Formation Of Fingers Research Articles

Effect of Substrate Roughness on Splatting Behavior of HVOF Sprayed Polymer Particles: Modeling and Experiments

A three-dimensional model of particle splatting on rough surfaces has been developed for high-velocity oxyfuel (HVOF) sprayed polymer particles and related to experimentally observed polymer splats. Fluid flow and particle deformation were predicted using a volume of fluid (VoF) method using Flow-3D software. Splatting behavior and final splat shapes were simulated on a realistic rough surface, generated by optical interferometry of an actual grit-blasted steel surface. Predicted splat shapes were compared with scanning electron microscopy images of nylon 11 splats deposited onto grit-blasted steel substrates. Rough substrates led to the formation of fingers and other asymmetric three-dimensional instabilities that are seldom observed in simulations of polymer splatting on smooth substrates.

Labyrinthine instability of a miscible magnetic drop

We present the first detailed experiment on the labyrinthine instabilities of miscible magnetic fluids in a Hele–Shaw Cell. The formation of miscible labyrinthine fingers appears much more irregular with sharp fingertips that differ from their immiscible counterparts significantly. These labyrinthine fingers show great qualitative resemblance with the accompanied numerical simulation.

De Novo Folding of the DNA‐Binding ATF‐2 Zinc Finger Motif in an All‐Atom Free‐Energy Forcefield

Finger formation: Predictive all-atom folding of a DNA-binding αββ-zinc-finger motif in a free-energy forcefield has been demonstrated. The three models (shown in different shades of blue in the picture) show the lowest energy structures found in the simulation. The low-energy region of the free-energy surface and important steps of the folding pathway have been analyzed to help elucidate zinc-finger formation and function.

Surface-energy-driven dewetting theory of silicon-on-insulator agglomeration

The thermal agglomeration of ultrathin (<30nm) single crystal silicon-on-insulator (SOI) films is a morphological evolution phenomenon with practical and scientific importance. This materials phenomenon represents both a critical process limitation for the fabrication of advanced ultrathin SOI-based semiconductor devices as well as a scientifically interesting morphological evolution problem. Investigations to date have attributed this phenomenon to a stress-induced morphological instability. In this paper, we demonstrate that SOI agglomeration is a surface-energy-driven dewetting phenomenon. Specifically, we propose that agglomeration occurs via a two-step surface-energy-driven mechanism consisting of (1) defect-mediated film void nucleation and (2) surface-diffusion-limited film dewetting via capillary edge and generalized Rayleigh instabilities. We show that this theory can explain all of the key experimental observations from the SOI agglomeration literature, including the locations of agglomeration initiation, the greater instability of patterned film edges, the destabilizing effect of decreasing silicon layer thickness and increasing temperature, the strikingly periodic silicon finger and island formation agglomeration morphology, and the scaling of agglomerated structure dimensions with the silicon layer thickness. General implications of this theory for the thermal stability of SOI and other common thin-film-on-insulator structures are also discussed.

Surfactant-induced fingering phenomena beyond the critical micelle concentration

We consider the spreading of a droplet of soluble surfactant, at concentrations beyond its critical micelle concentration (CMC), on a pre-existing thin liquid layer. Lubrication theory is used to derive a coupled system of four two-dimensional nonlinear evolution equations for the film thickness and surfactant concentration at the interface and in the bulk as both monomers and micelles. These equations are parameterized by a number of dimensionless groups that reflect the relative importance of Marangoni stresses, surface and bulk diffusion, capillarity, surfactant solubility, sorption kinetics and the nonlinearity of the equation of state. Our results for the base state indicate that two parameters in particular exert a significant influence on the flow profiles: the dimensionless mass of surfactant deposited, further, this protuberance separates from the drop to form a distinct secondary front that lies behind a leading front that usually accompanies the spreading process. Our examination of the linear and nonlinear stability of the system through a transient growth analysis and transient numerical simulations, respectively, indicates that these features are vulnerable to transverse perturbations, leading to the formation of fingers. The results obtained in the present work are in qualitative agreement with recently available experimental data.

Prediction of Bypassed Oil With Correlations in Side-Water Drive Reservoirs

Abstract Efficient management of oil reserves involves an understanding of the mechanisms that control the bypassing of oil in water drive reservoirs. The existing analytical models of water front advancement in side-water reservoirs do not account for the combined effects of water underruning and coning. This paper gives correlations for the prediction of the amount of bypassed oil in side-water systems. The correlations have been developed using numerical simulation and an experimental design framework. Considered in the correlations are the effects of dip angle, vertical- to-horizontal permeability ratio, oil viscosity, production rate, oil density, and well penetration. Introduction Displacement of oil by water in side-water systems is controlled by viscous forces, gravity forces, capillary forces, and heterogeneities. These mechanisms or forces may interact with each other during the displacement, originating the formation of multiple fingers, water channeling, and/or gravity underrunning (formation of a water tongue). For low flow velocities, gravity forces tend to dominate the displacement and a stable (constant slope) interface occurs(1). A stable front is desirable because it results in high recovery factors. However, the required flow velocity may be so low that the corresponding critical production rate would not be economical. Generally, production rates needed for economical recovery exceed the critical rates. Therefore, the front becomes unstable and a (gravity) water tongue develops along the bottom of the dipping structure, causing early water breakthrough and oil bypassing. In fact, simulation studies have shown that up to 69% of the oil could be bypassed in side-water systems with unfavourable mobility ratios(1, 2). Also, most of the well's production life is plagued by very high water cut. Knowledge of the motion of the oil-water interface is needed in reservoir engineering in order to determine the amount of oil that will be recovered by the end of the well's operation. The most well known analytical models for the determination of the motion of the oil-water interface are the models presented by Richarson and Blackwell(3), Dake(4), Dietz(5), Outmans(6), and Sheldon and Fayers(7). Potential use of these models for predicting a well's recovery is important due to the simplicity of calculations as compared to reservoir simulations, which become quite complex in modelling individual wells. Recently, the analytical models were verified for stable and unstable cases(1). The results indicated that Dake and Dietz are the best models because of their accuracy and ease of use(1). Despite convenience, analytical models are poor estimators of the water breakthrough time(1). Moreover, Dake's and Dietz's models are based on assumptions that may not represent the real physics of the displacement of oil by water in dipping structures. For example, the models assume isotropic reservoirs. They also assume completely segregated flow, i.e., consider the thickness of the capillary transition zone negligibly smaller than the thickness of the pay zone. In addition, these analytical models are two-dimensional, so they ignore the physical size of a well at the producing end of the dipping structure.

Defects in multilayer plastic films I: Interface defects in extrusion

This paper deals with defects in multilayer plastic films in the extrusion process. A methodology to link process parameters and fluid rheology to onset of certain types of defects is developed. The defects considered include zigzag features that can form on the surface or interfaces in the extruded multilayer films, and parabolic and finger-like features that can form at the interfaces. The zigzag defects occur due to excessive shear and the parabolic and viscous-finger defects develop in response to flow perturbations. Novel approaches to predict the formation of the latter defects based on steady-state flow calculations are presented in this paper. Tendency of formation of parabolic defects can be evaluated based on steady-state calculations, and possibility of formation of viscous fingers can be explored based on energy considerations. It has also been shown that a process window can be developed by simultaneously considering the process requirements for elimination of these defects.

Shape transformations of protein-like copolymer globules

Shapes of globules formed by amphiphilic multi-block-copolymers in a selective solvent are considered theoretically. We focus on copolymers consisting mostly of insoluble H-units forming large core surrounded by a shell of soluble P-blocks. It is shown that the globule becomes non-spherical when the effective shell tension is low enough. The resultant shape depends on the shell bending energy: it is prolate if this energy is larger than the elastic energy of the core, and oblate in the opposite case. The central result is the prediction of the formation of a surface pattern of fingers accompanying or even preempting the shape transition mentioned above. We elucidate and discuss the following finger morphologies: 1) nearly spherical knob; 2) a necklace of spherical beads extending away from the surface; 3) mostly cylindrical fingers; 4) large thorn-like fingers. The first 3 morphologies develop at equilibrium as the shell area increases (or, equivalently, the shell tension decreases). Considering the relevant kinetical aspects we show that formation of fingers is a nucleation and growth process, and that the energy of their equilibrium nucleation is likely to be high. Therefore, the finger formation may be delayed, and may actually occur in the regime where the plain spherical surface is metastable. It is the last morphology (thorn-like fingers) that characterizes the metastable regimes when the finger formation is controlled by a high activation energy. The universal features of the above predictions inviting experimental tests are discussed.

Non-Normal Effects on Salt Finger Growth

Abstract Salt fingers, which occur because of the difference in diffusivities of salt and heat in water, may play an important role in ocean mixing and circulation. Previous studies have suggested the long-time dominance of initially fastest growing finger perturbations. Finger growth has been theoretically derived in terms of the normal modes of the idealized system, which include a growing mode and a pair of decaying internal wave modes. Because these normal modes are not orthogonal, however, transient effects can occur related to the interaction between the modes, as explained by the generalized stability theory of non-normal growth. Initial growth of a perturbation that is not along a normal mode can be faster than the leading normal mode. In this study, the effects of non-normal growth on salt finger formation are investigated. It is shown that some salt finger perturbations that are a superposition of the growing mode and the decaying modes initially grow faster than pure growing normal mode perturbations. These non-normal effects are found to be significant for up to 10 or more e-folding times of the growing normal mode. The generalization of the standard idealized salt finger growth dynamics to include non-normal effects is found to lead to fastest-growing fingers that agree less well with observed fully developed salt fingers than the fastest-growing normal mode previously investigated.

Structures, profile consistency, and transport scaling in electrostatic convection

Two mechanisms at the origin of profile consistency in models of electrostatic turbulence in magnetized plasmas are considered. One involves turbulent diffusion in collisionless plasmas and the subsequent turbulent equipartition of Lagrangian invariants. By the very nature of its definition, this state can only be reached in the absence of imposed fluxes of the transported quantities. As such, the concept of turbulent equipartition cannot be used to interpret profiles in numerical simulations of interchange modes, as it has nevertheless been done in the past. It is shown in this article that for interchange modes, profile consistency is in fact due to mixing by persistent large-scale convective cells. This mechanism is not a turbulent diffusion, cannot occur in collisionless systems, and is the analog of the well-known laminar “magnetic flux expulsion” in magnetohydrodynamics. This expulsion process involves a “pinch” across closed streamlines and further results in the formation of pressure fingers along the separatrix of the convective cells. By nature, these coherent structures are dissipative because the mixing process that leads to their formation relies on a finite amount of collisional diffusion. Numerical simulations of two-dimensional interchange modes confirm the role of laminar expulsion by convective cells for profile consistency and structure formation. They also show that the fingerlike pressure structures ultimately control the rate of heat transport across the plasma layer and thus the transport scaling at large Rayleigh numbers. This contradicts mixing-length arguments which do not account for collisional processes. For interchange modes, the problem of coherent structure formation, profile consistency, and transport scaling are thus intimately linked.

Evolution of Rim Instabilities in the Dewetting of Slipping Thin Polymer Films

ABSTRACT Using optical microscopy, we investigated the amplification of instabilities of the moving rim which formed during dewetting of slipping polymer films. At the onset, the wavelength of the rim instability grew in time and proportional to the width of the rim. At later stages, these instabilities led to finger and subsequent droplet formation. Droplet size was found to be proportional to the width of the rim at break-off of droplets, which, in turn, was proportional to the initial film thickness. Our experiments suggest that the decrease of the dewetting velocity with increasing width of the rim is the key mechanism responsible for this instability. Droplet formation provided a possibility for self adjustment of the dewetting front resulting in a constant mean self-regulated dewetting velocity. This mean velocity was significantly higher than the velocity for the corresponding stable rim.

Displacement front stability of steam injection into high porosity diatomite rock

Steamflood displacement in porous media is considered to be stable, as compared to other gas-flooding techniques. Stability on the microscopic and core scale lends stability to steam movement on the reservoir scale. Initial aspects of this work use analytical methods to examine frontal stability in high-porosity rocks. Analytical methods indicate stable steam fronts for typical reservoir properties, but they also predict unstable displacement in high-porosity rock. The second portion of this work uses pattern level thermal simulation to study the stability of steam drives in high-porosity rocks. Two different permeability models (an isotropic model and a thief model) are compared at three average porosities (25%, 50% and 70%). Small thermal conductivities are shown to induce the formation of the steam fingers. More importantly, the simulation results show that as the rock porosity increases, steamfront stability decreases. This is exemplified by earlier breakthrough times for models that have greater average porosity. While the stability of a steam front does decrease, analysis indicates that the difference is likely not significant, around a 20% reduction in breakthrough time, compared to other aspects. For example, reservoir heterogeneity has a much greater impact on breakthrough time than does the relatively unstable displacement front associated with high-porosity rock.

Formation of fingers around the edges of a drop hitting a metal plate with high velocity

Water droplets (0.55 or 1.3 mm diameter) were photographed as they impinged on a stainless steel surface. The droplet impact velocity (10–50 m s−1) and the average roughness (0.03 or 0.23 μm) of the test surfaces were varied. The stainless steel substrate was mounted on the end of a rotating arm, giving linear velocities of up to 50 m s−1. Different stages of droplet impact were photographed by synchronizing the ejection of a single droplet with the position of the rotating arm and triggering of a camera. Finger-shape perturbations were observed around the edges of spreading droplets. The maximum diameter to which a droplet spread and the number of fingers formed around it were measured. The size and number of fingers increased with impact velocity and droplet diameter. At sufficiently high velocities, the tips of these fingers detached, producing satellite droplets. By increasing surface roughness, both the number of fingers and the maximum extent of spreading were decreased. At high impact velocities the spreading liquid film became so thin that it ruptured in several places. A mathematical model, based on linear Rayleigh–Taylor instability theory, was used to predict the wavelength of the fastest growing perturbation around a spreading droplet. The corresponding wavenumber agreed reasonably well with the number of fingers around the droplet.

Fingering phenomena associated with insoluble surfactant spreading on thin liquid films

We study the linear and nonlinear stability of a thick surfactant deposition spreading on a thin liquid film using transient growth analysis (TGA) and direct numerical simulations (DNS) of the two-dimensional lubrication equations, respectively. Results of the TGA of the one-dimensional spatially and temporally evolving base state reveal disturbance growth and the selection of a perturbation of intermediate wavenumber. This perturbation targets the ‘contact region’ between the deposition and the underlying thin liquid film and grows despite the absence of intermolecular forces. Increasing the initial thickness ratio of the deposition to the thin film and decreasing the relative magnitude of capillarity and surface diffusion further amplify perturbation growth. The DNS results clearly show the formation of fingers in the contact region behind the surfactant leading edge and provide further confirmation of the TGA findings.

Influence of fluorapatite on the properties of thermally sprayed hydroxyapatite coatings

Thermally sprayed hydroxyapatite has been the widely used on orthopaedic prosthesis to induce bone growth and facilitate bone attachment. However, hydroxyapatite has a greater affinity for the formation of an amorphous phase in the thermally sprayed coating that results in the release of excessive amount of mineral ions from the implant coating leading to a saturated environment in the immediate vicinity of the bone cells. Fluorapatite however is highly crystalline and offers the potential for lower mineral ion release by dissolution. Thus study investigates the influence of fluorapatite in a thermally sprayed hydroxyapatite coating. Mechanical blends of fluorapatite with hydroxyapatite were thermally sprayed, characterized with X-ray diffraction, SEM, FTIR, optical microscopy for microstructure, roughness and tested for solubility. Cathodoluminescence microscopy was used to examine the resorbed coating surface. Fluorapatite coatings crystallized more readily and produce a greater coating roughness. The roughness in fluorapatite coatings arises from less flattened droplets that show a tendency for finger formation. Addition of fluorapatite increases coating crystallinity. The use of slower resorbing fluorapatite produces less particle release which favors improved osseointegration. Less change in the surface topography during resorption can be used to an advantage to control the coating surface presented to cells and extra cellular matrix proteins.

Modeling Drop Shape on Contaminated Surfaces or Surfaces with Physical Structures

Surface contaminants are commonly found on films. They get transferred to the surface from incompletely cured silicone liners on the films or owing to migration of additives to the surface from within the film. During the process of ink jet printing (a noncontact printing process), surface contamination affects the shape of the drops (causing the formation of fingers and crescents) and hence image quality. This study uses modeling methods to examine how such surface contamination affects the drops shapes. Subsequently, it models the effect of surface structures (pits) on the drop shape. This study explores how image quality can be controlled in the presence of surface contamination and surface structures.

Teratogenic mechanisms of longitudinal deficiency and cleft hand.

In order to better understand the teratogenic mechanisms of congenital defects of the digits, we analyzed clinical cases and induced similar types of congenital hand anomalies in rat fetuses by oral administration of busulfan. In clinical cases, radial and ulnar deficiencies had common characteristic features. We induced radial and ulnar deficiencies in rat fetuses with the same drug. Radial and ulnar deficiencies induced in rats have similar clinical manifestations and these anomalies might be caused by the same teratogenic mechanism. Then, the formation of the digital rays was examined histologically. The results of histological examination suggested that these deficiencies were not caused by localized damage of the limb bud. They also suggested that the cause of missing digits in longitudinal deficiency is closely related to a deficit of mesenchymal cells in the limb bud. Cleft hand is considered to be one of the types of longitudinal deficiency. However, several investigators have suggested that the abnormal induction of finger rays in the process of formation of fingers induced central polydactyly, osseous syndactyly and also cleft hand. X-rays of the clinical cases and skeletal changes of the anomalies induced in rats appear to demonstrate that cleft hand formation proceeds from osseous syndactyly and central polydactyly. The results of our experimental study show that the critical periods of central polydactyly, osseous syndactyly and cleft hand are the same. They also suggest that central polydactyly, syndactyly and cleft hand might be induced when the same teratogenic factor acts on embryos at the same developmental stage in the human being. Because they have a similar causation, cleft hand, syndactyly and central polydactyly should be classified into the same entity, that is, abnormal induction of digital rays. Based on these clinical and experimental studies, we modified the Swanson classification. In our modified classification, typical cleft hand, syndactyly and polydactyly are included in the same category of abnormal induction of digital rays as the fourth new category.

Isothermal and non-isothermal oil–water flow and viscous fingering in a porous medium

Immiscible flow of heavy oil in a porous formation by high temperature pressurized water has been numerically studied. The physical region is a square domain in the horizontal plane with low and high pressure points at the opposite corners along one of the diagonals. Water, the invading fluid, when introduced at high pressure displaces the in situ oil towards the low pressure production zone. The extent of displacement of oil by water through the porous medium in a given amount of time and the appearance of preferential flow paths ( fingers) is the subject of the present investigation. The resistance to water–oil movement arises from the viscous forces in the fluid phases and the capillary force at their interface. Based on their relative magnitudes, various forms of displacement mechanisms can be realized. As the viscosity ratio of heavy oil to water is large, viscous forces in the oil phase become dominant and constitute the major factor for controlling the flow distortions in the porous formation. A mathematical model that can treat the individual fluid pressures, capillary effects and heat transfer has been employed in the present work. A fully implicit, two-dimensional numerical model has been used to compute the pressure and temperature fields. The domain decomposition technique has been adopted in the numerical solution since the problem is computationally intensive. Naturally occurring oil-rich reservoirs to which the present study is applicable are inhomogeneous and layered. A qualitative study has been carried out to explore the effect of permeability variations on the flow patterns. Numerical calculations show that non-isothermal effects as well as layering promote the formation of viscous fingers and consequently the sweep efficiency of the high pressure water front.

Granular finger formation in a rotating cylinder

It is well known that the front of a fluid sheet flowing over an inclined surface is unstable to spanwise perturbations. This instability, which manifests itself in the formation of fingers of fairly constant wavelength, reflects a competition between viscous stresses and surface tension. We present the results of an experiment involving a thin granular layer flowing within a horizontal rotating cylinder and report an assortment of stationary and temporally varying spatial patterns. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those encountered with Newtonian fluids. Because the materials used in these experiments are cohesionless and, thus, unable to sustain surface tension, this instability is surprising. As a step toward understanding these mechanisms, we develop a system of evolution equations that accounts for the steady motion of grains within the cylinder and for more complicated kinds of grain motions such as saltation and reptation. We find that the model is able to predict some of the qualitative features observed from our experiment.

Molecular dynamics study of the calcium ion transfer across the water/nitrobenzene interface.

A study on the calcium ion transfer across the water/nitrobenzene interface is presented. The potential of mean force was calculated and a good agreement was found between the experimental and the calculated free energy of transfer. This is a monotonically increasing function of the distance to the interface, and the process was found to be non-activated. The evolution of the first and second hydration shells was analysed as a function of the distance to the interface; the first hydration shell remains intact whereas the second hydration shell suffers a severe water loss. Water finger formation was also found, with behaviour similar to that already described for other ions in different interfaces. As far as we know, a direct comparison between the calculated number of water molecules dragged with an ion into the organic phase and the experimental results is presented for the first time and a very good agreement was found.