Slit Model Research Articles

2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation

In this work, we show that the standard slit pore model widely used for the characterization of activated carbons may be improved by introducing structural and/or energetical heterogeneity to the surface of pore walls. The existing one dimensional slit pore model assumes graphite-like energetically uniform pore walls. As a result of this assumption adsorption isotherms calculated by the non local density functional theory (NLDFT) do not fit accurately the experimental N2 data measured for real activated carbons. Assuming a graphene-based structural framework for activated carbons and using a 2D-NLDFT treatment of the fluid density in the pores we consider two options for model pores: energetically heterogeneous (EH) and geometrically corrugated (GC). For testing, we applied these two models to the pore size analysis of porous carbons that were giving poor results of the analysis with the standard slit model. We found that the typical artifacts of the homogeneous slit pore model were eliminated. Also, the agreement of the new models with experimental data was significantly better than that of the standard slit model.

Rheological behavior of PS polymer melt under ultra high speed injection molding

Determination of the rheological behavior of a polymer melt under high shear rate is generally considered to be crucial for accurate simulation modeling of ultra high speed injection molding, a process that has been attracting more attention from researchers. In this study, a melt viscosity measurement system under high shear rate was established using an instrumented injection molding machine combined with a slit die. Polystyrene melt was studied. From measured pressure drop and volumetric flow rate, the slit flow model was used for the calculation of viscosity at wall shear strain rates up to 105 s−1. Good agreement in shear viscosity was found between results from conventional capillary rheometry and in-line measurement made using an injection molding machine for strain rates of 7 × 103 to 104 s−1. Measured shear viscosity in the test range was found to follow shear thinning power law behavior at shear rates below 7 × 104 s−1. However, the measured viscosity values are significantly lower (28%–46%) than the database obtained from the Moldflow package software (Cross-WLF model) at melt temperatures of 200, 215, and 230 °C. Further, the reduction in the viscosity value increases as the injection speed increases. It seems that the wall-slip effect plays a dominant role, becoming more significant as the melt temperature increases. Alternatively, as shear strain rates approached or exceeded 7 × 104 s−1, shear viscosity deviations from shear thinning behavior were observed and reached a rate-independent plateau. The behavior is thought to be influenced by pressure effects on viscosity. In the present study we emphasize that the measured results are significant for the design and simulation of ultra high speed injection processes such as micromolding and thin-walled injection molding.

Characterization of thermo-rheological behavior of polymer melts during the micro injection moulding process

In-line process monitoring and rheological characterization can help to understand the behaviour of polymer melt flows during manufacture and to make injection moulding a measurable process for manufacturing high quality parts. This work developed an in-line rheology measurement system using a slit die attached to a micro injection moulding machine. A series of dumbbell mould inserts was used to form the slit die with thickness ranging from 600 μm to 200 μm. Two combined pressure and temperature sensors were embedded into the slit die to measure the pressure drop. Based on the slit flow model, it was found that the viscosity of Pebax melts depends on the slit thickness in the actual injection moulding process. The competing effects of wall slip and non-isothermal conditions will determine the melt viscosity. The plastication induced thermo-mechanical history can also influence polymer viscosity, although it is neglected in conventional rheology measurements.

Numerical simulation of the liquid distribution in a trickle-bed reactor

Numerical simulations of the two-phase flow distribution in a trickle-bed reactor used for fuel hydrodesulfurization are reported. As a first step, the heat and mass transfer, as well as the chemical reactions, are not considered. The reactor has four packed-beds and a distribution tray above the catalytic beds equipped with cylindrical chimneys. The flow distribution at the outlet of the circular chimney predicted by the simulations is not axisymmetric because of the spatial distributions of the liquid and gas inlets in the chimney. This causes that the liquid entering the packed beds is distributed in three main streams. For the simulation of the two-phase flow in the packed beds, an Eulerian three-phase model that considers the particles of catalyst as a granular static phase has been used following the Holub single slit model for particle–fluid interaction to compute the liquid–solid and gas–solid drag coefficients. Numerical simulations of the dispersion of water–air flow in a column of glass beads using this model were initially carried out and results were found to be in reasonable agreement with numerical and experimental data available in the literature. The simulations consider the flow dispersion in the central region of the reactor bed as well as in the region close to the cylindrical lateral wall of the reactor. In both cases most of the liquid spreading takes place in the top part of the bed. The distributions of the liquid volume fraction do not change significatively as the depth of the bed is increased except in the third bed and at the interface of two beds with different porosity.

Hydrodynamics and mass transfer in carbon-nanofiber/graphite-felt composite under two phase flow conditions

A carbon nanofiber (CNF)/graphite felt composite was synthesized by growing CNFs on the surface of graphite fibers and was used as the packing of a fixed bed reactor under two phase flow conditions. The pressure drop, axial dispersion and mass transfer in the liquid were studied by experiment and by piston dispersion exchange (PDE) model. It was shown that the pressure drop and total liquid up could be predicted by the slit model in an acceptable accuracy. The axial dispersion in the liquid phase in the composite and the mass transfer between the dynamic and static liquid are higher than in the packed bed of solid particles owing to the porous and fluffy CNF layer on the carbon felt fiber.

A slit method to determine the focal spot size and shape of TomoTherapy system

To obtain accurate x-ray source profile measurements using a slit-collimator, the slit-collimator should have a narrow width, large height, and be positioned near the source. However, these conditions may not always be met. In this paper, the authors provide a detailed analysis of the slit measurement geometry and the relationship between the slit parameters and the measured x-ray source profile. The slit model allows the use of a shorter and more easily available slit-collimator, while accurate source profile measurements can still be obtained. Measurements were performed with a variety of slit widths and/or slit to source distances. The relationship derived between the slit parameters and the measured profile was used to determine the true focal spot profile through a least square fit of the profile data. The model was verified by comparing the predicted profiles at a variety of slit-collimator parameters with the measured results on the TomoTherapy Hi-Art system. Both the treatment beam and the imaging beam were measured. For treatment mode, it was found that a source consisting of one Gaussian with a 0.75 mm full-width-half-maximum (FWHM) and 72% peak amplitude and a second Gaussian with a 2.27 mm FWHM and 18% peak amplitude matched measurement profiles. The overall source profile has a FWHM of 0.93 mm, but with a higher amplitude in the tail region than a single Gaussian. For imaging mode, the source consists of one Gaussian with a 0.68 mm FWHM and 82% peak amplitude and a second Gaussian with a 1.83 mm FWHM and 18% peak amplitude. The overall source profile has a FWHM of 0.77 mm. Our study of the focal spot measurement using slit-collimators showed that accurate source profile measurements can be achieved through fitting of measurement results at different slit widths and source-to-slit distances (SSD). Quantitative measurements of the TomoTherapy linac focal spot showed that the source distribution could be better described with a model consisting of two Gaussian components rather than a single Gaussian model as assumed in previous studies.

Modification of Ergun equation for application in trickle bed reactors randomly packed with trilobe particles using computational fluid dynamics technique

Based on a slit model, a pellet scale model has been developed for calculation of drag force imposed on trilobe catalyst particles in a packed bed reactor. The drag coefficient for single gas phase flow in a porous media has been calculated by CFD simulation and the results compared to the Ergun equation. The results show that the drag coefficient predicted by Ergun equation should be modified for various bed porosities, particle aspect ratio and gas densities. Therefore, a correction factor has been proposed to correct the Ergun equation constants in various conditions for trilobe particles. Comparison between the proposed corrected Ergun equation results and experimental data indicates considerable agreement.

Characterization of the PSD of activated carbons from peach stones for separation of combustion gas mixtures

Controlled series of microporous carbons were prepared through chemical activation with phosphoric acid from peach stones as the precursor material, corresponding to different preparation conditions. Adsorption isotherms of N2 at 77 K and of CO2 at 273 K were measured to be used in the characterization of the samples. The recently proposed mixed-geometry model (MGM), which assumes that the activated carbon is better represented by a mixture of slit and triangular geometry pores, is used to obtain the PSDs of the samples, on the basis of Grand Canonical Monte Carlo (GCMC) simulated ideal isotherms, both for N2 at 77 K and of CO2 at 273 K. Our results emerging from the analysis of two families of activated carbons reveal a consistent picture supporting the thesis that the PSDs of the same sample obtained trough N2 and CO2 adsorption are different, a still controversial issue in the literature. Comparison of predictions from the MGM with those of the pure slit geometry model (PSGM) shows that the former gives a more consistent picture and more similar PSDs for the two adsorbates used.

Research on Single-Side Long Edge of Hot Rolled Strip Caused by Asymmetrical Stiffness of Mill Stand

To analyze and solve the problem of single-side long edge of hot rolled strip in certain domestic factory, the asymmetrical deformation of rolls and strip in asymmetrical stiffness mill stand based on slit beam model, the strip profile and rolling force distribution at the exit of asymmetric stiffness stand mill were calculated using influence function method. Considering the character of in-site equipment and technology, a scheme of adjusting load distribution in finishing mill was made and the experiment was applied. Comparison of strip profile between new load distribution and the old one shows that the method can solve single-side long edge problem well.

Characterization of activated carbons from peach stones through the mixed geometry model

A good characterization of the pore size distribution of activated carbons is of crucial importance for gas separation and gas storage applications of microporous materials. It has been recently shown that characterization methods of activated carbons can be improved by considering the porous space as represented by a mixture of pores of different geometries, slit and triangular geometry. The triangular geometry was included as a necessity of considering the simultaneous interaction of an adsorbed molecule with three graphite walls to account for high observed values of the isosteric heat of adsorption at low pressures. Places where such interaction with three graphitic walls occurs can be clearly seen in some high resolution digitalized TEM images of activated carbons published in the literature. Many lignocellulosic substances have been used in the literature as the precursor material in the preparation of activated carbons. In the present work we use peach stones, which are very abundant in the region of Cuyo (Argentina), as well as in any other regions in the world where peaches are extensively cultivated, processed and canned. Different samples of activated carbons from this precursor are obtained through different processing methods. N 2 adsorption isotherms at 77 K are measured for these samples and fitted by using the mixed geometry model, obtaining the corresponding PSDs. Finally these characterization results are correlated to the preparation procedures for the different samples. The analysis of results reveals that the mixed geometry model provides a more consistent picture of the sample characteristics than the pure slit geometry model, reinforcing the conclusions of previous studies. The same analysis allows to determine clearly some general trends relating the preparation method with the morphological and adsorptive characteristics of the AC.

Distributed Point Source Method for Modeling Scattered Ultrasonic Fields in the Presence of an Elliptical Cavity

Scattering of ultrasonic waves by an elliptical cavity is modeled. The ratio of the semimajor to semiminor axes is varied from 1 to model a cylindrical cavity with a circular cross section to a large value to approximately model a Griffith crack. The distributed point source method (DPSM), which is a Green’s function-based semi-analytical technique, is adapted in the present modeling. DPSM generated results for slit opening and elliptical cavity are compared. In the elliptical cavity model, the entire cavity surface is considered traction free, whereas in the slit model, two parallel crack surfaces are assumed traction free and no special consideration is given to the crack tips. Because a Griffith crack under tensile loads opens like an ellipse, the elliptical cavity with a large semimajor to semiminor axes ratio can be considered as an open Griffith crack. Elliptical cavity model clearly shows large stress values near the crack tips. Earlier DPSM models did not consider these high stress concentrations. The assumption was that it would have negligible effect on the scattering pattern at the far field. The numerical results are presented for a cavity of length 4 mm when bounded ultrasonic beams of 1 and 2.25 MHz frequency strike the solid half-space.

A Theoretical Study of the Separation Principle in Size Exclusion Chromatography

The principle of polymer separation in size exclusion chromatography (SEC) is studied based on a classical equilibrium partitioning theory. The task is to examine the correlation between the mean span dimension of polymer chains and their equilibrium partition coefficients with confining pores. Using an extended formulation of the recently developed confinement analysis from bulk structures (CABS) method, we calculate the partition coefficients for both linear and branched polymer chains with cylindrical pores—a model pore geometry that is considered to be more realistic for voids in SEC columns than the commonly considered slit model. The partition coefficients plotted as a function of the mean span dimension relative to the pore diameter are truly universal for wide pores and nearly so for flexible polymer chains with different architectures (linear, star, two-branch-point, and comb) in the range of the partition coefficient relevant to SEC separation. We also examine the correlation between the mean sp...

衝撃貫入試験におけるボタンビットの貫入特性

A force-penetration relationship is considered to be closely related to the deformation and fracture mechanism at the bit-rock interface. In this study, a testing machine in which a piston, a rod or a bit can be easily changed was developed for laboratory impact-penetration test simulating the in-situ percussive drilling. A series of percussive drilling tests with a button bit against Inada granite were carried out to examine and discuss the drilling performace. Stress waves were measured at two locations 1.91 m apart along the rod, and then force-penetration curve of the button bit was calculated by measured strain/stress wave. Main results are summarized as follows:1) Delay of traveling time at bit can be expressed by a slit bit model.2) Variation in the slope of force-penetration curves in laboratory tests was very similar to that in in-situ percussive drilling.3) In spite of large scatter in the slope of force-penetration curves, the elastic deformations of rock surface were almost constant.

Characterization of PSD of activated carbons by using slit and triangular pore geometries

A mixed geometry model for activated carbons, representing the porous space as a collection of an undetermined proportion of slit and triangular pores, is developed, evaluated theoretically and applied to the characterization of a controlled series of samples of activated carbon obtained from the same precursor material. A method is proposed for the determination of the Pore Size Distribution (PSD) for such a mixed geometry model, leading to the unique determination of the proportion of pores of the two geometries fitting adsorption data. By using the Grand Canonical Monte Carlo (GCMC) simulation method in the continuum space, families of N2 adsorption isotherms are generated both for slit and triangular geometry corresponding to different pore sizes. The problem of the uniqueness in the determination of the PSD by fitting an adsorption isotherm using the mixed geometry model is then discussed and the effects of the addition of triangular pores on the PSD are analyzed by performing a test where the adsorption isotherm corresponding to the known PSD is generated and used as the “experimental” isotherm. It is found that a pure slit geometry model would widen the PSD and shift it to smaller sizes, whereas a pure triangular geometry model would produce the opposite effect. The slit and triangular geometry families of isotherms are finally used to the fit experimental N 2 adsorption data corresponding to a family of activated carbons obtained from coconut shells through a one-step chemical activation process with phosphoric acid in air, allowing for the determination of the micropore volume, the proportion of slit and triangular pores and the PSD corresponding to the mixed geometry. The same experimental data were fit using both the conventional slit pore model and the mixed geometry model. From the analysis of the effect of different preparation procedures on the resulting PSDs, it is concluded that the proposed mixed geometry model may probably better capture the morphology and energetics of activated carbons prepared by chemical activation under mild temperatures.

Fatigue‐relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch

ABSTRACTThe notch stress intensity factor (NSIF) based analytical frame is applied to the slit tips (or weld roots) of welded joints with inclusion of the T‐stress component. This T‐stress can be determined from FE models evaluating the ligament stresses close to the pointed slit tip. An alternative analytical frame is presented for the corresponding keyhole notches based on analytical solutions from the literature, which are applied to the ligament stresses.In the slit tip models, the mean local strain energy density (SED) with inclusion of the T‐stress effect is determined analytically and numerically in comparison, using two different fatigue‐relevant control radii, R0= 0.28 mm and R0= 0.15 mm, the former value well proven for thick‐sheet welded joints made of structural steel. The latter smaller value is tentatively proposed for thin‐sheet welded joints, in the direction suggested in the recent literature where a reduction of the microstructural support length for laser beam welds and resistance spot welds is recommended. The FEM‐based and analytical stress concentration factors (SCF) for the lap joint keyhole model and also the SED values for the corresponding pointed slit tips are found to be in good agreement. The J‐integral consisting of the first and second component (the latter containing the T‐stress) is compared with the corresponding SED values.

Trickle bed mechanistic model for (non-)Newtonian power-law foaming liquids

Physical models for the description of the hydrodynamics of trickle-bed reactors for foaming Newtonian and power-law liquids are virtually inexistent in the literature. An attempt is made in this work to develop a hydrodynamic model for cocurrent gas–liquid downflow involving foaming (non-)Newtonian power-law liquids through packed beds at non-ambient temperatures and moderate pressures. The model was an extension of the well-trodden slit model variants proposed for (non-)Newtonian power-law coalescing-liquid systems. Its validation using recently published experimental data [Aydin, B., and Larachi, F., 2008. Trickle bed hydrodynamics for (non-)Newtonian foaming liquids in non-ambient conditions. Chem. Eng. J. 143, 236–243.] allowed a quantitative representation of foaming flow hydrodynamics in terms of the two-phase pressure gradient and the liquid holdup up to 90 °C and 0.7 MPa. The model, requiring no arbitrary adjustable parameters, in addition related foam stability to quantitative descriptors such as the liquid-film-borne bubble holdup and diameter, and free (or headspace)-gas holdup. The model also exhibited logical and fully interpretable trends with regard to foam stability, reactor temperature and pressure, liquid and gas superficial velocities.

Rheological behavior of POM polymer melt flowing through micro-channels

Determination of the rheological behavior of the polymer melt within micro-structured geometry is vital for accurate simulation modeling of micro-molding. The lack of commercial equipment is one of main hurdles in the investigation of micro-melt rheology. In this study, a melt viscosity measurement system for POM melt flowing through micro-channels was established. For measured pressure drop and volumetric flow rate, both capillary and slit flow models were used for the calculation of viscosity. The calculated results were also compared with those of PS resin to discuss the effect of morphology structure on the viscosity characteristics of polymer within micro-channels. It was found that the measured POM viscosity values in the test ranges are significantly lower (about 29–35% for a channel size of 150 μm) than those obtained with a traditional capillary rheometer. Meanwhile, the percentage reduction in the viscosity value and the ratio of slip velocity relative to mean velocity all increase with decreasing micro-channel size, but less significantly when compared with PS resin. In the present study we emphasize that the rheological behavior of the POM resin in microscopic scale is also different from that of macroscopic scale as PS resin but displays a less significant lower. It also revealed that the wall slip occurs more easily for the PS resin within micro-channels than POM resin due to enlarge the effect of molecular weight.

축방향 홈이 있는 Taylor-Couette 유동의 실험적 연구

Taylor-Couette flow has been studied extensively and lots of variables which affect the flow instability are being reported. The wall geometry effect of Taylor-Couette flow, however, has been less studied. In this study, we investigated the effect of axial slit of outer cylinder. This kind of configuration can be easily seen in rotating machinery. Particle image velocimetry method was used to measure the velocity fields in longitudinal and latitudinal planes. The index matching method was used to avoid light refraction. The velocity fields between the slit and plain model which has the smooth wall were compared. From the experiments, both models have the same flow mode below Re = 143. The transition from circular Couette flow to plain Taylor vortex flow began at Re = 103, and the next transition to wavy vortex flow occurred at 124. The effect of slit wall appeared when the Reynolds number is larger than Re = 143. Above this Reynolds number, there was no stable mode and plain and wavy Taylor vortex flow randomly appeared.Copyright © 2007 by ASME

Modeling of Gas−Liquid Packed-Bed Reactors with Momentum Equations and Local Interaction Closures

An algebraic model for the estimation of gas−liquid packed-bed hydrodynamic parameters is developed, based on one-dimensional material and momentum balances for gas and liquid phases. Underlying momentum exchange closures are critically analyzed, which leads to discarding some interaction models between the phases and development of new models based on local hydrodynamics. The present approach is based on more-relevant assumptions for the particle scale geometry than the slit models presented in the literature. The resulting model requires a one-parameter iterative solution, from which both pressure drop and liquid holdup are obtained. The model can be used without any extra complication in situations where the boundary conditions are specified either at the inlet or at the outlet of the reactor. It is suitable for modeling both low- and high-pressure operations, trickling as well as pulsing flow, upflow and downflow arrangements, and processes with Newtonian as well as non-Newtonian liquids. Finally, the...

Preparation of ultramicro-, micro-, and supermicroporous carbon adsorbents by template procedure

The new template procedure for preparing ultramicro-, micro-, and supermicroporous carbon adsorbents is proposed on the basis of the use of two polymers with different thermal stabilities as a template matrix and a carbonizable carbon source. The polymeric template matrix is removed by thermal decomposition in the low-temperature pyrolysis of the polymer mixture, whereas the second polymer component of a mixture is transformed into a carbonizate. The resultant monolithic carbonizate is the polymeric matrix replica and represents a molecular-sieve ultramicroporous carbon adsorbent, which adsorbs water vapor at 293 K and does not adsorb nitrogen vapor at 77 K. The activation of this carbonizate with water vapor leads to a series of micro-and supermicroporous carbon adsorbents with a broad range of the parameters of a pore structure: BET specific surface area SBET is 610–2130 m2/g, micropore volume W0 is 0.20–0.69 cm3/g, micropore half-width x0 (slit model) is 0.20–0.70 nm, mesopore specific area Sme is 20–1000 m2/g, and characteristic adsorption energy E0 is 15.6–27.4 kJ/mol.