Small Separation Distances Research Articles

Model for the interaction between a bubble and an elastic particle

At the Providence meeting, a model describing the interaction of a spherical bubble with a rigid spherical particle was presented [Hay and Hamilton, J. Acoust. Soc. Am. 119, 3408 (2006)]. Here, elasticity of the particle is considered. The model accounts for pulsation and translation and is accurate to fifth order in terms of the ratio of characteristic radius to separation distance. The dynamical equations are derived using the Lagrangian formalism of Ilinskii et al. [Proc. 17th ISNA, edited by Atchley et al. (AIP, New York, 2006), pp. 303–310]. Bubbles and elastic solid particles are considered with radii on the order of microns and driven at megahertz frequencies. The radial particle motion is quasistatic under these conditions. For moderate bubble pulsations at which the liquid may be considered incompressible, translational motion of the bubble and particle is insensitive to whether the particle is elastic or rigid. Consideration is also given to truncation of the model at fifth order. Derivation of the model equations to arbitrary order was facilitated by the development of a computer algebra program. The importance of including higher‐order terms for small separation distances is illustrated. [T.A.H. was supported by an NSF Graduate Research Fellowship.]

Heat transfer characteristics of three interacting methane/air flame jets impinging on a flat surface

An experimental study has been conducted for three interacting methane/air flame jets (arranged in a triangular configuration) impinging normally on a flat surface. Surface heat flux distributions have been determined for various dimensionless inter-jet spacings ( S/ d = 3, 4, 6 and 7.58) and separation distances between the exit plane of the burners and the target plate ( H/ d = 2, 2.6, 5 and 7). All experiments were conducted for stoichiometric mixture at a Reynolds number of 800. The surface heat flux distributions were intimately related to flame shapes. For small inter-jet spacings and small separation distances, flames were deflected outward from the centroid of the triangular arrangement due to strong interaction between the jets. The heating was quite non-uniform at very large inter-jet spacings. Zones of low heat flux were obtained when the tip of inner reaction zones were intercepted by the plate ( H/ d = 2). There were sharp peaks in the heat flux distribution when the tips of the inner reaction zones just touched the impingement surface ( H/ d = 2.6). Heat flux distribution was non-uniform at small separation distances ( H/ d = 2 and 2.6). For the system of flame jets under consideration, the optimum configuration, considering the magnitude of the average heat flux and the uniformity in the heat flux distribution, was corresponding to H/ d = 5 and S/ d = 3.

Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10 - μ m . Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank–Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range 40 – 160 nm were floated using fine bubbles of typical average diameter 150 μ m . The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of 100 nm . With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.

Dislocation and stacking fault core fields in fcc metals

Atomistic models were used to determine the properties of dislocation core fields and stacking fault fields in Al and Cu using embedded atom method (EAM) potentials. Long-range, linear elastic displacement fields due to nonlinear behaviour within dislocation cores, the core field, for relevant combinations of Shockley partial dislocations for edge, screw, and mixed (60° and 30°) geometries were obtained. Displacement fields of stacking faults were obtained separately and used to partition the core field of dissociated dislocations into core fields of partial dislocations and a stacking fault expansion field. Core field stresses were derived from which the total force, including the Volterra field plus core field, between dislocations for several dislocation configurations was determined. The Volterra field dominates when the distance between dislocations exceeds about 50b but forces due to core fields are important for smaller separation distances and were found to affect the equilibrium angle of edge dislocation dipoles and to contribute to the force between otherwise non-interacting edge and screw dislocations. Interactions among the components of a dissociated dislocation modify the equilibrium separation for Shockley partials suggesting that methods that determine stacking fault energies using measurements of separation distances should include core fields.

Spatial Continuity of Tree Attributes in Bottomland Hardwood Forests in the Southeastern United States

Abstract Sustainable forest management and conservation require understanding of underlying basic structural and competitive relationships. To gain insight into these relationships, we analyzed spatial continuity of tree basal area (BA) and crown projection area (CPA) on twelve 0.64-ha plots in four mixed bottomland hardwood stands in Louisiana, Arkansas, and Mississippi. Variogram range indicated that BA spatial continuity of trees with dbh >10.0 cm extended an average 4.5 m. This distance equaled the quadratic mean crown radius (QMCR) of the overstory trees. Overall, 95% of the variability in BA was accounted for by the spatially structured variance and could be modeled as spatial dependence. Removal of suppressed trees from the analyses reduced the variability in BA at small separation distances and increased the variogram range. The average spatial continuity of unsuppressed trees averaged 18.2 m and was 17.6, 18.5, and 18.5 m based on the BA variograms, CPA variograms, and cross-variograms, respectively. This distance corresponded to four times the QMCR of the overstory trees and extended far enough to encompass the first- and second-order neighbors. The results suggest an existence of complex competitive influences and confirm findings in nonwoody vegetation that competitive effects can propagate beyond the direct neighbors. FOR. SCI. 51(6):532–540.

Protein separation on a technical scale using a radial symmetric free flow zone electrophoresis cell

In this paper a new, continuously operated, radially symmetric electrophoresis device is presented, which is intended for preparative application in downstream processing of biological products. Due to the small separation distance of at most a few millimeters, Joule heating can be neglected. The accelerated, inward directed flow contributes to the suppression of turbulence and free convection. A detailed description of the design of the apparatus is followed by a discussion of the two-dimensional flow pattern and the protein trajectories within the electric field. A sample stream of 400 mL/h containing three proteins (BSA, myoglobin and cytochrome c ) was processed, yielding an almost complete separation of the three components with high values of purity and recovery. Investigations of the possible maximal throughput and different band broadening effects are discussed.

Eccentric electrophoretic motion of a sphere in circular cylindrical microchannels

The eccentric electrophoretic motion of a spherical particle in an aqueous electrolyte solution in circular cylindrical microchannels is studied in this paper. The objective is to investigate the influences of separation distance and channel size on particle motion. A theoretical model is developed to describe the electric field, the flow field and the particle motion. A finite element based direct numerical simulation method is employed to solve the model. Numerical results show that, when the particle is eccentrically positioned in the channel, the electric field and the flow field are not symmetric, and the strongest electric field and the highest flow velocity occur in the small gap region. It is shown that the rotational velocity of the particle increases with the decrease of the separation distance. With the decrease of the separation distance, the translational velocity increases in a smaller channel; while it decreases first and then increases in a relatively large channel. When a particle moves eccentrically at a smaller separation distance from the channel wall, both the translational velocity and the rotational velocity increase with the decrease of the channel size.

Spatial variability of orange roughy around the Northwest Hills on the Chatham Rise, New Zealand

We used research trawl survey data to describe the small-scale distribution and spatial continuity of orange roughy catch rates around the Northwest Hills complex of seamount features on the Chatham Rise to the east of New Zealand. Analyses revealed three distinct spatial patterns. The larger scale spatial structure in the catch rates was defined by the contours running east–west along the Chatham Rise. Orange roughy were caught in a depth band between 850 and 1200 m , a depth distribution that is well known. Superimposed on this larger scale structure was a north–south trend in the highest catch rates at 180 ∘ longitude. This was created by higher catch rates on the seamounts. There were large differences in catch rates at small separation distances due to the seamount effect. However, not all the high catches were associated with seamounts, some being taken on the ‘flat’ areas around the hills. At distances away from the seamounts greater than the decorrelation length scale the spatial distributions of orange roughy catch rates were not random, and did not conform to a Poisson process used to characterise random distributions. Data visualisation of the spatial distributions of orange roughy and groups of bycatch revealed strong patchiness and spatial separation by depth of swimbladder fish, elasmobranchs and squid and oreos. This has important implications for acoustic surveys. Orange roughy overlapped most closely with swimbladder fish distributions, suggesting they may be obscured by species with higher acoustic target strengths. The observed separation of acoustically distinct fish groups by depth makes ground-truthing of acoustic backscatter easier. However, patchiness complicates prediction of where the acoustically distinct fish groups will occur. We conclude that extensive trawling provides a necessary complement to acoustic survey in order to estimate the biomass of orange roughy.

A NEW MODEL FOR THE ELECTRICAL DOUBLE LAYER INTERACTION BETWEEN TWO SURFACES IN AQUEOUS SOLUTIONS

A new theoretical model is developed to evaluate the total potential energy of interaction between two charged flat plates in aqueous solutions. Instead of using the Boltzmann distribution to predict the ionic concentrations of counterion and coion, which is not correct for small confined spaces, this modified model determines the ionic concentrations of counterion and coion based on the Poisson equation, the Nernst equation, and the mass conservation condition. Instead of the approximations used in the traditional model, the osmotic pressure is directly evaluated based on the ionic concentration distributions predicted by this new model. Finally, the total interaction energy is examined and compared with that predicted by the traditional model. It has been found that for high ionic concentration solutions, the traditional model tends to overestimate the total interaction energy due to the approximations employed in simplifying the osmotic pressure. However, for dilute solutions, the traditional model tends to underestimate the total interaction energy at small separation distance due to the misuse of the Boltzmann distribution in calculating the ionic concentration.

Second-Order Equations for Rendezvous in a Circular Orbit

Introduction T HIS Note develops an approximate analytical solution of the two-body orbital boundary-value problem, known as Lambert’s problem, using a time-explicit analytical solution of the relative motion problem. Explicitly stated, the problem is to determine the initial velocity of a satellite, given two position vectors and a time of flight between them. Although the classical origin of the problem related to the determination of planetary orbits, present-day applications are in the area of intercept and rendezvous guidance, where the initial velocity of a maneuvering spacecraft for which its position will coincide with a target position at a specified time must be determined. A short history of Lambert’s problem is given in Ref. 1. Numerical solutions of the problem have been developed by Battin and Vaughan1,2 and Gooding3 for example; however, for small separation distances, such as those encountered in many intercept and rendezvous problems, analytical solutions may be determined using a relative motion formulation. A closed-form solution of Lambert’s problem has been developed previously by Clohessy and Wiltshire in Ref. 4 and has been applied to a variety of intercept and rendezvous problems, as in Refs. 5–10, for example. This solution results from a linear approximation of the equations of motion, and thus the validity range is limited. A higher-order approximation of the equations of motion may extend the range of applicability and lead to an increased level of accuracy. There have been several attempts at developing relative motion equations that take nonlinear dynamics into account.11−14 The solutions presented in Refs. 11–14 result from a straightforward expansion, a method that constructs a truncated Taylor series representation of the exact solution. Anthony and Sasaki,12 Kechichian,13 and Kelly14 show how the nonlinear relative motion equations may be used to solve Lambert’s problem. While these solutions are more accurate than the solutions resulting from the linearized model, the validity region is limited to short periods of time due to the presence of secular terms. For a fixed time, solutions derived from the straightforward expansion will converge to the value of the exact solution as the number of terms in the expansion grows. For a fixed number of terms, however, the accuracy is diminished as time increases and the secular terms begin to dominate the solution. Karlgaard and Lutze15 used a multiple-scale perturbation method to determine a solution of the relative motion problem that included the effects of second-order terms kept in the expansion of the Keplerian equations of motion about a circular reference orbit. The multiple-scale approach allowed elimination of the secular terms by determination of the appropriate differential equations that

Modelling of droplet interaction in convective gas flows

This paper concerns the modelling of the interaction of droplets in a convective gas flow. In spray computations, typically, the interaction of droplets during heating, vaporisation, ignition, and combustion is neglected. This approximation has been found to be poor since neighbouring droplets constitute an energy sink and a fuel source for the gas surrounding the droplets. Therefore, an effort needs to be made to relax this simplification. The present paper presents preliminary results of the interaction of two spheres in a convective flow field where the emphasis lies on the gas-phase effects. The computations show that the characteristics of the gas flow changes substantially as the separation distance between the two spheres changes. Under conditions for which steady axi-symmetric flow exists over a single sphere, the flow is completely asymmetric when there is hydrodynamic interaction with another sphere. Also there is repulsion between the droplets at small separation distances. The present three-dimensional study will be extended to the case of combusting, interacting droplets so that a general model will be available for use in spray combustion systems.

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich. (Some figures in this article are in colour only in the electronic version) 1ucf.edu/∼cyyoung

Nonlinear Orbital Dynamic Equations and State-Dependent Riccati Equation Control of Formation Flying Satellites

Precise maneuvers of formation flying satellites require a general orbital dynamic equation and an effective nonlinear control method. In this paper, nonlinear orbital dynamics of relative motion equations are derived for a constant distance separation formation flying problem. This general orbital dynamic equation allows elliptic, noncoplanar, and large separation distances between spacecraft as well as traditional circular, coplanar, and small separation distance cases. Furthermore, for the in-plane formation flying scenario with large constant angle of separation between satellites, we derive the change in position and velocity equations. A nonlinear control method called the state-dependent Riccati equation control method is utilized to solve the formation flying control problem. This novel control method for a nonlinear system allows the intuitive design tradeoff between the control action and the state error similar to the classical linear-quadratic-regulator control method. Two numerical simulations demonstrate the effectiveness of the new state-dependent Riccati equation control method with the newly developed relative motion equations.

Effects of Polymer Bridging and Electrostatics on the Rheological Behavior of Aqueous Colloidal Dispersions†

AbstractEffects of a low molecular weight physically adsorbed polyethylene oxide (PEO) and the range of the electrostatic repulsion on the rheological behavior of silica dispersions (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing the polymer concentration in the system and also effectiveness of the polymer as a dispersant under extreme conditions (high ionic strength). Results indicate that at small separation distances and low polymer coverage, the polymer chains are long enough to adsorb on the surface of two particles simultaneously causing bridging flocculation in the system and hence increasing the viscosity and linear viscoelastic functions of the dispersion. A significant increase was observed in the viscosity of the dispersion at salt concentrations high enough to eliminate electrostatics between the particles. Under these conditions,the viscosity of the system increased significantly when PEO was added to the dispersion showing that at high electrolyte concentrations, a neutral polymer such as PEO is not able to stabilize the system.

Nanocrystallinity effects in lithium battery materials

Nanostructured materials offer the possibility to make use of small transport lengths and small separation distances almost like in fluids, but unlike fluids, the higher structural stability of the solid state can be taken advantage of. Recent findings in the field of Li-batteries highlight the potential for room temperature applications. This paper addresses advantages and disadvantages of nanostructured matter with respect to stability, storage capacity, voltage and charging/discharging rates. In this context we discuss a novel interfacial storage mechanism for lithium which, in the mesoscopic case, forms a bridge between batteries and capacitors.

Solitons in the presence of a static spin vacancy on a 2D Heisenberg antiferromagnet

We study the behavior of the Belavin–Polyakov soliton with size R localized at the origin in the presence of a static spin vacancy at distance r 0 away in a two-dimensional isotropic antiferromagnet. It is found that an effective interaction between the two defects is attractive for small distances of separation ( r 0< R) and repulsive for large separations ( r 0> R). For the case in which the spin vacancy is located at the soliton center ( r 0=0), we found that, besides the Belavin–Polyakov soliton, another different type of soliton is possible and its configuration, energy and size were obtained analytically.

Electromagnetic resonances in individual and coupled split-ring resonators

We study experimentally and numerically the electromagnetic resonances in split ring resonators (SRRs), around 1 GHz. For an individual SRR, we show that both electric and magnetic fields can induce resonances, the magnetic one being the strongest. The utilization of such resonant structures as efficient microwave filter is also demonstrated. The coupling between two or more SRRs can be quite complex and strongly depends on their geometrical arrangement. For small separation distances, very strong coupling, leading to sharp resonances with high quality factors are observed. In that case a magnetic field circulation which connects neighboring elements is established. The practical implications of these results for the fabrication of a left-handed metamaterial are discussed.

Detailed heat transfer measurements of impinging jet arrays issued from grooved surfaces

Heat transfer augmentation of impinging jet-array with very small separation distances ( S/ D j <1) is attempted by using the grooved orifice plate through which the nozzles with different diameters are fitted. The combined effects of groove and nozzle-size distribution in an array have demonstrated considerable influences on heat transfers via their impacts on inter-jet reactions. With a specified coolant flow rate; the detailed heat transfer distributions over the impinging surfaces of three tested arrays are compared to reveal the optimal selections of separation distance and array configuration. Heat transfer modifications caused by varying jet Reynolds number ( Re) and separation distance ( S/ D j ) over the ranges of 1000⩽ Re⩽4000 and 0.1⩽ S/ D j ⩽8 are examined for each test array. In conformity with the experimentally revealed heat transfer physics, a regression-type analysis is performed to develop the correlations of spatially-averaged Nusselt numbers, which permit the individual and interactive effect of Re and S/ D j to be evaluated.

Deposition of Spherical Particles onto Cylindrical Solid Surfaces: I. Numerical Simulations

In this article, analytical and numerical solutions are given for the deposition of spherical particles onto cylindrical solid surfaces. If only the retarded van der Waals (vdW) force and the electrical double-layer (EDL) force between the spherical particle and the cylindrical surface are considered, such a deposition process is governed by a one-dimensional (1D) mass transfer equation for which both analytical and numerical solutions are obtained. A parametric study was conducted to examine the effects of these two colloidal forces on the deposition process. The numerical results show that the attractive vdW force, as represented by the dimensionless adhesion number Ad, is a necessary condition for deposition to occur. However, it affects only the drop number concentration distribution and, to a limited extent, the mass transfer rate. In general, the 1D deposition process is dominated by the EDL force, as represented by the dimensionless EDL parameter Dl and the reduced radius τ=κa of the spherical drop. It is noted that τ plays a key role in determining the effect of the EDL force on the mass transfer rate since an appreciable EDL force exists only within small separation distances (≤3τ−1). In addition to the two colloidal forces, the deposition process was also investigated in the presence of gravity and with a vertically applied electrical force. With these two external forces, the deposition becomes a two-dimensional (2D) boundary value problem for which a numerical solution was achieved using the implicit Crank–Nicolson method. Their effects on the 2D deposition process were studied.

Multispacecraft measurements of plasma and magnetic field variations in the magnetosheath: Comparison with Spreiter models and motion of the structures

Large (from tens of percent up to several times) ion flux (or density) and magnetic field magnitude variations are typical magnetosheath features. Case and statistical comparisons of simultaneous solar wind observations, magnetosheath observations, and the gasdynamic model for the magnetosheath flow of Spreiter et al. (Planet. Space Sci. 14 (1966) 223) show that two types of magnetosheath plasma and magnetic field variations exist: • in some cases, they are a repetition or amplification of solar wind or IMF disturbances which pass through the bow shock; • but in the most cases, these variations are endogenous; i.e., they originate inside the magnetosheath. Persistence times and/or correlation lengths for the magnetosheath plasma variations were investigated via detailed comparison of simultaneous magnetosheath measurements from several spacecraft. For small separation distances (about 0.5 R E) we used the satellite pair INTERBALL-1/MAGION-4; for larger distances (up to 10–30 R E on the same or on the opposite flanks of the magnetosheath) we used the INTERBALL-1/GEOTAIL/IMP 8 measurements. In some cases, we observed a remarkable coincidence of the magnetosheath plasma behavior from the spacecraft separated by more than 10 R E. It seems that the compression plasma structures move tailward together with the magnetosheath plasma flow.