground processes. However, the associations between surface deformation and groundwater storage changes in different landscape types in the region are still unclear. Based on Sentinel-1 and GRACE (Gravity Recovery and Climate Experiment) data, this study monitored and verified the surface deformation and groundwater storage changes in different landscape types, such as those of the Kubuqi Desert, Hetao Irrigation District, Jinbei Mining Area, and Shendong Mining Area, in the Loess Plateau of China from 2020 to 2021. Through time series and cumulative analysis using the same spatial and temporal resolution, the associations between these two changes in different regions are discussed. The results show that: (1) the surface deformation rates in different landscape types differ significantly. The minimum surface deformation rate in the Kubuqi Desert is −5~5 mm/yr, while the surface deformation rates in the Hetao Irrigation District, the open-pit mine recovery area in the Jinbei Mining Area, and the Shendong Mining Area are −60~25 mm/yr, −25~25 mm/yr, and −95.33~26 mm/yr, respectively. (2) The regional groundwater reserves all showed a decreasing trend, with the Kubuqi Desert, Hetao Irrigation District, Jinbei Mining Area, and Shendong Mining Area declining by 359.42 mm, 103.30 mm, 45.60 mm, and 691.72 mm, respectively. (3) The surface elasticity deformation had the same trend as the temporal fluctuation in groundwater storage, and the diversion activity was the main reason why the temporal surface deformation in the Hetao Irrigation District lagged behind the change in groundwater storage by 1~2 months. The measure of “underground water reservoirs in coal mines” slows down the rate of collapse of coal mine roof formations, resulting in the strongest time-series correlation between mild deformation of the surface of the Shendong mine and changes in the amount of groundwater reserves (R = 0.73). This study analyzes the associations between surface deformation and groundwater storage changes in different landscape areas of the Loess Plateau of China and provides new approaches to analyzing the dynamic associations between the two and the causes of changes in both variables.

Response of surface effect on plane wave reflection at the boundary of flexomagnetic substrate

The article delves into the reflection of bulk plane waves in a flexomagnetic slab with second-order gradient elasticity. Employing generalized Gurtin-Murdoch surface elasticity, the study provides analytical insights into amplitude ratios and energy flux ratios for reflected bulk waves. The investigation focuses on understanding the behavior and energy conversion of incident bulk waves in the reflected P-SV system, highlighting the influences of residual surface stress, surface elasticity, and flexomagnetic polarization. The outcomes of the study indicate the high amplitude in the presence of residual stress. The findings contribute to fundamental knowledge for nanoscale piezomagnetic structures and potential applications in magnetic acoustic wave devices.

Intermolecular forces and surface stress residual effects on the size-dependent performance analysis of nanocrystalline micro/nano gyroscopes

This work investigates an electrostatically-actuated vibrating beam micro/nano-gyroscope made of nanocrystalline silicon material. The comprehensive size-dependent micro/nanogyroscope model is developed by couple stress and surface elasticity theories. Then, considering the effects of intermolecular forces (Casimir force and van der Waals force) and surface stress residual, an in-depth investigation was conducted on the performance of the micro/nanogyroscope. The calculation results display that the maximum static deflection, pull-in voltage and natural frequency change obviously with the increase of surface stress residual as the scale varies from micrometer to nanoscale. However, the effect of intermolecular forces on the performance of gyroscopes is exactly the opposite, which improves the prediction of system structural softening deformation phenomenon. Considering the influence of the Casimir and van der Waals forces in micro/nano gyroscopic system will help gyroscopes to obtain reliability and functionality sensitivity, increase the accuracy of predicting static deformation, natural frequency and differential frequency. Moreover, a frequency-domain method using the difference between the two vibration natural frequencies is studied, with changing the scale of the gyroscope under the effect of the intermolecular forces. The numerical simulations exhibit that when considering smaller structure sizes of the gyroscope, strong coupling occurs between the intermolecular forces and surface stress residual, which is helpful for the design of micro/nano gyroscopes.

Evolution Mechanism of Solid-Phase Catalysts During Catalytic Growth of Single-Walled Carbon Nanotubes.

Using solid nanoparticles (NPs) as catalysts is the most effective method to achieve catalytic growth of single-walled carbon nanotubes (SWCNTs) with ultrapure chirality. Until now, SWCNTs with a suitable chirality purity have not been prepared in experiments. That is, the evolution of solid NPs during the catalytic growth of SWCNTs is in contradiction with the original concept of a changeless structure. Hence, in this work, the evolution mechanism of solid cobalt NPs during the nucleation process of SWCNTs is analyzed through molecular dynamics. Similar to the experimental observations, the results show that a drastic structural fluctuation of the NPs occurs during the nucleation of SWCNTs. This structural fluctuation is caused by the fact that the elastic strain energy and surface energy of the NPs can be tuned when a carbon gradient exists between the subsurface and interior of the NP. Furthermore, such a carbon gradient can be reduced by changing the carbon feeding rate. This work not only reveals the evolution mechanism of solid catalysts during the nucleation of SWCNTs but also provides prospects for realizing solid catalysts with a changeless structure by tuning the experimental parameters.

Interaction of sakuranetin with unsaturated lipids forming Langmuir monolayers at the air-water interface: A biomembrane model

This study investigates the interaction between sakuranetin, a versatile pharmaceutical flavonoid, and monolayers composed of unsaturated phospholipids, serving as a surrogate for cell membranes. The phospholipids were 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE). We conducted a series of experiments to comprehensively investigate this interaction, including surface pressure assessments, Brewster angle microscopy (BAM), and polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS). Our findings unequivocally demonstrate that sakuranetin interacts with these phospholipids, expanding the monomolecular films. Notably, regarding POPC, the presence of sakuranetin led to a reduction in stability and a decline in surface elasticity, which can likely be attributed to intricate molecular rearrangements at the interface. The visual evidence of aggregations in BAM images reinforces the interactions substantiated by PM-IRRAS, highlighting sakuranetin's interaction with the polar and nonpolar regions of POPC. However, it is worth noting that these aggregations do not appear to contribute significantly to the viscosity of the mixed film, and our investigations did not reveal any substantial hysteresis. In contrast, when examining POPE, we observed a minor reduction in thermodynamic stability, indicative of fewer rearrangements within the monolayer. This notion was further reinforced by the limited presence of aggregations in the BAM images. Sakuranetin also increased the rigidity of the lipid monolayer; nevertheless, the monolayer remained predominantly elastic, facilitating easy re-spreading on the surface, especially for the first lipid. PM-IRRAS analysis unveiled interactions between sakuranetin and POPE's polar and nonpolar segments, compellingly explaining the observed monolayer expansion. Taken together, our data suggest that sakuranetin was more effectively incorporated into the monomolecular layer of POPE, indicating that membranes comprised of POPC might exhibit a greater degree of interaction in the presence of this pharmacologically active compound.

Dynamic properties of the layers of cupin-1.1 aggregates at the air/water interface

Spread layers of amorphous aggregates of the structural domain of plant protein vicilin, cupin-1.1, at the water – air interface were studied by the surface tensiometry, dilational surface rheology, Brewster angle and atomic force microscopy. The layer properties differed strongly from the results for the layers of previously studied proteins. The dependency of the dynamic elasticity of the layer on surface pressure had two local maxima with the second peak being four times higher than the first one. In the region of the first maximum the obtained results are similar to those for dispersions of polymer microgels with a hairy corona. At the beginning of surface compression separate threads of the corona are stretched along the surface and the surface elasticity increases. The further compression results in the formation of loops and tails leading to a decrease of the elasticity. The second local maximum of the dynamic surface elasticity is presumably caused by the interactions of the rigid cores of the aggregates leading finally to the formation of multilayer structures at high surface pressures. In this case, the surface elasticity starts to decrease as a result of the segment exchange between different layers at the interface.

Mathematical Analysis on Dispersion Relation of Rayleigh Wave for an Initially Stressed Magneto-Poroelastic Material with Corrugated and Impedance Boundary

This study showcases the Mathematical modelling of elastic surface waves and the analysis of dispersion relations of Rayleigh-type of wave in an initially stressed homogeneous porous magneto-elastic material having corrugated and impedance boundary exhibitions. Adoption of the classical harmonic method of wave analysis, non-dimensionalization of the resulting equations of motion, and corrugated-impedance boundary conditions produced by the modeled problem are also captured. The dispersion equation was analytically and graphically presented. Effects of the contributing physical quantities, such as impedance and corrugated boundary parameters, on Rayleigh waves for the chosen material are analyzed. The magnetic field’s influences and the wavenumber associated with the corrugated boundary surfaces on the material increase the dispersion relations of the Rayleigh wave profile on the material. In addition, we noted that the dispersion relations of the wave increases for increasing phase velocity and some parameters of voids. Also, a void parameter triggered a decrease on the dispersion profile of the Rayleigh wave when increased while noting some uniform exhibitions from other voids coefficients. This work holds the potential to provide more insights into studies involving displacement distributions in earthquake sciences, stress-strain analysis in Structural Engineering materials, among others.

The fluid dynamics of a viscoelastic fluid dripping onto a substrate.

Extensional flows of complex fluids play an important role in many industrial applications, such as spraying and atomisation, as well as microfluidic-based drop deposition. The dripping-on-substrate (DoS) technique is a conceptually-simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. It incorporates the capillary-driven thinning of a liquid bridge, produced by a single drop as it is slowly dispensed from a syringe pump onto a solid partially-wetting substrate. By following the filament thinning and pinch-off process the extensional viscosity and relaxation time of the sample can be determined. Importantly, DoS allows experimentalists to measure the extensional properties of lower viscosity solutions than is possible with commercially available capillary break-up extensional rheometers. Understanding the fluid mechanics behind the operation of DoS will enable users to optimise and extend the performance of this protocol. To achieve this understanding, we employ a computational rheology approach, using adaptively-refined time-dependent axisymmetric numerical simulations with the open-source Eulerian code, Basilisk. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable and accurate solution of the viscoelastic constitutive equation. Here, we focus on understanding the roles of surface tension, elasticity and finite chain extensibility in controlling the elasto-capillary (EC) regime, as well as the perturbative effects that gravity and substrate wettability play in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model that captures the initial rate of thinning when the dynamics are dominated by a balance between inertia and capillarity. This model also captures the structure of the transition region to the nonlinear EC regime in which the rapidly growing elastic stresses in the thread balance the capillary pressure as the filament thins towards breakup. Finally, we propose a fitting methodology based on the analytical solution for FENE-P fluids to improve the accuracy in determining the effective relaxation time of an unknown fluid.

Effect of surface viscoelasticity on top jet drops produced by bursting bubbles.

Jet drops resulting from bubble bursting at a liquid surface play a key role in various mass transfer processes across the interface, including sea spray aerosol generation and pathogen transmission. However, the impact of structurally compound interfaces, characterized by complex surface rheology introduced by surface-active contaminants, on the jet drop ejection still remains unclear. Here, we experimentally investigate the influence of surface viscoelasticity on the size and velocity of the top jet drops from surface bubble bursting, examining both pure protein and mixed protein-surfactant solutions. We document that for bubble bursting at a pure-protein-laden surface where surface elasticity dominates, the increase in Ec, i.e. the interfacial elastocapillary number as the ratio between the effects of interfacial elasticity and capillarity, efficiently increases the radius and decreases the velocity of the top jet drop, ultimately inhibiting the jet drop ejection. On the other hand, considering the mixed protein-surfactant solution, we show that the top jet drop radius and velocity exhibit a different variation trend with Ec, which is attributed to the additional dissipation on the capillary waves as well as the retardation and resistance on the converging flow for jet formation from surface viscoelasticity. Our work may advance the understanding of bubble bursting dynamics at contaminated liquid surfaces and shed light on the potential influence of surface viscoelasticity on the generation of bubble bursting aerosols.

Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects

The paper is concerned with the derivation of asymptotically consistent equations governing long-wave vibrations of an ultrathin elastic strip-beam taking into account surface effects within the framework of the Gurtin-Murdoch theory of the surface elasticity. Two dimensional equations of motion of an elastic isotropic medium are used as the initial ones. In the general case, the strip-beam is under the action of variable unsteady surface forces. The presence of residual shear stresses is assumed on the face surfaces. The ratio of the strip thickness to the characteristic length of bending deformation is considered as a small parameter. Within the framework of the Gurtin-Murdoch theory, two cases are considered, providing for the presence of large a) residual stresses on the faces, b) effects of surface inertia. Using the method of asymptotic integration over the transverse direction, relations for displacements and stresses in an ultra-thin strip-beam are obtained, and equivalent one dimensional the Timoshenko type equations taking into account surface effects are derived. As an example, free vibrations of a simply supported beam accounting for the surface effects are considered.