Narrow Fingers Research Articles

Seismic attenuation due to patchy saturation

[1] In porous rocks saturated in patches by two immiscible fluids, seismic compression causes the fluid with the larger bulk modulus to respond with a larger change in fluid pressure than the fluid with the smaller bulk modulus which results in fluid movement and seismic attenuation. For virtual rock samples having fluid distributions obtained using the invasion percolation model, attenuation is determined using finite difference numerical experiments based on the laws of poroelasticity. Analytical models are also proposed to explain the numerical results. When oil invades water, the equilibration is controlled by the geometry of the invading oil which has a narrow range of small diffusion lengths resulting in a single relaxation frequency at high frequencies and not much seismic band attenuation. When water invades oil, the defending oil controls the equilibration, and a power law emerges for how attenuation varies with frequency due to the fractal nature of how saturation is varying with scale in the defending oil. For air invading water, the geometry of the defending water controls the equilibration, and a large amount of attenuation is observed over a wide range of frequencies including the seismic band due to the wide range in water patch sizes. However, when water invades air, the narrow fingers of invading water control the equilibration, and there is a single relaxation frequency at high frequencies that does not result in much seismic band attenuation.

Finger tip behavior in small gap gradient Hele-Shaw flows

Finger tip splitting and finger tip narrowing phenomena are not commonly observed during early flow stages in parallel-plate rectangular Hele-Shaw cells. However, an interesting experimental study performed by Zhao [Phys. Rev. A 45, 2455 (1992)] showed that finger tip behavior can be significantly affected by the addition of a small gradient to the gap of the cell, so that the plates are no longer exactly parallel. It was found that pattern forming events at the finger tip are dictated by the sign of the gap gradient, where positive (negative) sign produces wider (narrower) fingers. We approach the nonparallel-plate situation analytically through a perturbative mode coupling theory and show that these important finger tip features can be predicted at early nonlinear stages of the dynamics.

On the relationship between finger width, velocity, and fluxes in thermohaline convection

Double-diffusive finger convection occurs in many natural processes. The theories for double-diffusive phenomena that exist at present consider systems with linear stratification in temperature and salinity. The double-diffusive systems with step change in salinity and temperature are, however, not amenable to simple stability analysis. Hence factors that control the width of the finger, velocity, and fluxes in systems that have step change in temperature and salinity have not been understood so far. In this paper we provide new physical insight regarding factors that influence finger convection in two-layer double-diffusive system through two-dimensional numerical simulations. Simulations have been carried out for density stability ratios (Rρ) from 1.5 to 10. For each density stability ratio, the thermal Rayleigh number (RaT) has been systematically varied from 7×103 to 7×108. Results from these simulations show how finger width, velocity, and flux ratios in finger convection are interrelated and the influence of governing parameters such as density stability ratio and the thermal Rayleigh number. The width of the incipient fingers at the time of onset of instability has been shown to vary as RaT−1∕3. Velocity in the finger varies as RaT1∕3∕Rρ. Results from simulation agree with the scale analysis presented in the paper. Our results demonstrate that wide fingers have lower velocities and flux ratios compared to those in narrow fingers. This result contradicts present notions about the relation between finger width and flux ratio. A counterflow heat-exchanger analogy is used in understanding the dependence of flux ratio on finger width and velocity.

CHANDRAANDXMMOBSERVATIONS OF THE COMPOSITE SUPERNOVA REMNANT G327.1-1.1

We present new X-ray imaging and spectroscopy of a composite supernova remnant G327.1-1.1 using the Chandra and XMM-Newton X-ray observatories. G327.1-1.1 has an unusual morphology consisting of a symmetric radio shell and an off center nonthermal component that indicates the presence of a pulsar wind nebula (PWN). Radio observations show a narrow finger of emission extending from the PWN structure towards the northwest. X-ray studies with ASCA, ROSAT, and BeppoSAX revealed elongated extended emission and a compact source at the tip of the finger that may be coincident with the actual pulsar. The high resolution Chandra observations provide new insight into the structure of the inner region of the remnant. The images show a compact source embedded in a cometary structure, from which a trail of X-ray emission extends in the southeast direction. The Chandra images also reveal two prong-like structures that appear to originate from the vicinity of the compact source and extend into a large bubble that is oriented in the north-west direction, opposite from the bright radio PWN. The emission from the entire radio shell is detected in the XMM data and can be characterized by a thermal plasma model with a temperature of 0.3 keV, which we use to estimate the physical properties of the remnant. The peculiar morphology of G327.1-1.1 may be explained by the emission from a moving pulsar and a relic PWN that has been disrupted by the reverse shock.

NMR imaging of fluid pathways during drainage of softwood in a pressure membrane chamber

An experiment was implemented to study fluid flow in a pressure media. This procedure successfully combines nuclear magnetic resonance imaging with a pressure membrane chamber in order to visualize the non-wetting and wetting fluid flows with controlled boundary conditions. A specially designed pressure membrane chamber, made of non-magnetic materials and able to withstand 4 MPa, was designed and built for this purpose. These two techniques were applied to the drainage of Douglas fir sapwood. In the study of the longitudinal flow, narrow drainage fingers are formed in the latewood zones. They follow the longitudinal direction of wood and spread throughout the sample length. These fingers then enlarge in the cross-section plane and coalesce until drainage reaches the whole latewood part. At the end of the experiments, when the drainage of liquid water in latewood is completed, just a few sites of percolation appear in earlywood zones. This difference is a result of the wood anatomical structure, where pits, the apertures that allow the sap to flow between wood cells, are more easily aspirated in earlywood than in latewood.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Analysis and Suppression of Side Radiation in Leaky SAW Resonators

This paper discusses side acoustic radiation in leaky surface acoustic wave (LSAW) resonators on rotated Y-cut lithium tantalite substrates. The mechanism behind side radiation, which causes a large insertion loss, is analyzed by using the scalar potential theory. This analysis reveals that side radiation occurs when the guiding condition is not satisfied, and the LSAW most strongly radiates at the frequency in which the LSAW velocities in the grating and busbar regions approximately correspond to each other. Based on these results, we propose a "narrow finger structure," which satisfies the guiding condition and drastically suppresses the side radiation. Experiments show that the resonance Q of the proposed structure drastically improves to over 1000 by suppressing the side radiation, which is three times higher than for a conventional structure. Applying the proposed resonators to the ladder-type SAW filters, ultra-low-loss and steep cut-off characteristics are achieved in the range of 800 MHz and 1.9 GHz.

Resistance characterization of Cu stress-induced void migration at narrow metal finger connected with wide lead

In this work, copper stress-induced voiding (SIV) at narrow metal finger connected with wide lead is investigated. Three failure modes are explored and discussed with different failure sites. A driving force for void migration resulted from hydrostatic stress gradient is also studied. Meanwhile, in order to assess the impact of copper void on multi-level interconnects, a model based on finite element analysis (FEA) is developed to simulate the resistance change with regard to voiding location, void morphology and interconnect scenario. Finally, a correlation between SIV and resistance change is obtained, which can serve as references for reliability evaluation and risk assessment.

Copper stress migration at narrow metal finger with wide lead

Copper stress migration (SM) at narrow metal finger connected with wide lead is investigated in this work. Voiding phenomenon is explored with respect to specific failure site. Metal geometric factors including lead width, lead length and finger length are also discussed in terms of SM failure rates. Meanwhile, in order to study the failure mechanism, a finite element analysis (FEA) is conducted to evaluate the influences from vacancy migration path, hydrostatic stress gradient and different metal geometries. As a result, a characterization regarding SM at narrow metal finger with wide lead is obtained for the reference of reliability assessment and process improvement.

Multi-resolution adaptive modeling of groundwater flow and transport problems

Many groundwater flow and transport problems, especially those with sharp fronts, narrow transition zones, layers and fingers, require extensive computational resources. In this paper, we present a novel multi-resolution adaptive Fup approach to solve the above mentioned problems. Our numerical procedure is the A daptive F up C ollocation M ethod (AFCM), based on Fup basis functions and designed through a method of lines (MOL). Fup basis functions are localized and infinitely differentiable functions with compact support and are related to more standard choices such as splines or wavelets. This method enables the adaptive multi-resolution approach to solve problems with different spatial and temporal scales with a desired level of accuracy using the entire family of Fup basis functions. In addition, the utilized collocation algorithm enables the mesh free approach with consistent velocity approximation and flux continuity due to properties of the Fup basis functions. The introduced numerical procedure was tested and verified by a few characteristic groundwater flow and transport problems, the Buckley–Leverett multiphase flow problem, the 1-D vertical density driven problem and the standard 2-D seawater intrusion benchmark–Henry problem. The results demonstrate that the method is robust and efficient particularly when describing sharp fronts and narrow transition zones changing in space and time.

Numerical simulations of fingering instabilities in surfactant-driven thin films

We study the surfactant-induced fingering phenomena in thin liquid films both below and beyond the critical micelle concentration using direct numerical simulations. Two-dimensional numerical solutions of the coupled nonlinear lubrication equations for the film thickness and surfactant interfacial and bulk concentrations are obtained for different values of the deposited surfactant mass M and underlying film thickness b. We show that these parameters have a profound effect on the fingering characteristics. At low to intermediate M, the deposited mound is relatively mobile and acts to “feed” the fingers that grow downstream efficiently; these fingers are essentially at the same elevation as the mound. At relatively high M values, narrower fingers form near the foot of a less mobile mound in a thinned region; this retards the supply rate of fluid from the mound. We also show that increasing b leads to less vigorous fingering. Our results are in agreement with trends observed experimentally.

Elastic flow-front fingering instability in flowing polymer solutions

An experimental investigation of the flow-front behavior of dilute and semi-dilute polymer solutions has been carried out to gain a better understanding of the underlying mechanisms leading to the occurrence of an unstable flow at the advancing flow-front during the filling of a rectangular Hele-Shaw cell. Our experimental results have revealed the existence of an elastic finger-like instability at the advancing flow-front that develops in semi-dilute solutions of high molecular weight polymers, with an onset time of approximately a few hundred milliseconds. Although at shear rates above critical, narrow finger patterns develop at the flow-front, their amplitude and number remain roughly constant throughout the flowing. At critical condition, no secondary flow was observed in the vicinity of the front region where the unstable flow develops. Transient response of the normal stress difference and the shear stress in the plate-and-plate geometry at shear rate above critical (for the elastic fingering instability in the Hele-Shaw cell) did not reveal any anomalous that could lead to the formation of such finger-like instabilities. These instabilities were observed for both the ideal elastic Boger fluids and shear thinning viscoelastic fluids.

Explosive instabilities: from solar flares to edge localized modes in tokamaks

The mechanisms for the explosive loss of plasma confinement that occurs in solar flares, magnetospheric sub-storms, tokamak disruptions and edge localized modes remain largely unexplained. Modelling the rapid onset of such events provides a considerable challenge to theory. A possible explanation for these events, nonlinear explosive ballooning, is discussed. In this mechanism a narrow finger of plasma erupts from inside the plasma growing explosively and pushing aside other field lines—the instability spreads from a small region until it disturbs lines across a large section of plasma. The model predicts the observed features of some high β tokamak disruptions.

Interface scaling in a two-dimensional porous medium under combined viscous, gravity, and capillary effects.

We have investigated experimentally the competition between viscous, capillary, and gravity forces during drainage in a two-dimensional synthetic porous medium. The displacement of a mixture of glycerol and water by air at constant withdrawal rate has been studied. The setup can be tilted to tune gravity, and pressure is recorded at the outlet of the model. Viscous forces tend to destabilize the displacement front into narrow fingers against the stabilizing effect of gravity. Subsequently, a viscous instability is observed for sufficiently large withdrawal speeds or sufficiently low gravity components on the model. We predict the scaling of the front width for stable situations and characterize it experimentally through analyses of the invasion front geometry and pressure recordings. The front width under stable displacement and the threshold for the instability are shown, both experimentally and theoretically, to be controlled by a dimensionless number F which is defined as the ratio of the effective fluid pressure drop (i.e., average hydrostatic pressure drop minus viscous pressure drop) at pore scale to the width of the fluctuations in the threshold capillary pressures.

Viscous fingering in non-Newtonian fluids

We study the viscous fingering or Saffman–Taylor instability in two different dilute or semi-dilute polymer solutions. The different solutions exhibit only one non-Newtonian property, in the sense that other non-Newtonian effects can be neglected. The viscosity of solutions of stiff polymers has a strong shear rate dependence. Relative to Newtonian fluids, narrower fingers are found for rigid polymers. For solutions of flexible polymers, elastic effects such as normal stresses are dominant, whereas the shear viscosity is almost constant. Wider fingers are found in this case. We characterize the non-Newtonian flow properties of these polymer solutions completely, allowing for separate and quantitative investigation of the influence of the two most common non-Newtonian properties on the Saffman–Taylor instability. The effects of the non-Newtonian flow properties on the instability can in all cases be understood quantitatively by redefining the control parameter of the instability.

The nonlinear behavior of a sheared immiscible fluid interface

The two-dimensional Kelvin–Helmholtz instability of a sheared fluid interface separating immiscible fluids is studied by numerical simulations. The evolution is determined by the density ratio of the fluids, the Reynolds number in each fluid, and the Weber number. Unlike the Kelvin–Helmholtz instability of miscible fluids, where the sheared interface evolves into well-defined concentrated vortices if the Reynolds number is high enough, the presence of surface tension leads to the generation of fingers of interpenetrating fluids. In the limit of a small density ratio the evolution is symmetric, but for a finite density difference the large amplitude stage consists of narrow fingers of the denser fluid penetrating into the lighter fluid. The initial growth rate is well predicted by inviscid theory when the Reynolds numbers are sufficiently high, but the large amplitude behavior is strongly affected by viscosity and the mode that eventually leads to fingers is longer than the inviscidly most unstable one.

Imbibition of saline solutions into dry and prewetted porous media

Infiltration of saline solutions and pure water into homogeneous packs of prewetted and air-dry silica sands was investigated using a light transmission system. Four sand grades and five solutions were considered. Narrow fingers with a sharp, almost saturated, wetting front were observed in the air-dry sands. The water content left behind the fingertip of saline solutions was higher than for pure water, resulting in a greater lateral expansion of the saline fingers over time. The rate of lateral expansion scaled with the square root of time, likely due to classic liquid sorption with the possible addition of water vapor diffusion. At early time, the salty fingers moved faster, but were ultimately overtaken by the pure water fingers. In prewetted sand, the wetting fronts were diffuse and never exceeded 26% saturation, less than third that seen in the initially air-dry media. The plumes in the prewetted sand were also much wider and their shape varied. In the prewetted sand the elevated surface tension of the saline solutions was the major cause for the observed differences in finger width and velocity, yet appeared to be insignificant in air-dry sand. Here, in addition to the density effect, absorption of the saline solution to the silica sand influenced the depth of wetting, finger velocity, and subsequent lateral expansion.

Viscous fingering in a shear-thinning fluid

We study the Saffman–Taylor instability in a rectangular Hele-Shaw cell. The driven fluid is a dilute (or semidilute) polymer solution, with a viscosity that exhibits shear thinning. Other non-Newtonian properties such as elastic effects are negligible under the present experimental conditions; the system thus allows for separate investigation of the influence of shear thinning on the instability. The experiments show that, for weak shear-thinning, the results for the width of the fingers as a function of the capillary number collapse onto the universal curve for Newtonian fluids, provided the shear-thinning viscosity is used to calculate the capillary number. For stronger shear thinning, narrower fingers are found. The experiment allows also for a study of the applicability of Darcy’s law to shear thinning fluids. For Newtonian fluids, this law gives the finger velocity as a function of the pressure gradient. For weakly shear-thinning fluids, we find that an effective Darcy’s law, in which the constant viscosity is replaced by the shear-thinning viscosity, gives good agreement with the experiments. For stronger shear thinning, the predictions from the effective Darcy’s law deteriorate. Satisfactory agreement with experimental data can be obtained when using a “shear-thinning” Darcy’s law, which can be derived using a power law model for the shear rate dependence of the viscosity.

Microstructure of the auroral acceleration region as observed by FAST

The Fast Auroral Snapshot (FAST) explorer satellite was designed to investigate the microscale structure of the auroral acceleration region that was unresolved by previous satellites. This paper will present highlights from the first 2 years of the FAST mission and compare them with previous observations and auroral models. In particular, we find good agreement with the overall field‐aligned current systems previously discovered; however, we present evidence that the downward currents are often carried by energetic upgoing electrons. These upgoing electrons are correlated with diverging electrostatic shocks, indicating that quasi‐static parallel electric fields are responsible for their energization. Some of these field‐aligned fluxes contain large‐amplitude fast solitary waves which produce strong modulations of the electrons. Observations in inverted‐V arcs show that the parallel acceleration region contains narrow (∼10 km) fingers of potential that extend along the magnetic field. On these narrow kilometer scales, ion beam energies are found to agree with the inferred potential determined from the perpendicular electric field or from the widening of the electron loss cone, implying acceleration is typically quasi‐static on ion transit times. We also find evidence that both the ion and electron upgoing beams produced by the parallel electric fields have plateaued parallel distribution functions. Fast solitary waves are a prime candidate to stabilize the electron beams and may provide the resistance that allows the downward directed parallel electric fields to form in the highly conducting ionosphere. Intense ion cyclotron waves and ion solitary waves are often observed during ion beams, but the stabilizing waves have not been identified. In addition, intense electromagnetic ion cyclotron waves are also observed in inverted‐V arcs, along with strongly modulated electron fluxes, indicating that turbulent acceleration is occurring in addition to simple acceleration by a static potential drop.

Movement and remediation of trichloroethylene in a saturated heterogeneous porous medium: 1. Spill behavior and initial dissolution

An intermediate-scale flow cell experiment was conducted to study the flow of liquid and the transport of dissolved trichloroethylene (TCE) in a saturated, heterogeneous porous medium system. The 1.67-m long by 1.0-m high by 0.05-m wide flow cell was packed with three layers and five lenses consisting of four different sands. All lenses and layers had horizontal interfaces, except the lowest interface, which was pointed down in the middle. Groundwater flow was imposed by manipulating the water levels in two head chambers. Over 500 ml of dyed TCE was allowed to infiltrate at a constant rate into the porous medium from a narrow source located on the surface. A dual-energy gamma radiation system was used to determine TCE saturations at 1059 locations. Fluid samples were collected from 20 sampling ports to determine dissolved TCE concentrations. The TCE migrated downwards in the form of several relatively narrow (3–8 mm) fingers. Visual observations and measured TCE saturations indicated that the spilled TCE accumulated on top of, but did not penetrate into, fine-grained sand lenses and layers but that some TCE infiltrated into medium-grained sand lenses. This behavior is a result of the different nonwetting-fluid entry and permeability values of the sands. Most of the TCE finally pooled on top of a fine-grained sand layer located in the bottom part of the flow cell. A multifluid code (STOMP: subsurface transport over multiple phases), accounting for TCE entrapment, was used to simulate the movement of liquid TCE. Using independently obtained hydraulic parameter values, the code was able to qualitatively predict the observed behavior at the interfaces of the lenses and sand layers. Simulation results suggest that most of the liquid TCE at the lowest interface was in free, continuous form, while most of the other TCE remaining in the flow cell was entrapped and discontinuous. A simple pool dissolution model was used to predict observed dissolved TCE concentrations. Results show that the measured concentrations could only be predicted with unrealistically high transverse dispersivity values. The observed TCE concentrations are a result of a combination of entrapped and pool dissolution.