Interfacial Boundary Layer Research Articles

Mass transport of interfacial waves in a two-layer fluid system

Effects of viscous damping on mass transport velocity in a two-layer fluid system are studied. A temporally decaying small-amplitude interfacial wave is assumed to propagate in the fluids. The establishment and the decay of mean motions are considered as an initial-boundary-value problem. This transient problem is solved by using a Laplace transform with a numerical inversion. It is found that thin ‘second boundary layers’ are formed adjacent to the interfacial Stokes boundary layers. The thickness of these second boundary layers is of O(ε1/2) in the non-dimensional form, where ε is the dimensionless Stokes boundary layer thickness defined as $\epsilon = \hat{k}\hat{\delta}=\hat{k}(2\hat{v}/\hat{\sigma})^{1/2}$ for an interfacial wave with wave amplitude â, wavenumber $\hat{k}$ and frequency $\hat{\sigma}$ in a fluid with viscosity $\hat{v}$. Inside the second boundary layers there exists a strong steady streaming of O(α2ε−1/2), where $\alpha = \hat{k}\hat{a}$ is the surface wave slope. The mass transport velocity near the interface is much larger than that in a single-layer system, which is O(α2) (e.g. Longuet-Higgins 1953; Craik 1982). In the core regions outside the thin second boundary layers, the mass transport velocity is enhanced by the diffusion of the mean interfacial velocity and vorticity. Because of vertical diffusion and viscous damping of the mean interfacial vorticity, the ‘interfacial second boundary layers’ diminish as time increases. The mean motions eventually die out owing to viscous attenuation. The mass transport velocity profiles are very different from those obtained by Dore (1970, 1973) which ignored viscous attenuation. When a temporally decaying small-amplitude surface progressive wave is propagating in the system, the mean motions are found to be much less significant, O(α2).

Mass transport in water waves over an elastic bed

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

Low Temperature Diffusion of Alkali Earth Cations in Thin, Vitreous SiO2 Films

Ionic diffusion of two mobile alkali earth impurities, calcium and magnesium, has been observed in thin vitreous silicon dioxide (silica) films at temperatures as low as 80°C. A metal oxide semiconductor MOS capacitor has been utilized as the test structure for this device investigation. Controlled amounts of each impurity were introduced onto thermally oxidized surfaces of p‐type silicon wafers prior to device contact metallization through immersion in strongly basic solutions, then the impurities were driven into the silica films during final metal sintering. Initially, transient ion diffusion currents have been measured during elevated temperature device stressing under both unbiased (shorted) and biased stress conditions; then the currents were integrated to determine the time dependence of mobile charge transferred from the gate interface to the substrate interface. Capacitor C‐V flatband voltage shifts have also been examined to verify the amount of mobile charge transferred through the silicon dioxide films under biased as well as unbiased stress conditions. Negative flatband voltage shifts have been observed under unbiased (shorted) stress conditions, indicating the calcium and magnesium were present in the silica films as mobile cations. These observations were subsequently supported by secondary ion mass spectroscopy impurity concentration profiles within the silica films. Finally, impurity diffusion activation energies have been determined for both ions from time dependent charge flux curves between 80 and 180°C. Both activation energies were observed to exhibit strong dependencies upon applied electric field intensity during device stressing. These results are in agreement with an existing mobile ion transport model that includes both an emission‐limited (interface boundary layer) activation energy term as well as a drift‐limited (bulk trapping) term.

Interfacial fluxes at a grid-stirred diffusive interface

Results from a grid-mixing experiment in a diffusive thermohaline system are described. A model is proposed to separate the effects of interfacial flux and interfacial movement (entrainment) on property changes in the mixed layer and the present results for heat and salt fluxes are compared with previous studies in unstirred diffusive systems. Comparison of an eddy time-scale and a time-scale for development of instability in the interfacial boundary layers suggests a means of determining whether stirring or double-diffusive instability controls the interfacial transports. For the present conditions there was a negligible effect of diffusive stratification on entrainment rates, and interfacial fluxes were increased by the stirring. It is suggested that the ratio R F R ϱ , where R F is the interfacial flux ratio and R ϱ is the interfacial stability ratio, should be a function of the overall bulk Richardson number, Ri.

Developing blood flow in the entrance region of an artery

Presented herein are the studies of the flow behaviour of blood in the entrance region of a segment of an artery. The artery has an axisymmetric mild stenosis developed right from the entry cross section. The blood has been represented by a Bhingham fluid model which also takes the core region, formed due to axial migration of the red blood cells, into account. The flow in the artery has been divided into two regions developing boundary layer and a central core region. A fourth degree velocity profile satisfying the boundary conditions at the wall and the matching conditions at the core and the boundary layer interface is introduced in the governing momentum integral equation. The indicated integration provides a relation for the boundary layer thickness for each axial position. The results for the pressure distribution, entrance length and the wall shear stresses are discussed for the various values of the parameters involved in the analysis. The analysis predicts that the entrance length increases as the stenosis grows and therefore the heart has to put in more energy into transporting blood. It seems that there is some inbuilt mechanism which keeps the entry region of every segment to a minimum in normal arteries at each junction. This length increases in pathological states leading to various types of hypertensive diseases due to the formation and growth of the stenosis.

The impact of impurity incorporation on heterojunction bipolar transistors grown by metalorganic molecular beam epitaxy

It has been well documented that the ability of metalorganic molecular beam epitaxy (MOMBE) to grow heavily doped, well-confined layers of either n- or p-type is a significant advantage for the heterojunction bipolar transistor (HBT). This feature arises primarily from the ability to use gaseous dopant sources in the absence of interfacial gas boundary layers. While the absence of a boundary layer is an advantage for doping, it can be a disadvantage in other areas such as AlGaAs purity. This paper will discuss how these difficulties can be overcome through the use of novel Al or Ga precursors thus allowing deposition of high quality GaAs-based HBTs. The resulting reduction in background impurities and hence compensation allows for the use of lower dopant concentrations in the AlGaAs thus producing significant improvement in the leakage behavior of the base-emitter junction. Even further improvement can be achieved through the use of InGaP. Using novel Ga precursors, such as tri-isobutylgallium (TIBG), the problems associated with the sensitivity of composition to growth temperature are greatly reduced, allowing for the reproducible deposition of device structures containing InGaP emitter layers. In addition to impurity related performance degradation associated with the emitter, degradation over time due to defects or impurities, most likely hydrogen, in the base region has also been observed. The various sources of hydrogen present during growth have been identified suggesting that it may be possible to prevent hydrogen uptake. However, even in structures where hydrogen has been incorporated, a brief in-situ anneal appears adequate to drive off the hydrogen and eliminate the degradation in gain with operating time observed in large-area devices.

Mass transport effect within the solid-liquid interface boundary layers in solution crystal growth

Mass transport effect within the solid-liquid interface boundary layers in solution crystal growth

Study of potassium titanyl phosphate (KTP) flux growth by holographic phase-contrast interferometric microphotography

This paper describes a special set of equipment we designed, which is suitable to be used to study the high temperature solution growth process by optical method. The variation regularities of the solid-liquid interface boundary layer in the potassium titanyl phosphate (KTP) crystal growth and dissolution process have been investigated by holographic phase-contrast interferometric microphotography. It has been found that under the condition of free convection, the relation between the thickness of the boundary layer and supersaturation is linear. Moreover, the variation of refractive index caused by the change of solute concentration in the boundary layer will form an exponential function of the distance from the crystal face.

Growth of Heterojunction Bipolar Transistors by Metalorganic Molecular Beam Epitaxy

ABSTRACTHeterojunction bipolar transistors (HBTs) are becoming increasingly important for highspeed electronic applications. This paper will discuss how the unique growth chemistry of metalorganic molecular beam epitaxy (MOMBE) can be used to produce high performance HBTs. For example, it has been well documented that MOMBE's ability to grow heavily doped, well-confined layers of either n- or p-type is a significant advantage for this device. This feature arises primarily from the ability to use gaseous dopant sources in the absence of interfacial gas boundary layers. While this is an advantage for doping, it can be a disadvantage in other areas such as AlGaAs purity or InGaP lattice matching. This paper will discuss how these difficulties can be overcome through the use of novel Al or Ga precursors thus allowing deposition of high quality GaAs-based HBTs. By using trimethylamine alane (TMAA), background impurity concentrations can be reduced substantially. Further improvements in purity require cleaner Ga precursors or alternatively novel Ga substitutes. The resulting reduction in compensation allows for the use of lower dopant concentrations in the AlGaAs thus producing significant improvement in the leakage behavior of the base-emitter junction. Even further improvement can be achieved through the use of InGaP. Using novel Ga precursors, such as tri-isobutylgallium (TIBG), the problems associated with the sensitivity of composition to growth temperature are greatly reduced, allowing for the reproducible deposition of devices containing InGaP emitter layers.

Effects of Near Interfacial Microstructure on Interlaminar Fracture Toughness of Hybrid Metal-Polymer Composites

ABSTRACTResults of detailed study on interlaminar fracture toughness of hybrid aramid-epoxy/aluminum laminate composites are presented. A fracture mechanics approach has been adopted and Mode-I, Mode-II tests for a wide range of loading rates have been used. Hybrid composite failure loci has been studied using SEM technique. Results were analyzed from the point of view of metal substrate/aramid fibre surface free energy effect on near interfacial (in the boundary layers) microstructure and fracture toughness of elastomer modified epoxy resins. It has been shown, that toughened epoxy resin morphology (rubber particles size and volume content) and, as a result, fracture resistance of the boundary layers were strongly dependent upon the adsorption processes, that could take place during adhesion contact formation and curing. To increase interfacial fracture toughness of hybrid composites due to the improvement of near interfacial resin microstructure and boundary layer fracture resistance, as for aluminum-epoxy and for aramid-epoxy failure loci, metal sheets/aramid fibres surface properties and interfacial residual thermal stresses should be optimized. The last result has been achieved by means of si lane primer treatment of aluminum laminates and tensile loading of cured composite.

High resolution ultrasonic interferometry for quantitative nondestructive characterization of interfacial adhesion in multilayer (metal/polymer/metal) composites

We describe an ultrasonic method for the quantitative and nondestructive characterization of interfacial adhesion. Near an interface, such as polymer/metal, there exists a thin interfacial boundary layer at the nm length scale where the polymer may have properties different from those of the bulk polymer. On the other hand, ultrasonics measures linear mechanical properties of materials on a length scale which is that of the wavelength, usually in the range of several μm. Hence, it is usually stated that standard ultrasonic techniques cannot probe interfaces effectively. Here, we report on an ultrasonic interferometry technique that is built around metal/polymer/metal structures and that exhibits high sensitivity to interfacial properties, even at usual ultrasonic wavelengths. A rigorous mathematical model for the ultrasonic response of multilayered media that accounts for viscoelasticity is presented. Results of numerical calculations point out scaling features for interfacial properties in terms of speci...

An Analysis on Impact Responses of Isotropic Laminated Plate by Approximated Three-Dimensional Theory.

The stresses and deformations in an isotropic laminated plate (steel plate adhered to acrylic plate with different thicknesses) due to impact were analyzed. In-plane stresses were obtained with good accuracy by the plate bending theory. To obtain the out-of-plane stresses, in-plane stresses were substituted into the three-dimensional dynamic theory of elasticity and a numerical integration method was employed. This method is called an approximated three-dimensional theory in this paper. When the plate was impacted on the acrylic side with a long steel bar, an almost circular delamination was created on the interfacial boundary layer of the laminated plate. In the experimental record of the impact force history, a clear signal could be recognized at the creation of the delamination. Employing the data of the experimental impact load history as input for the numerical calculation, out-of-plane stresses on the interfacial layer were obtained. The size of the circular delamination were considered in terms of the resultant shear stress on the boundary layer.

Three‐dimensional hydrodynamics on finite elements. Part II: Non‐linear time‐stepping model

AbstractThe development and application of a non‐linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi‐implicit time‐stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field‐scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.

Effect of Ti+, Ar+, N+ and He+ Ion Implantation on Aramid Fiber Adhesive Properties

AbstractComposites made with high performance polymer fibers can achieve axial properties comparable to those which use inorganic reinforcements, but with somewhat inferior interfacial properties. A high degree of chain alignment in polyaramids, such as Kevlar, produces weak interactions between adjacent polymers, resulting in poor transverse strength in the fiber, and low interfacial shear strength in composite systems. The latter controls many composite properties, such as transverse, shear and flexural strengths. Also, by reducing the tendency to form weak interfacial boundary layers, good fiber-matrix adhesion can enhance environmental stability. For these reasons, modifications to reinforcement fiber surfaces that promote fiber-matrix adhesion are frequently used to improve the performance of composites.

Double-Diffusive Fluxes in a Salt Gradient Solar Pond

The possible influence of double-diffusive stratification on the vertical transport of salt and heat in a mixed-layer simulation model for a salt gradient solar pond is examined. The study is concerned primarily with the interfacial fluxes across the boundary between the gradient zone and upper convecting zone of solar ponds, though the arguments presented should be applicable to other “diffusive” interfaces as well. In the absence of mechanical stirring in the upper convecting zone (e.g., by wind), double diffusive instabilities could govern the vertical flux of heat and salt by adjusting interfacial gradients of temperature and salinity which control transport by molecular diffusion. Because these gradients are generally too sharp to be resolved by numerical models, the fluxes can either be modeled directly or be parameterized by grid-dependent “effective diffusivities.” It is shown that when mechanical stirring is present in the mixed layer, double-diffusive instabilities will not be allowed to grow in the interfacial boundary layer region. Thus, double-diffusive fluxes become important only in the absence of stirring and, in effect, provide a lower bound to the fluxes that would be expected across the interface.

Momentum exchange at the sea surface by wind stress and understress

AbstractMomentum exchange at the interface between two fluids is considered using general reasoning on energy dissipation in the coupled planetary boundary layers.It is shown that the surface shearing stress can be expressed as a function of the relative surface geostrophic velocity between the two fluids, and that the surface velocity is a linear combination of the two surface geostrophic velocities. This latter result is in agreement with a result previously derived by E. B. Kraus directly from the momentum equations.The analysis enables the ratio of the dissipation rates between the two fluids in the interfacial boundary layer to be determined. For the coupled ocean‐atmosphere, we find this ratio to be approximately (p1/p2)12 : where p1 and p2 are the densities of air and water, and we have made use of observations of the surface drift velocity and a dimensional argument which both suggest that the drag coefficients in the two fluids are approximately equal.From the form of the expression for the surface shearing stress, it is clear that both fluids lose energy in the coupled boundary layer, and also that they either transfer energy to each other or extract energy from each other by interaction at the interface.These energy fluxes are carried by two elemental stresses due to the general circulations of the atmosphere and the ocean respectively and which we call ‘wind stress’ and ‘understress’.The mutual loss of energy implies that the interface exerts a drag on both the atmosphere and the ocean, and the interfacial energy exchanges show that the ocean does work on the atmosphere analogous to the work done by the atmosphere on the ocean.

Momentum exchange at the sea surface by wind stress and understress

Momentum exchange at the interface between two fluids is considered using general reasoning on energy dissipation in the coupled planetary boundary layers. It is shown that the surface shearing stress can be expressed as a function of the relative surface geostrophic velocity between the two fluids, and that the surface velocity is a linear combination of the two surface geostrophic velocities. This latter result is in agreement with a result previously derived by E. B. Kraus directly from the momentum equations. The analysis enables the ratio of the dissipation rates between the two fluids in the interfacial boundary layer to be determined. For the coupled ocean-atmosphere, we find this ratio to be approximately (p1/p2)12 : where p1 and p2 are the densities of air and water, and we have made use of observations of the surface drift velocity and a dimensional argument which both suggest that the drag coefficients in the two fluids are approximately equal. From the form of the expression for the surface shearing stress, it is clear that both fluids lose energy in the coupled boundary layer, and also that they either transfer energy to each other or extract energy from each other by interaction at the interface. These energy fluxes are carried by two elemental stresses due to the general circulations of the atmosphere and the ocean respectively and which we call ‘wind stress’ and ‘understress’. The mutual loss of energy implies that the interface exerts a drag on both the atmosphere and the ocean, and the interfacial energy exchanges show that the ocean does work on the atmosphere analogous to the work done by the atmosphere on the ocean.

A differential model for salt-stratified, double-diffusive systems heated from below

A differential model is developed and used to predict the transient response of a salt-stratified, double-diffusive system heated from below. Predicted mixed layer heights and temperature distributions are in good agreement with data and in reasonable agreement with predictions based on simpler one- and two-layer models. Key features of the system, such as the substantial density difference across the interfacial boundary layer, negligible variation of the salinity profile in the stable region, and locations of highly anisotropic fluid motion are well described by the model. Predicted turbulence characteristics are plausible, and predicted mixed layer growth rates are consistent with accepted correlations involving a convective velocity and a mixed layer Richardson number.

Analysis of two-phase eutectoid transformation

A theoretical model is formulated to describe solid state eutectoid transformation. Solutions incorporating appropriate boundary conditions are derived from transient and steady states. It is shown that the transient solution describes build-up of the interfacial boundary layer, whereas the steady state solution extends into the phase. The presence of this boundary layer with considerable concentration and temperature gradients suggests a solid state analogue to constitutional super cooling, as in the liquid to solid transformation.

Analysis of Two Phase Eutectoid Transformation

A theoretical model is formulated to describe solid state eutectoid transformation. Solutions incorporating appropriate boundary conditions are derived for transient and steady states. It is shown that the transient solution describes build up of the interfacial boundary layer, whereas the steady state solution extends into the phase. The presence of this boundary layer with considerable concentration and temperature gradients sug gests a solid state analogue to constitutional super cooling, as in the liquid to solid transformation.