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.

An Efficient Front-Tracking Method For Fully Nonlinear Interfacial Waves

A fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial (2-layer) waves. To circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed Eulerian and Lagrangian concept is proposed: the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction. Accordingly, a modified dynamic condition is required to properly compute the boundary potentials. To demonstrate the effectiveness of the current method, two important problems for the interfacial wave dynamics, the generation and evolution processes, are investigated. Firstly, analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results. Furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories. (c) 2008 Elsevier Inc. All rights reserved.

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the-moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.

Microstructural evolution and formation of nanocrystalline intermetallic compound during surface mechanical attrition treatment of cobalt

Nanocrystalline intermetallic Co3Fe7 was produced on the surface of cobalt via surface mechanical attrition (SMA). Deformationinduced diffusion entailed the formation of a series of solid solutions. Phase transitions occurred depending on the atomic fraction of Fe in the surface solid solutions: from hexagonal close-packed (<4% Fe) to face-centered cubic (fcc) (4-11% Fe), and from fcc to body-centered cubic (>11% Fe). Nanoscale compositional probing suggested significantly higher Fe contents at grain boundaries and triple junctions than grain interiors. Short-circuit diffusion along grain boundaries and triple junctions dominate in the nanocrystalline intermetallic compound. Stacking faults contribute significantly to diffusion. Diffusion enhancement due to high-rate deformation in SMA was analyzed by regarding dislocations as solute-pumping channels, and the creation of excess vacancies. Non-equilibrium, atomic level alloying can then be ascribed to deformation-induced intermixing of constituent species. The formation mechanism of nanocrystalline intermetallic grains on the SMA surface can be thought of as a consequence of numerous nucleation events and limited growth. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Atomistic simulations of crack nucleation and intergranular fracture in bulk nanocrystalline nickel

We report large scale molecular dynamics simulations of dynamic cyclic uniaxial tensile deformation of pure, fully dense nanocrystalline Ni, to reveal the crack initiation, and consequently intergranular fracture is the result of coalescence of nanovoids by breaking atomic bonds at grain boundaries and triple junctions. The results indicate that the brittle fracture behavior accounts for the transition from plastic deformation governed by dislocation to one that is grain-boundary dominant when the grain size reduces to the nanoscale. The grain-boundary mediated plasticity is also manifested by the new grain formation and growth induced by stress-assisted grain-boundary diffusion observed in this work. This work illustrates that grain-boundary decohesion is one of the fundamental deformation mechanisms in nanocrystalline Ni.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Numerical investigation on a simulation model of floating zone convection

A simulation model with adiabatic condition at the upper rod and constant temperature at the lower rod is studied numerically in this paper. The temperature distribution in a simulation model is closer to the one in the half part of a floating full zone in comparison with the one in a usual floating half zone model with constant temperature at both rods, because the temperature distribution of a floating full zone is symmetric for the middle plane in a microgravity environment. The results of the simulation model show that the temperature profiles and the how patterns are different from those of the usual floating half zone model. Another type of half zone model, with a special non-uniform temperature distribution at the upper rod and constant temperature at the lower rod, has been suggested by recent experiments. The temperature boundary condition of the upper rod has a maximum value in the center and a lower value near the free surface. This modified simulation model is also simulated numerically in the present paper. Copyright (C)1996 Elsevier Science Ltd.

Lattice instability at a fast moving crack tip

A molecular dynamics method is used to analyze the dynamic propagation of an atomistic crack tip. The simulation shows that the crack propagates at a relatively constant global velocity which is well below the Rayleigh wave velocity. However the local propagation velocity oscillates violently, and it is limited by the longitudinal wave velocity. The crack velocity oscillation is caused by a repeated process of crack tip blunting and sharpening. When the crack tip opening displacement exceeds a certain critical value, a lattice instability takes place and results in dislocation emissions from the crack tip. Based on this concept, a criterion for dislocation emission from a moving crack tip is proposed. The simulation also identifies the emitted dislocation as a source for microcrack nucleation. A simple method is used to examine this nucleation process. (C) 1996 American Institute of Physics.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd