Role Of Vertical Component Of Surface Tension Of The Droplet On The Elastic Deformation Of Pdms Membrane

Poly(dimethylsiloxane) (PDMS) has been widely used in lab-on-a-chip and micro- total analysis systems (mu-TAS), thus wetting and electrowetting behaviors of PDMS are of great importance in these devices. PDMS is a kind of soft polymer material, so the elastic deformation of PDMS membrane by a droplet cannot be neglected due to the vertical component of the interfacial tension between the liquid and vapor, and this vertical component of liquid-vapor surface tension is also balanced by the stress distribution within the PDMS membrane. Such elastic deformation and stress distribution not only affect the exact measurement of contact angle, but also have influence on the micro-fluidic behavior of the devices. Using ANSYS code, we simulated numerically the elastic deformation and stress distribution of PDMS membrane on a rigid substrate due to the liquid-vapor surface tension. It is found that the vertical elastic deformation of the PDMS membrane is on the order of several tens of nanometers due to the application of a droplet with a diameter of 2.31 mm, which is no longer negligible for lab-on-a-chip and mu-TAS. The vertical elastic deformation increases with the thickness of the PDMS membrane, and there exists a saturated membrane thickness, regarded as a semi-infinite membrane thickness, and the vertical elastic deformation reaches a limiting value when the membrane thickness is equal to or thicker than such saturated thickness. (C) Koninklijke Brill NV, Leiden, 2008.

Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet

In this paper, the role of vertical component of Surface tension of a droplet on the elastic deformation of a finite-thickness flexible membrane was theoretically analyzed using Hankel transformation. The vertical displacement at the Surface was derived and can be reduced to Lester's or Rusanov's solutions when the thickness is infinite. Moreover, some Simulations of the effect of a liquid droplet on a membrane with a finite thickness were made. The numerical results showed that there exists a saturated membrane thickness of the order of millimeter, when the thickness of a membrane is larger than such a value, the membrane can be regarded as a half-infinite body. Further numerical calculations for soft membrane whose thickness is far below the saturated thickness were made. By comparison between the maximum vertical displacement of an ultrathin soft membrane and a half-infinite body, we found that Lester's or Rusanov's solutions for a half-infinite body cannot correctly describe Such cases. In other words, the thickness of a soft membrane has great effect on the surface deformation of the ultrathin membrane induced by a liquid droplet. (C) 2009 Elsevier Inc. All rights reserved.

Elastic deformation of wafer surfaces in bonding

A model has been proposed for describing elastic deformation of wafer surfaces in bonding. The change of the surface shape is studied on the basis of the distribution of the periodic strain field. With the condition of diminishing periodic strain away from the interface, Airy stress function has been found that satisfies the elastic mechanical equilibrium. The result reveals that the wavy interface elastically deforms a spatial wavelength from the interface. (C) 2000 American Institute of Physics. [S0021-8979(00)04219-5].

Separating Growth from Elastic Deformation during Cell Enlargement1

Plants change size by deforming reversibly (elastically) whenever turgor pressure changes, and by growing. The elastic deformation is independent of growth because it occurs in nongrowing cells. Its occurrence with growth has prevented growth from being observed alone. We investigated whether the two processes could be separated in internode cells of Chara corallina Klien ex Willd., em R.D.W. by injecting or removing cell solution with a pressure probe to change turgor while the cell length was continuously measured. Cell size changed immediately when turgor changed, and growth rates appeared to be altered. Low temperature eliminated growth but did not alter the elastic effects. This allowed elastic deformation measured at low temperature to be subtracted from elongation at warm temperature in the same cell. After the subtraction, growth alone could be observed for the first time. Alterations in turgor caused growth to change rapidly to a new, steady rate with no evidence of rapid adjustments in wall properties. This turgor response, together with the marked sensitivity of growth to temperature, suggested that the growth rate was not controlled by inert polymer extension but rather by biochemical reactions that include a turgor-sensitive step.

Evolution of conducting channels in metallic atomic contacts under elastic deformation

We investigate both experimentally and theoretically the evolution of conductance in metallic one-atom contacts under elastic deformation. While simple metals like Au exhibit almost constant conductance plateaus, Al and Pb show inclined plateaus with positive and negative slopes. It is shown how these behaviors can be understood in terms of the orbital structure of the atoms forming the contact. This analysis provides further insight into the issue of conductance quantization in metallic contacts revealing important aspects of their atomic and electronic structures.

Effect of mechanical deformation on permeation of hydrogen in iron

Rate of hydrogen permeation was measured under static as well as dynamic mechanical deformation conditions, Cylindrical tensile test specimens were used for the study and hydrogen permeation was measured electrochemically, It was observed that the hydrogen diffusivity decreased as plastic deformation increased for the static deformation experiments while elastic deformation had no significant effect on diffusivity but increased the steady state permeation flux, For the dynamic loading experiment, an elastic deformation increased the hydrogen permeation rate almost linearly. Onset of plastic deformation led a sudden decrease of permeation rate and the reduced rate was rapidly recovered when the plastic deformation ceased. These rapid changes in the permeation rates were explained that the absorbed hydrogen was trapped by dislocations and creation rate and density of dislocations changed drastically when plastic deformation started and stopped.

The effect of elastic modulus and equilibrium vapor adsorption on capillary forces

Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn

Deformation Studies of Tungsten-Gold Contacts at the Nanometer Scale.

The deformation behavior of atomically clean, nanometer sized tungsten / gold contacts was studied at room temperature in ultra-high vacuum. An instrument that combines atomic force microscopy (AFM), scanning tunneling microscopy (STM), and field ion microscopy (FIM) into a single experimental apparatus was designed, constructed, and calibrated. A cross-hair force sensor having a spring constant of - 442 N/m was developed and its motion was monitored during indentation experiments with a differential interferometer. Tungsten tips of controlled size (12.8 nm < tip radius < 2 1.6 nm) were first shaped and characterized using FIM and then indented into a Au (1 10) single crystal to depths ranging from 1.5 nrn to 18 nm using the force sensor. Continuum mechanics models were found to be valid in predicting elastic deformation during initial contact and plastic zone depths despite our small size regime. Multiple discrete yielding events lasting < 1.5 ms were observed during the plastic deformation regime; at the yield points a maximum value for the principal shear stress was measured to be 5 + 1 GPa. During tip withdrawal, "pop-out" events relating to material relaxation within the contact were observed. Adhesion between the tip and sample led to experimental signatures that suggest neck formation prior to the break of contact. STM images of indentation holes revealed various shapes that can be attributed to the (1 1 1 ) (1 10) crystallographic slip system in gold. FIM images of the tip after indentation showed no evidence of tip damage

Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions

Solvation. pressure due to adsorption of fluids in porous materials is the cause of elastic deformation of an adsorbent, which is accessible to direct experimental measurements. Such a deformation contributes to the Helmholtz free energy of the whole adsorbent-adsorbate system due to accumulation of compression or tension energy by the solid. It means that in the general case the solid has to be considered as not solely a source of the external potential field for the fluid confined in the pore volume, but also as thermodynamically nonmert component of the solid-fluid system. We present analysis of nitrogen adsorption isotherms and heat of adsorption in slit graphitic pores accounting for the adsorption deformation by means of nonlocal density functional theory. (c) 2006 Elsevier Ltd. All rights reserved.

Dynamics of Granular Crystals with Elastic-Plastic Contacts

We study the behavior of granular crystals subjected to impact loading that creates plastic deformation at the contacts between constituent particles. Granular crystals are highly periodic arrangements of spherical particles, arranged into densely packed structures resembling crystals. This special class of granular materials has been shown to have unique dynamics with suggested applications in impact protection. However, previous work has focused on very low amplitude impacts where every contact point can be described using the Hertzian contact law, valid only for purely elastic deformation. In this thesis, we extend previous investigation of the dynamics of granular crystals to significantly higher impact energies more suitable for the majority of applications. Additionally, we demonstrate new properties specific to elastic-plastic granular crystals and discuss their potential applications as well. We first develop a new contact law to describe the interaction between particles for large amplitude compression of elastic-plastic spherical particles including a formulation for strain-rate dependent plasticity. We numerically and experimentally demonstrate the applicability of this contact law to a variety of materials typically used in granular crystals. We then extend our investigation to one-dimensional chains of elastic-plastic particles, including chains of alternating dissimilar materials. We show that, using the new elastic-plastic contact law, we can predict the speed at which impact waves with plastic dissipation propagate based on the material properties of the constituent particles. Finally, we experimentally and numerically investigate the dynamics of two-dimensional and three-dimensional granular crystals with elastic-plastic contacts. We first show that the predicted wave speeds for 1D granular crystals can be extended to 2D and 3D materials. We then investigate the behavior of waves propagating across oblique interfaces of dissimilar particles. We show that the character of the refracted wave can be predicted using an analog to Snell's law for elastic-plastic granular crystals and ultimately show how it can be used to design impact guiding "lenses" for mitigation applications.

Infrastructure sustainability : differential axial shortening of concrete structures

High density development has been seen as a contribution to sustainable development. However, a number of engineering issues play a crucial role in the sustainable construction of high rise buildings. Non linear deformation of concrete has an adverse impact on high-rise buildings with complex geometries, due to differential axial shortening. These adverse effects are caused by time dependent behaviour resulting in volume change known as ‘shrinkage’, ‘creep’ and ‘elastic’ deformation. These three phenomena govern the behaviour and performance of all concrete elements, during and after construction. Reinforcement content, variable concrete modulus, volume to surface area ratio of the elements, environmental conditions, and construction quality and sequence influence on the performance of concrete elements and differential axial shortening will occur in all structural systems. Its detrimental effects escalate with increasing height and non vertical load paths resulting from geometric complexity. The magnitude of these effects has a significant impact on building envelopes, building services, secondary systems, and lifetime serviceability and performance. Analytical and test procedures available to quantify the magnitude of these effects are limited to a very few parameters and are not adequately rigorous to capture the complexity of true time dependent material response. With this in mind, a research project has been undertaken to develop an accurate numerical procedure to quantify the differential axial shortening of structural elements. The procedure has been successfully applied to quantify the differential axial shortening of a high rise building, and the important capabilities available in the procedure have been discussed. A new practical concept, based on the variation of vibration characteristic of structure during and after construction and used to quantify the axial shortening and assess the performance of structure, is presented.

A numerical method to quantify differential axial shortening in concrete buildings

Differential distortion comprising axial shortening and consequent rotation in concrete buildings is caused by the time dependent effects of “shrinkage”, “creep” and “elastic” deformation. Reinforcement content, variable concrete modulus, volume to surface area ratio of elements and environmental conditions influence these distortions and their detrimental effects escalate with increasing height and geometric complexity of structure and non vertical load paths. Differential distortion has a significant impact on building envelopes, building services, secondary systems and the life time serviceability and performance of a building. Existing methods for quantifying these effects are unable to capture the complexity of such time dependent effects. This paper develops a numerical procedure that can accurately quantify the differential axial shortening that contributes significantly to total distortion in concrete buildings by taking into consideration (i) construction sequence and (ii) time varying values of Young’s Modulus of reinforced concrete and creep and shrinkage. Finite element techniques are used with time history analysis to simulate the response to staged construction. This procedure is discussed herein and illustrated through an example.

Interactive axial shortening of columns and walls in high rise buildings

Concrete is commonly used as a primary construction material for tall building construction. Load bearing components such as columns and walls in concrete buildings are subjected to instantaneous and long term axial shortening caused by the time dependent effects of "shrinkage", "creep" and "elastic" deformations. Reinforcing steel content, variable concrete modulus, volume to surface area ratio of the elements and environmental conditions govern axial shortening. The impact of differential axial shortening among columns and core shear walls escalate with increasing building height. Differential axial shortening of gravity loaded elements in geometrically complex and irregular buildings result in permanent distortion and deflection of the structural frame which have a significant impact on building envelopes, building services, secondary systems and the life time serviceability and performance of a building. Existing numerical methods commonly used in design to quantify axial shortening are mainly based on elastic analytical techniques and therefore unable to capture the complexity of non-linear time dependent effect. Ambient measurements of axial shortening using vibrating wire, external mechanical strain, and electronic strain gauges are methods that are available to verify pre-estimated values from the design stage. Installing these gauges permanently embedded in or on the surface of concrete components for continuous measurements during and after construction with adequate protection is uneconomical, inconvenient and unreliable. Therefore such methods are rarely if ever used in actual practice of building construction. This research project has developed a rigorous numerical procedure that encompasses linear and non-linear time dependent phenomena for prediction of axial shortening of reinforced concrete structural components at design stage. This procedure takes into consideration (i) construction sequence, (ii) time varying values of Young's Modulus of reinforced concrete and (iii) creep and shrinkage models that account for variability resulting from environmental effects. The capabilities of the procedure are illustrated through examples. In order to update previous predictions of axial shortening during the construction and service stages of the building, this research has also developed a vibration based procedure using ambient measurements. This procedure takes into consideration the changes in vibration characteristic of structure during and after construction. The application of this procedure is illustrated through numerical examples which also highlight the features. The vibration based procedure can also be used as a tool to assess structural health/performance of key structural components in the building during construction and service life.

Bending properties of Ag nanowires with pre-existing surface defects

Materials used in the engineering always contain imperfections or defects which significantly affect their performances. Based on the large-scale molecular dynamics simulation and the Euler–Bernoulli beam theory, the influence from different pre-existing surface defects on the bending properties of Ag nanowires (NWs) is studied in this paper. It is found that the nonlinear-elastic deformation, as well as the flexural rigidity of the NW is insensitive to different surface defects for the studied defects in this paper. On the contrary, an evident decrease of the yield strength is observed due to the existence of defects. In-depth inspection of the deformation process reveals that, at the onset of plastic deformation, dislocation embryos initiate from the locations of surface defects, and the plastic deformation is dominated by the nucleation and propagation of partial dislocations under the considered temperature. Particularly, the generation of stair-rod partial dislocations and Lomer–Cottrell lock are normally observed for both perfect and defected NWs. The generation of these structures has thwarted attempts of the NW to an early yielding, which leads to the phenomenon that more defects does not necessarily mean a lower critical force.

Mechanical bending properties of sodium titanate (Na2Ti3O7) nanowires

We report on the mechanical properties of sodium titanate nanowires (Na2Ti3O7 NW) through a combination of bending experiments and theoretical analysis. Na2Ti3O7 NWs with lateral dimensions ranging from 20–700 nm were synthesized by a hydrothermal approach. A focused ion beam (FIB) was used to manipulate the selected Na2Ti3O7 NW over a hole drilled in an indium tin oxide substrate. After welding the nanowire, a series of bending tests was performed. It was observed that the Na2Ti3O7 NW exhibits a brittle behavior, and a nonlinear elastic deformation was observed before failure. By using the modified Euler–Bernoulli beam theory, such nonlinear elastic deformation is found to originate from a combination of surface effects and axial elongation (arising from the bending deformation). The effective Young's modulus of the Na2Ti3O7 NW was found to be independent of the wire length, and ranges from 21.4 GPa to 45.5 GPa, with an average value of 33 ± 7 GPa. The yield strength of the Na2Ti3O7 NW is measured at 2.7 ± 0.7 GPa.