Density Of Solid Phase Research Articles

Progress of conversion in a shrinking wet cylindrical wood particle pyrolyzing in a hot fluidized bed

A two-dimensional (2D) mathematical model in cylindrical coordinates has been formulated and used to predict the progress of conversion in a cylindrical wood particle undergoing pyrolysis in a fluidized bed. The transient model takes into account the heat consumed and shrinkage during drying and pyrolysis reactions in addition to anisotropy and changing thermal properties during the conversion. Predicted centre temperature has been compared with measurements found in the literature for validating the model. Calculations have been carried out for a 10 mm long and 10 mm diameter wooden cylinder in a bed of sand at 1107 K and fluidized by nitrogen. Developing profiles of temperature, solid-phase density, moisture content and degree of conversion at various stages have been presented. It is found that the conversion progresses faster and the gradients are steeper across the grains than along them. A comparison with a 1D model shows that thermal wave propagation predicted by the 2D model is faster than that of 1D.

Parametric Sensitivity Analysis of Fast Load Changes of a Dynamic MCFC Model

Molten carbonate fuel cells are well suited for stationary power production and heat supply. In order to enhance service lifetime, hot spots, respectively, high temperature gradients inside the fuel cell have to be avoided. In conflict with that, there is the desire to achieve faster load changes while temperature gradients stay small. For the first time, optimal fast load changes have been computed numerically, including a parametric sensitivity analysis, based on a mathematical model of Heidebrecht. The mathematical model allows for the calculation of the dynamical behavior of molar fractions, molar flow densities, temperatures in gas phases, temperature in solid phase, cell voltage, and current density distribution. The dimensionless model is based on the description of physical phenomena. The numerical procedure is based on a method of line approach via spatial discretization and the solution of the resulting very large scale optimal control problem by a nonlinear programming approach.

Determination of solid phase chemical diffusion coefficient and density of states by electrochemical methods: Application to iridium oxide-based thin films

Potentiostatic intermittent titration technique (PITT) and electrochemical impedance spectroscopy (EIS) were investigated as methods to determine solid phase chemical diffusion coefficient (D) and electronic density of states (DOS). These techniques were then applied to iridium oxide (IrOx) and iridium-tantalum oxide (IrTaOx) thin films prepared by sputter deposition. The experiments, performed in 1M propionic acid between −0.2 and 0.8V vs Ag∕AgCl, showed effects of interfacial side reactions, whose contribution to the electrochemical response could be identified and corrected for in the case of PITT as well as EIS. It was found that D is strongly underestimated when using PITT with the common Cottrell formalism, which follows from non-negligible interfacial charge transfer and Ohmic resistances. EIS indicated an anomalous diffusion mechanism, and D was determined to be in the 10−11–10−10cm2∕s range for IrOx and IrTaOx. Both PITT and EIS showed that the intercalated charge as a function of potential exhibits a shape that resembles the theoretical DOS of crystalline iridium oxide, especially for IrTaOx.

Compaction processes in granular beds composed of different particle sizes

A piston impacting a granular bed will cause the material to compact; the strength of a granular bed is significant during weak impact relating to piston speeds of 100m∕s. The strength associated with the granular structure is described as the intergranular stress; this is the resistance of a granular bed to compaction which can be measured by carefully constructing experiments. The compaction process may then be modeled by solving a hyperbolic system of equations that utilizes these data to close the system. The compaction behavior of a porous material is particle-size dependent; to accurately describe the response of two granular beds that may be of different particle sizes and distributions, it is essential that the intergranular stress is derived for each particle bed. This work uses recent compaction experiments to derive intergranular stress curves for prepressed conventional HMX material that is of nonuniform distribution with a mean diameter of 40μm and a microfine HMX of more uniform distribution of mean diameter <5μm. Steady-state compaction waves in the solid material are analyzed: initially the solid is assumed to behave as an incompressible medium. The speed and extent of compaction can be simply determined through the solution of a quadratic equation. Following this, the assumption is relaxed allowing changes in solid-phase density; a complicated equation of state makes the use of numerical methods mandatory. The speed of steady-state waves in HMX due to low impact compaction can be determined within 2% accuracy using the simple closed solution based on solid incompressibility, which is a function of the initial material porosity and density, piston speed, and the intergranular stress of the granular bed. This analysis reveals the difference between the weak impact response of a coarse nonuniform bed and a fine almost uniform granular bed that are initially loaded to 75% of the theoretical maximum density. The fine particle beds have increased resistance to compaction meaning that the extent of compaction is reduced and the speed of compaction waves are faster. The long-term objective of this research is the study of combustion and detonation in granular beds; a two-phase flow capability is required to simulate this type of problem. A multiphase flow model is utilized to simulate the complete low impact response of HMX that includes gas-phase effects. The time-dependent flow rapidly attains steady-state conditions; these solutions agree with the steady-state solutions of the reduced problem described above. Dissipation due to compaction is analyzed and compared with other dissipative processes within the system.

Thermoelectric properties of silver-doped n-type Bi 2Te 3-based material prepared by mechanical alloying and subsequent hot pressing

Effect of Ag-doping on thermoelectric properties of n-type Bi 2(Te 0.94,Se 0.06) 3 is studied. Bulk Bi 2(Te 0.94,Se 0.06) 3 sample with single solid solution phase and high relative density (over 95%) is obtained by mechanical alloying and subsequent hot press sintering. The as-sintered sample has a microstructure of randomly distributed plate grains and its size is about 1 μm. A V-shaped variation for the electrical properties with Ag doping is found which corresponds to different Ag atomic position in lattice among the doping range studied. A maximum figure of merit of about 1.7 × 10 −3/K is achieved.

Freezing transition and correlated motion in a quasi-two-dimensional colloid suspension.

Recent experiments have demonstrated that the deviation of the single-particle displacement distribution from Gaussian form in a dense quasi-two-dimensional colloid suspension is a result of heterogenous dynamics that involves cooperative motions of neighboring colloid particles [J. Chem. Phys. 47, 9142 (2001)]. In this paper, we report the results of molecular dynamics (MD) simulations of a quasi-two-dimensional assembly of nearly hard-sphere colloid particles. The colloid-colloid interaction we use is short ranged and everywhere repulsive; it is related to the Marcus-Rice (MR) and modified MR interactions used in a previous study [Phys. Rev. E 58, 7529 (1998)]. As is the case for those systems, the one we study supports liquid, hexatic, and solid phases. Our calculations show that the deviation of the single-particle displacement distribution from Gaussian form is present in the liquid phase, and that a sharp increase in its magnitude occurs at the liquidus density and extends into the crystalline phase. For densities greater than the liquidus density we find three dynamical relaxation processes that include, at intermediate times, a slowing down in the rate of growth of the diffusive displacement of a particle due to the cage effect. As the density increases toward the solidus density, the dependence of the mean squared displacement on time, at intermediate times, changes from sublinear to zero. The onset of the long-time relaxation mode corresponds to the time at which the deviation of the particle displacement distribution from Gaussian form is a maximum. At this time, which increases exponentially with the density, the self-part of the van Hove function exhibits multiple maxima with respect to r while the distinct part of the van Hove function is a maximum at the origin, thereby signaling jump dynamics. At long times the particle mean square displacement has diffusive character at all densities including solid phase densities. A remarkable feature of our findings is the continuity of character of the particle displacement from the liquid phase through the hexatic phase and into the solid phase. Cooperative jumps that lead to diffusive process in crystals can be explained by a mechanism that involves many such correlated hops in random locations and random directions (but along the crystallographic axes) thereby generating effective random walk behavior. We argue that the collective motion we have found is generated by superpositions of instantaneous normal mode vibrations along diffusive paths. The diffusive paths are along the directions with strong bond orientation correlation, and start to grow in amplitude rapidly on entry into the hexatic phase.

Equilibrium and nonequilibrium molecular dynamics methods for determining solid–liquid phase coexistence at equilibrium

The solid–liquid equilibrium phase transition of a one-component Lennard-Jones system is determined by equilibrium and nonequilibrium molecular dynamics simulation methods. One method uses the observation that the scaling exponent of the pressure or energy of a shearing Lennard-Jones liquid is approximately 1 at the solid phase. This enables us to locate the density of the coexisting solid phase. The coexisting liquid phase density is then obtained by constructing a tie line between the coexisting solid phase point and the liquid phase curve. Alternatively, the coexisting liquid phase density can be efficiently obtained by observing the change in pressure as a function of strain rate and density. The coexisting solid phase density can be then obtained from a tie line from the liquid curve to the solid curve. These calculations are the first reported use of combined equilibrium and nonequilibrium molecular dynamics methods for phase coexistence at equilibrium. Our results are in very good agreement with those obtained by alternative simulation methods for phase equilibria.

Direct observation of intraparticle equilibration and the rate-limiting step in adsorption of proteins in chromatographic adsorbents with confocal laser scanning microscopy

The adsorption of different proteins in a single biospecific and hydrophobic adsorbent particle for preparative protein chromatography has been observed directly by confocal laser scanning microscopy as a function of time at a constant bulk concentration c b. The bulk concentration was in the non-linear part of the adsorption isotherm. At all times the concentration of free protein at the particle surface was almost equal to the bulk content indicating that external mass transfer resistance is not rate limiting for the adsorption under these conditions. Inside the particles a distinct maximum in adsorbed and free protein concentration that moved inside to a distance of ≈0.2 R ( R particle radius) from the particle surface, was observed. This is due to a decreasing solid-phase density and adsorptive capacity in the particle between 0.8 R and R indicating that the fraction of macropores (or void space) is larger in the outer than in the inner part of the adsorbent particles. By increasing the bulk concentration by a factor of 10 the equilibration time was reduced by about the same magnitude. This is in agreement with the concentration dependence of the effective pore diffusion coefficient D p,eff= D p/{ ϵ p[1+ nK/( K + c) 2]} derived from the mass conservation relations describing the adsorption process. The time dependence protein adsorption up to ≈90% of the equilibration value q* could be described by a bilinear free driving force model. The rapid equilibration in the outer part of the particle with a half-life time of ≈100 s in the studied systems accounted for 0.3–0.4 q*. The slower equilibration with a up to ten times longer half-life time, was the adsorption in the inner part of the particle that outside 0.5 R accounts for 0.5–0.6 q*. These data were compared with literature data for batch adsorption of proteins in biospecific, hydrophobic and ion-exchange adsorbents. They could also be described by a bilinear free driving force model, with about the same quantitative results as obtained for similar conditions in the single particle experiments. The static adsorption parameters, maximum binding site concentration n, and dissociation constant for the protein binding to a binding site K, were determined from Scatchard plots. For the same protein–adsorbent system the plots changed from linear to non-linear with increasing n. This change occurred when the average distance between adjacent binding sites become of the same order of magnitude as the size of the binding site or adsorbed protein. This causes a shielding of free binding sites increasing with n and the concentration of adsorbed protein, yielding a concentration dependence in K. These results show that for a high throughput and rapid adsorption in preparative chromatography, the adsorption step should be carried out in the non-linear part of the adsorption isotherm with concentrations up to c b where q*/ c b≥10 to obtain high protein recoveries. To avoid tailing due to the flow of adsorbed proteins in the inner part of the particles further into the particles at the start of the desorption, and to speed up desorption rates, protein adsorption in the particle within 0.5 R from the particle center should be avoided. This requires the further development of suitable pellicular particles for preparative protein chromatography that meet this requirement.

Dense amorphous bulk silicon-carbon-nitrogen ceramics

The synthesis and processing of dense silicon-based bulk ceramic materials derived from the thermal decomposition of preceramic organosilicon polymers such as polysilazanes and polysilanes was achieved by three different routes A, B, and C. Additive-free silicon carbonitride bodies of the composition Si1.7C1.0N1.6 were produced according to route A, with up to 94% relative density by the pressureless pyrolysis of compacted infusible polysilazane powders at low processing temperatures (1000 °C). The resulting silicon carbonitride was single-phase and amorphous according to X-ray- and TEM-investigations and exhibited a low solid-phase density of 2.33 g/cm3. The maximum room temperature fracture strength of additive-free silicon carbonitride was 370 MPa. Crystallization of the as-synthesized silicon carbonitride bulk samples occurred at temperatures exceeding 1400 °C.In a second process, route B, densification of polysilazane-derived amorphous silicon carbonitride powder was achieved by liquid phase sintering with alumina and yttria as sintering additives in nitrogen atmospheres and at temperatures up to 1900 °C. This process resulted in the formation of dense polycrystalline β-Si3N4/β-SiC-composites. The average room temperature fracture strength and fracture toughness of the gas pressure sintered composite were in the range of 650 MPa and 10.2 MPa√m, respectively.Polycrystalline Si3N4/SiC-composites were obtained in a third process, route C, by the pyrolysis and subsequent sintering of α-Si3N4-powder/polysilane blends. The Si3N4-powder serves as an inert filler reducing the volume shrinkage associated with the polymer-to-ceramic transformation. Dense Si3N4 and Si2N2O bulk ceramics were formed according to route B by the liquid phase sintering of amorphous silicon nitride powder synthesized by the polysilazane pyrolysis under ammonia.

INFLUENCE OF PHYSICAL PROPERTIES OF SOLID-LIQUID PHASE ON DEBRIS FLOWS

The velocity and sediment concentration of sediment-water mixture flow change by the physical properties; e. g., mass density of solid and liquid phase, viscosity of liquid, interparticle friction angle of solid particle, etc. The laminar viscous term is introduced into the constitutive relations developed formerly by Egashira et al. to solve those. The effects of physical properties of solid and liquid phase on debris flow are investigated by means of experimental data as well as of numerical solutions for velocity profile, sediment concentration profile, flux sediment concentration and flow resistance. The results suggest that the present constitutive relations evaluate any changes of debris flow caused by physical properties of solid-liquid phase.

Uptake of Traces of Selenite by Manganese Dioxide from Aqueous Solutions

Sorption of selenite onto manganese dioxide has been investigated with respect to shaking time, concentration of sorbent and sorbate, nature of electrolyte, and influence of cations and anions. The sorption of other metal ions has been studied using optimal conditions selected for maximum sorption of selenite. The surface area, average pore diameter, porosity, and solid phase density of the sorbent have been measured. The sorption data followed only the Dubinin–Radushkevich (D–R) sorption isotherm among all the isotherms tested. The sorption capacity of 51.2 nmol·g−1 and a constant β related to sorption energy have been estimated to be −0.007521 mol2·kJ−2. The sorption energy is found to be 8.15 kJ·mol−1. The kinetics of the sorption follows the Lagergren equation in the initial stages. The first-order rate constant, k′, was evaluated to be 0.498 min−1 and of intraparticle diffusion rate 3.06 × 10−5 mol·g−1·min−2. Among all the anions and cations tested, only carbonate, Fe(III), and citrate reduced the sorption significantly. The sorption data for other metal ions showed that Te(IV) can be separated from ions showing higher degree of sorption; especially Se(IV), As(III), Sb(V), and Eu(III). It can be concluded that manganese dioxide may be used for the separation of certain metal ions, their preconcentration from very dilute solutions, and for decontamination and treatment of industrial effluents.

Adsorption of CO2 and N2 on Soil Organic Matter: Nature of Porosity, Surface Area, and Diffusion Mechanisms

The surface area of soil organic matter (SOM) is a crucial parameter for the interpretation of sorption mechanisms of organic contaminants. The surface area of three SOM samples was studied by using CO2 and N2 gas adsorption, revealing that SOM is a microporous material with a high surface area of 94−174 m2 g-1. The ethylene glycol monoethyl ether (EGME) retention technique has major drawbacks for application to SOM samples, as liquid EGME changes the SOM solid phase density. Nitrogen (N2) is subject to molecular sieving at 77 K due to activated diffusion in micropores. CO2 is not limited by activated diffusion since higher experimental temperatures are applied (273 K). About 95−99% of the SOM surface area is formed by micropores with maximum restrictions of approximately 0.5 nm. Results suggest that the diffusion coefficient of CO2 is influenced by the cross-linking density of the matrix and that the microporous structure is not strongly affected by hydration of the sample. On the basis of pore dimension...

Predictions of unsteady flame spread and burning processes by the vorticity‐stream function formulation of the compressible navier‐stokes equations

A two‐dimensional mathematical model of flame spread and solid burning is presented. For the gas phase, it consists of variable density, fully elliptic Navier‐Stokes momentum, energy and chemical species mass equations. Combustion processes are treated according to a one‐step, finite‐rate, reaction. The solid phase model describes a porous cellulosic fuel for a range of thicknesses from the thermally thin to the thermally thick limit. Conductive and convective heat transfer takes place as the solid degrades, by two first order Arrhenius reactions, to volatiles and chars. Variations of solid phase densities account for fuel burn‐out. Effects of gas phase and surface radiation are also included. A steady formulation of gas phase equations with respect to the unsteady solid phase mathematical model is proposed, gas phase characteristic times being much shorter than those of the solid phase. The non‐constant density Navier‐Stokes equations are formulated in terms of vorticity and stream function, avoiding the pressure‐velocity coupling and, at the same time, the adoption of a sample‐fixed coordinate system allows unsteady flame spread processes to be simulated. The solution is computed numerically by means of an iterative, operator‐splitting method based on implicit finite‐difference approximations. Numerical simulations of the dynamics of flame spread over cellulosic solids are presented and extinction limits as a consequence of reduced rates of fuel generation are determined.

Polymer-derived Si-based bulk ceramics, part I: Preparation, processing and properties

The synthesis and processing of dense silicon-based bulk ceramic materials derived from the thermal decomposition of preceramic organosilicon polymers such as polysilazanes and polysilanes was achieved by three different routes A, B, and C. Additive-free silicon carbonitride bodies of the composition Si 1.7C 1.0N 1.6 were produced according to route A, with up to 94% relative density by the pressureless pyrolysis of compacted infusible polysilazane powders at low processing temperatures (1000 °C). The resulting silicon carbonitride was single-phase and amorphous according to X-ray- and TEM-investigations and exhibited a low solid-phase density of 2.33 g/cm 3. The maximum room temperature fracture strength of additive-free silicon carbonitride was 370 MPa. Crystallization of the as-synthesized silicon carbonitride bulk samples occurred at temperatures exceeding 1400 °C. In a second process, route B, densification of polysilazane-derived amorphous silicon carbonitride powder was achieved by liquid phase sintering with alumina and yttria as sintering additives in nitrogen atmospheres and at temperatures up to 1900 °C. This process resulted in the formation of dense polycrystalline β-Si 3N 4/β-SiC-composites. The average room temperature fracture strength and fracture toughness of the gas pressure sintered composite were in the range of 650 MPa and 10.2 MPa√m, respectively. Polycrystalline Si 3N 4/SiC-composites were obtained in a third process, route C, by the pyrolysis and subsequent sintering of α-Si 3N 4-powder/polysilane blends. The Si 3N 4-powder serves as an inert filler reducing the volume shrinkage associated with the polymer-to-ceramic transformation. Dense Si 3N 4 and Si 2N 2O bulk ceramics were formed according to route B by the liquid phase sintering of amorphous silicon nitride powder synthesized by the polysilazane pyrolysis under ammonia.

Calculation of the ground-state energy V0 of quasifree positrons in rare-gas fluids.

The energy ${\mathit{V}}_{0}$ of the bottom of the conduction band (relative to vacuum) of quasifree positrons in rare-gas fluids is calculated as a function of fluid density. The calculations are performed within the framework of the Wigner-Seitz approximation [Phys. Rev. 43, 804 (1933)] for nonpolar fluids, using a semiempirical analytical potential to model the positron--rare-gas-atom interactions. For all the rare gases studied, ${\mathit{V}}_{0}$ is negative and decreases almost linearly with increasing density. Extended to the solid-phase density range, our ${\mathit{V}}_{0}$ calculations are in good agreement with available experimental data for rare-gas crystals.

Textural characteristics of silica aerogels from SAXS experiments

Small angle X-ray scattering measurements on silica aerogels give systematically low values for the solid phase density. In order to explain these results, a hierarchical structure is proposed. Textural parameters such as specific surface area, size and density of clusters, and pore size are a function of the number of levels in the structure. Experimental values are consistent with values calculated for a hierarchy of two to four levels, depending on the initial sol concentration. The model can explain the fractal features for lower density aerogels.

A composition density functional theory for mixtures based upon an infinitely polydisperse reference. II. Freezing in hard sphere mixtures

A theory recently proposed by the authors [Kofke and Glandt, J. Chem. Phys. 92, 658 (1990)] is applied to the study of freezing in hard spheres and hard sphere mixtures. The theory, which expresses the free energy of an arbitrary mixture as a functional of the composition density of an infinitely polydisperse (IP) reference, is used to evaluate the properties of mixtures of hard spheres constrained to the Wigner–Seitz cells of an fcc lattice. Semigrand Monte Carlo simulations are used to determine the properties of the IP reference mixture, which is also constrained to an fcc lattice. Freezing is determined by comparing the predicted properties of the Wigner–Seitz crystal with the known properties of the fluid phase. A freezing transition is found for monodisperse hard spheres; the estimated solid-phase density and the transition pressure differ from the accepted values by 2% and 8%, respectively. The treatment is also used to study freezing in polydisperse mixtures with Gaussian distributions of diameters. In accordance with the findings of others, an upper bound is found to the variance of the distribution, beyond which freezing no longer occurs. However, the maximum variance predicted here is approximately one order of magnitude less than that previously found. Discrepancies here and in the pure-fluid results are attributed largely to ergodic difficulties in the simulations of the IP reference. Finally, the possibility of a phase transition in IP mixtures is demonstrated through a calculation of the freezing point of IP hard spheres.

A model of a non-homogeneous pseudofluidized layer with particle exchange between the non-homogeneity and the layer

A non-stationary model of a non-homogeneous pseudofluidized layer with local solid-phase non-homogeneities moving in the continuous layer /1/ is considered. Contrary to the previous studies /1, 2/, we assume that the solid-phase mass locked in the spherical packet of particles modelling the non-homogeneity may vary through the influx of particles into the packet or efflux of particles from the packet into the continuous phase of the layer. Particle concentrations inside and outside the packet remain constant. We assume that the solid-phase density is high compared with the density of the fluidizing agent (e.g., solid particles suspended in a gas stream), and the interaction between the phases is linear with respect to the relative velocity of the particles. In this formulation, the problem is similar to the growth (dissolution) of bubbles in a liquid and of drops in a liquid or a gas /3–5/. The purpose of the study is to derive a system of equations linking the dynamics of the local solid-phase non-homogeneity with the velocity of its motion in the pseudofluidized layer. Packet “lifetime” is estimated. Some examples are considered.

Transport Properties of B-, P-Doped and Undoped 50 kHz PECVD Microcrystalline Silicon

AbstractUndoped 500 nm-thick silicon layers with a crystalline fraction around 95% and an average grain size of 20 nm have been deposited at 350°C by 50 kHz triode PECVD in a H2/SiH4 mixture, in the presence of a magnetic field. Their room temperature (rt) dc conductivity μrt is 0.03 Δ−1cm−1 for a Hall mobility of 0.8 cm 2V−1s−1.The study by SIMS, infrared absorption, grazing angle x-ray diffraction and Raman scattering spectroscopies of the doped samples shows how the crystalline fraction and the grain size drop as the B2H6/SiH4 and PH3/SiH4 volumic ratios increase from 10 ppm to 1%.The rt dc conductivity reaches 2 Δ−1 cm−1 (Hall mobility: 15 cm2V−ls−1) for a solid phase density of 1019 cm−3 boron atoms, and 30 Δ−1cm−1 (Hall mobility: 55 cm2V−ls−1) at the maximum P incorporation of 8 × 1020cm−3.

Annealing behaviour of copper and nickel containing high concentrations of krypton studied by positron annihilation and other techniques

Bulk copper and nickel samples containing 3 and 5 at. % krypton respectively have been studied by conventional positron annihilation techniques. Most of the emphasis has been placed on the changes in positron lifetime and angular correlation parameters during isochronal annealing from ambient up to near the metal melting points. The study was complemented by transmission and scanning electron microscopy, together with macroscopic measurements of weight and dimensions. These techniques, combined with previous studies, provide a fairly detailed picture of both the as-prepared materials, where the krypton is present as a high density of solid phase precipitates (solid bubbles), and the subsequent marked response of the substructure to annealing. A number of features are of particular interest. The onset temperature for bubble coalescence events is correlated with the melting temperature of the solid Kr inside the bubbles. At higher temperatures extensive swelling is observed prior to and simultaneously with the release of the majority of the krypton. The structure after the Kr release contains micrometre-sized pores and approximately 10 nm bubbles. This structure partly recovers at higher temperatures, but sufficient krypton is retained in the pores to maintain a large swelling up to close to the metal melting points. Positrons are found to become trapped at the Kr-metal interface in Kr bubbles, and there is clear evidence for a quantitative relation between lifetime and Kr density. Both these features are in agreement with the recent theory of Jensen and Nieminen (1987). Finally, positron trapping into dislocations is observed to occur at a rate much lower than that predicted from published specific trapping rates.