Fill Height Research Articles

A comparison of mixture and separated-phase models of heat transfer in a stationary wet granular bed

Solvent removal by thermal drying of granular mixtures is encountered in many industrial operations. A mixture model that treats the granular solid and the liquid solvent along with any interstitial gas phase as a single phase, is a useful first approximation to estimate the time required to heat the system to the wet-bulb temperature at which the solvent starts to vaporize. An analytical solution for the transient, axisymmetric temperature distribution in a stationary wet granular mixture in a heated cylindrical vessel is developed as an approximation to the typical geometry of an industrial dryer . Besides being a good first approximation to obtain an order-of-magnitude estimate of the heating time, the analytical solution serves as an excellent verification case for numerical simulations. A parametric study to assess the effect of fill height and wall temperature on the heating time is performed. Before analyzing the mass transfer aspects of the drying phenomena, it is critical to understand the fundamentals of interphase heat transfer in multiphase mixtures that can be found in such assemblies. Therefore, a 0-D separated-phase (multiphase) heat transfer model is developed to account for the effect of interphase heat transfer in the prediction of heating time of wet granular mixtures in cylindrical vessels. The 0-D model is extended to 3-D simulations using a newly developed OpenFOAM solver with multiphase heat transfer capability. The same problem that was solved using the analytical solution is solved using the 0-D model, and in 3-D using the newly developed OpenFOAM solver, to study the effect of interphase heat transfer on the prediction of heating time. It was found that inclusion of interphase heat transfer in the heat diffusion equations has a significant impact on the predictions of heating time. Further analysis of the problem results in the identification of the non-dimensional thermal interphase transfer number that determines the conditions under which a mixture model can be used in place of a separated phase model in problems involving heat transfer.

Studying the Effects of Negative Skin Friction on Single Piles in Basrah Governorate

The finite element method capable of simulating the behavior of deep foundations subjected to negative skin friction in Basrah soil is investigated. Single piles under drag forces are analyzed using the PLAXIS program with an axisymmetric model. Linear elastic, Soft Soil and Mohr-Coulomb constitutive relations are adopted, where higher order triangular element is chosen for pile and soil clusters. Both pile and soil are modeled using (15)-node triangular elements. Three sites in Basrah province (Umm Qasr Port, Khor Al-Zubair, and Shatt AlArab Hotel) were selected to perform this study. The soil profile and layer characteristics are obtained from the soil investigation reports. Where the negative skin friction is evaluated due to filling loads. It is Conclusion thatSmall relative displacements are necessary to activate the negative skin friction. The elastic shorting for pile effect negative skin friction, due to increase relative displacement. The elastic shorting of the driven pile is more than that of the bored pile due to the less cross-sectional area of the driven pile. The results revealed proportional relation between the developed drag forces and pile section dimensions, interface friction factor, and fill height, with a maximum effect on the section dimension and minimum effect on the interface factor. The locations of neutral points are not sensitive to the above-mentioned factors.

Detonation cell size of liquid hypergolic propellants: Estimation from a non-premixed combustor

An experimental approach for estimating the detonation cell size for liquid hypergolic propellants is presented and applied for monomethylhydrazine (MMH) and a MON-3 variant of nitrogen tetroxide (NTO) in a non-premixed combustor. The method utilizes a correlation between cell size and reactant fill height in an annular combustor geometry. Reactant fill height is inferred using a control-volume analysis to relate the geometry of the reactant fill zone to the propellant flow rate, detonation wave-speeds and number, and annular gap size. High-speed videography is used to measure the number of waves and their speed over a range of quasi-steady continuous detonation conditions. The detonation criteria is also proven valid in the transient conditions as the decrease of the fill height below a critical value identified in this work matches modal transitions with decreasing number of waves. A power law relating the cell width with induction length further supports the validity of the present technique down to cell sizes of 1–10 µm, a scale not practically resolvable with conventional methods.

Investigation on the effect of skew angle on dead and live-loads in RC skew box culverts for Road Under Bridge (RUB) design

Skew box culverts are common on railway lines and highways when non-perpendicular crossings are encountered. Although various studies on the influence of skewness on culvert design have been undertaken, the majority of the work has focused on the Road Over Bridge (ROB) design. In the present study, an investigation of the effect of skew angle and topsoil fill height on the live and dead load characteristics of a two-cell reinforced concrete (RC) skew box culvert for Road under Bridge (RUB) design has been carried out. The dead and live loads considered in the present work have been calculated following the Indian Railway Standard (IRS) Bridge rule – 2014, Indian Railway Standard (IRS) Substructures and Foundation of Bridges – 2013, and Indian Standard (IS) 875part 3 – 1987. The soil fill height above the top slab varied from 2 m to 10 m with a 2 m increment for the current investigation, with skew angles ranging from 0° to 75° at intervals of 15°. The influence of skewness and soil fill height is explored in a detailed manner in this work, and the findings are provided in contrast to a straight box culvert. The dispersion diagram showing the distribution of loads is developed for the various skew angles and soil fill heights. The results revealed that the effect of skew has no influence on SIDL, lateral earth pressure, earth pressure from surcharge loads, and live load intensities from wind and footpath. However, the intensity of dynamic loads due to the axle movement of trains, derailment of trains, and Plasser’s Quick Relaying System (PQRS) loads decreases with increased skew angle. But the effect of longitudinal forces caused by the braking and traction of the trains increased as the skew angle increased. Also, the influence of skew is more pronounced at lower fill heights. The Engineers may find the results of this study valuable for building RC skew box culverts for RUB applications.

Investigating the Quality Performance of Production of Some Selected Drinks using Hotelling T-Square Control Chart

Consumers make complaint about the state of home-made goods. Some of the consumers claim that foreign goods are of high quality compared to home-made goods. We discovered that many indigenous industries are no more in existence and so this brought the desire to carry out this research work so as to find out whether products from our indigenous brewery industry fall within the acceptance region and devoid of the consumers’ complaint. For clarity and easy handling of this topic, data were collected on the four major components that are produced [STAR, MALTINA AND GOLDBERG] for months. The data collected covered a period of four months and the readings were twice a day. This was culled from the company’s register and averaged. Control charts, Standard Deviation charts and Cumulative Sum Technique charts (CUSUM) and Hotellings T-square were used in the analysis. The results were presented with the use of chart and tables. The results indicated the three beer product considered fall within the acceptance region considering their fill height and the level of carbon iv oxide [co 2 ]. Keywords : Control charts, Cumulative Sum Technique charts, Hotellings T-square, fill height, level of carbon iv oxide [co 2 ]. DOI: 10.7176/IEL/12-1-02 Publication date: January 31 st 2022

Triage method for load rating bridge size two-cell reinforced concrete box culverts for the AASHTO LRFD design load

Reinforced concrete bridge size box culverts (RCBCs), with structure length greater than or equal to 6.1 m (20 ft), are an integral part of the transportation infrastructure. Load rating RCBCs is essential, and the critical component is generally the top slab. The objective of this study is to propose a triage methodology to quickly and conservatively determine the rating factor (RF) for the top slab of a two-cell RCBC. The derivation of the demand equations is illustrated in this manuscript for the top slab and the AASHTO HL-93 live load. The finite element program CANDE is used to evaluate the influence of the cell clear height (H), cell clear span (S), fill height (HF ), and the backfill modulus (E) on the demand loads. Multiple regression analyses showed that H had no significant effect on the dead load demands, while H and E had no significant effect to the live load demands. Conservative linear demand equations (LDEs) are presented to calculate the dead and live load demands leading to a quick determination of the RF. LDEs for single and multi-cell culverts can be derived following the LDE procedure outlined herein.

The impact of geofoam on the bending moment characteristics of reinforced concrete box culverts for road under bridge (RUB) design

Reinforced concrete (RC) box culverts for Road under Bridge design (RUB) have been widely used in the construction of railways. RUB box culverts are typically exposed to dead loads, live load intensities from dynamic effects, and lateral earth pressure. The amount of reinforced concrete in the box culvert depends on the expected lateral earth pressure and superimposed dead loads from the top filling material. The magnitude of increased vertical load from the top filling material generates stresses and deformations on all the faces of the box culvert. To counteract the high pressure, either more reinforced concrete in the box culvert or lightweight material as backfill is used. Expanded polystyrene (EPS) geofoam as a lightweight geosynthetic is commonly used in transportation infrastructure to minimize horizontal and vertical stresses on culverts. This research investigates the effect of top filling properties on the bending moment characteristics of two cell reinforced concrete skew box culverts for the RUB design. The STAAD Pro software was used to model and analyze the cast-in-situ RUB box structure with profiles of 10.5 × 5.6. For this study, the fill height above the top slab of the culvert has been varied from 0.5 m to 10 m with increments of 0.5 m. The structure was analyzed for two different top filling materials; initial (with normal soil) and then with EPS geofoam materials. The results of the study indicate that using geofoam as a top-filling material reduces the bending moment on the center of the top slab of the box structure, midspan of the bottom slab of the second cell, and bottom edge of the outer wall of the second cell by 76 %, 70 %, and 73.3% respectively compared to the use of conventional soil fill. Also, the results from the analyses revealed that box structures with geofoam as filling materials reduced the earth pressure. The geofoam as fill material does not influence the bending moment values of the box sections beyond a fill height of 8 m.

Effect of relative density of 2D granular materials on the arching effect through numerical trapdoor tests

The relative density and the fill height of granular materials influence the arching effect significantly, from either the overall behavior of granular materials or the formation of the arching effect. In this study, a comprehensive comparison of the arching effect at four fill heights with three relative densities is conducted by numerical trapdoor tests using the two-dimensional (2D) discrete element method. The results indicate that the stick–slip behavior of the arching ratio (the ratio of the average vertical stress on the trapdoor to the overburden stress; the ratio decreases to a minimum value, followed by recovering to the ultimate value) is more obvious for the case with lower fill height at a given relative density or that with higher density at a given fill height. The partial and the full arching can be distinguished by whether the loosen zone propagates to the surface. Two different critical states are identified for the partial and the full arching, respectively. These critical states are insensitive to the relative density. A characteristic height is identified around twice the width of the trapdoor, at which the critical state of the partial arching transfers to that of the full arching with the increase of the relative density.

Investigation of reflective shuttling detonation cycle by schlieren and chemiluminescence photography

A reflective shuttling detention combustor (RSDC) is a two-dimensional combustor with two reflection walls. Unlike a rotating detonation combustor (RDC), an RSDC can visualize the entire area of the combustor via an optical technique. In addition, the RSDC can reproduce the counter-rotating detonation mode in RDC. In present study, CH* luminescence and schlieren image were observed to investigate the dynamics of the RSDC. The reflective wall distance was set to 45 mm (Type L) and 25 mm (Type S). As the results, the wave speed of 1226±64m/s in the single wave mode in Type S was76% of that in Type L. It was found that the detonation propagation speed decreased with a reduction in the reflection wall distance. Superimposing the luminescence images on the schlieren images revealed that the mixture was mainly burned by deflagration behind shock wave. In addition, the experimental mixture fill height was in good agreement with model in which the mixture filling process was temporarily stopped by detonation and refilled at a constant speed. Using the maximum fill height obtained by the model, it was found that the detonation mode was in the region of 3±0.6 of the dimensionless quantity (the reflection wall distance divided by the wave number and maximum value of the mixture fill height).

Multiplicity for idealized rotational detonation waves

Simulations of three-dimensional rotational detonation waves are conducted to understand the mechanisms of wave bifurcation. A compressible reacting Euler solver is developed within the framework of OpenFOAM, and a fixed mass flux boundary condition is developed to avoid complex injector dynamics. Influences of inflow mass flow rates and initiations of ignition spots are studied. As the inflow mass flow rate increases, one detonation wave is maintained. Constrained by the circumference of the combustor, the maximum fill height is achieved when the maximum post-shock pressure expansion is reached. Further increasing mass flow rates does not lead to wave bifurcation or higher mean fill height. By introducing multiple ignition regions, an identical number of stable waves are ignited and maintained, which signifies that wave numbers are not uniquely determined by the inlet boundary conditions. The minimum fill height (or largest velocity deficit) owing to either the lowest mass flow rate or the maximum wave number is obtained when the pressure expansion distance is comparable to the hydrodynamic thickness. The scaling of fill height is subsequently explained through a theoretical relation based on mass conservation. It is shown that neither increasing mass flow rates nor existence of multiple waves is a sufficient condition for wave bifurcation. The fill height is intrinsically connected with wave numbers, and both cannot be predicted solely based on boundary conditions. Future work will relax some idealizations in this work to further quantify the limit for the fill height.

Numerical and experimental analyses for rubber-sand particle mixtures applied in high-filled cut-and-cover tunnels

With the rapid development of the automobile industry and transportation, the disposal of scrap tires has become an internationally recognized economic and environmental problem. Fortunately, high-filled cut-and-cover tunnels (first construction and then layered backfill) provide ideal solutions for waste treatment and resource reuse as mixtures of scrap tire rubber particles and sand are used as lightweight fill material (LFM) in high-fill cut-and-cover tunnels (HFCCT). Because the backfill above the cut-and-cover tunnel (CCT) requires a large quantity of material, an appropriate ratio of scrap tire rubber particles and sand should be selected as the LFM mixture. If LFM of different thicknesses is buried above the CCT, it will inevitably bring varying degrees of influence on the earth pressure around the CCT, leading to structural deformation and soil settlement above the CCT. In this paper, a method of combining numerical simulation and model test is presented to help analyze the macroscopic and micromechanical properties of LFM through the stress–strain change and the contact force chain distribution. In the model test, certain factors influencing the earth pressure, the structural deformation, and the soil settlement mentioned above are considered, including the fill height and the embedding depth of the LFM. The results show that when the rubber fraction by volume (RF) is between 30% and 45%, the deformation and load-bearing capacity of the LFM are the most stable. Moreover, a suitable rubber fraction by volume (RF = 40%) and backfill height (between 0.63 ∼ 0.83 times the height of the CCT) can eliminate the stress concentration at the top center of the CCT.

Spring-Based Trapdoor Tests Investigating Soil Arching Stability in Embankment Fill under Localized Surface Loading

Pile-supported (PS) embankments have been used increasingly to support highways and railways on soft subsoils. In addition to the self-weight of the embankment, this embankment system is often subjected to surface localized loading, such as traffic loading. In this embankment system, soil arching is a key load transfer mechanism. Stability of soil arching under localized surface loading is important because traffic loading applied on the embankment surface can transfer onto and between pile heads and affect the degree of mobilization and degradation of soil arching. Conventional trapdoor systems have a rigid trapdoor, control its displacement manually/automatically, and cannot represent load-induced subsoil settlement below the embankment. This study utilized a trapdoor supported on low-stiffness or high-stiffness compression springs that moved under the load above the trapdoor (called a spring-based trapdoor) to evaluate the effects of continuous trapdoor displacement on the soil arching stability under static footing loading. To investigate the trapdoor rigidity effect, a trapdoor consisting of three segments (called a flexible trapdoor) was utilized in this study as well. The trapdoor test results showed that soil arching was mobilized during fill placement as the fill height and the trapdoor displacement increased. Subsequently, under static footing loading, the degree of soil arching increased at a low applied pressure; however, it degraded under higher footing loading that caused a larger trapdoor displacement. The high-stiffness trapdoor increased the degradation pressure required to eliminate soil arching even though it reduced the degree of soil arching under a low applied pressure compared with the low-stiffness trapdoor. The flexible trapdoor resulted in a uniform stress distribution on the trapdoor but reduced the total load transferred to the supports. The conventional trapdoor resulted in a lower soil arching ratio compared with the spring-based trapdoor during the soil arching mobilization, but had a higher soil arching degradation rate than the spring-based trapdoor due to continuous soil movement.

Development of a Two-Chamber MHD Tundish for Metal Ca

Introduction. The multifunctional magnetodynamic tundish prototype is the first world magnetodynamic mixer and batcher for steel, which has a capacity of up to 10 tons of melt and an inductor electric power of 600 kW. Ithas been successfully introduced into industry. Further works aim at adapting this device to continuous casting, in particular at obtaining semi-continuous cast billets at metallurgical micro-plants.Problem Statement. Today, the study of the effect of electromagnetic field on melt stirring and removal of non-metallics in the inlet chamber of MD-T is an urgent task.Purpose. The purpose of this research is to substantiate and to create MD-T as a two-chamber aggregate additionally equipped with a few electromagnetic & MHD devices for different purposes, to be used at metallurgical micro-mills.Materials and Methods. Physical modelling has been applied for studying liquid metal stirring under the action of electromagnetic field and the removal of non-metallics.Results. The behavior of the liquid jet falling from the ladle into the centrifugal chamber has been studied. The influence of the rational liquid level in the centrifugal chamber, which is exposed to the direct action of the electromagnetic field, has been estimated. It has been established that the effect of rotation of the total liquid volumehas been achieved at the height of application of electromagnetic field, which is 0.2—0.3 of the total fill height. Increasing the height of the application of a magnetic field leads to the capture of the upper layers of the liquid.Conclusions. There have been proposed a new design of magnetodynamic tundish (MD-T) for continuous casting of steel. The use of tundish with a rotational motion of the flow may significantly reduce the number of large oxide inclusions (larger than 10 µm) in steel. The device has been successfully tested and its application will improve the quality of cast billets, extend the functionality of equipment and technologies, and enable the realization of modern high-efficiency processes of continuous casting.

Bottom-Up Gold Filling in New Geometries and Yet Higher Aspect Ratio Gratings for Hard X-ray Interferometry

An extreme bottom-up filling variant of superconformal Au electrodeposition yielding void-free filling of recessed features is demonstrated with diffraction gratings composed of a two-dimensional patterned “chessboard” array of square vias of aspect ratio (depth/width) ≈ 23 as well as one-dimensional arrays of trenches having aspect ratios exceeding 50 and 65. Deposition on planar and patterned substrates is examined in several near-neutral x mol∙l−1 Na3Au(SO3)2 + 0.64 mol∙l−1 Na2SO3 electrolytes (x = [0.08, 0.16, 0.32]) containing ≈50 μmol∙l−1 Bi3+ additive. The electrolytes are similar to those used in earlier work, although the upper bound on Na3Au(SO3)2 concentration is twofold greater than previously described. Filling results are complemented by associated current and deposition charge transients whose features, particularly with well controlled pH, exhibit repeatable behaviors and timescales for incubation with passive deposition followed by bottom-up, void-free filling. While incompletely filled features can exhibit substantial via-to-via variation in fill height, self-passivation that follows complete bottom-up filling results in highly uniform filling profiles across the substrates. Visibility measurements capture the quality and uniformity of the as-formed wafer scale gratings. X-ray phase contrast imaging demonstrates their potential for imaging applications.

Multidimensional Numerical Modeling of Combustion Dynamics in a Non-Premixed Rotating Detonation Engine With Adaptive Mesh Refinement

Abstract In the present work, a novel computational fluid dynamics (CFD) methodology was developed to simulate full-scale non-premixed rotating detonation engines (RDEs). A unique feature of the modeling approach was the incorporation of adaptive mesh refinement (AMR) to achieve a good trade-off between model accuracy and computational expense. Unsteady Reynolds-averaged Navier–Stokes (RANS) simulations were performed for an Air Force Research Laboratory (AFRL) non-premixed RDE configuration with hydrogen as fuel and air as the oxidizer. The finite-rate chemistry model, along with a ten-species detailed kinetic mechanism, was employed to describe the H2-Air combustion chemistry. Three distinct operating conditions were simulated, corresponding to the same global equivalence ratio of unity but different fuel/air mass flowrates. For all conditions, the capability of the model to capture essential detonation wave dynamics was assessed. An exhaustive verification and validation study was performed against experimental data in terms of a number of waves, wave frequency, wave height, reactant fill height, oblique shock angle, axial pressure distribution in the channel, and fuel/air plenum pressure. The CFD model was demonstrated to accurately predict the sensitivity of these wave characteristics to the operating conditions, both qualitatively and quantitatively. A comprehensive heat release analysis was also conducted to quantify detonative versus deflagrative burning for the three simulated cases. The present CFD model offers a potential capability to perform rapid design space exploration and/or performance optimization studies for realistic full-scale RDE configurations.

Quantification of Rotating Detonations Using Chemiluminescence at Varied Widths

Rotating detonation combustors (RDCs) are studied with significant interest in recent years, due to their promulgated benefits over other pressure gain combustion systems. Although notable strides have been made, the fundamental understanding of rotating detonation wave dynamics is still nascent. Toward this end, high-speed chemiluminescence imaging is used to spatiotemporally track the detonation wave as it propagates through annular RDCs of three different channel widths at varied flow rates and equivalence ratios. Several algorithms are used to attain quantitative metrics on the observed rotating detonations, namely, speed, strength, height, and stability. It is shown that higher flow rates of 0.4 and (and hence higher fresh mixture fill height due to increased mass flux) produce small wave speed deficits, more consistency in wave propagation denoted by less variance in structure from lap to lap, as well as higher luminosity (proportional to combustion strength). It is also shown that at these high flow rates before wave bifurcation, rotating detonation waves exhibit the canonical diamond-shaped cellular pattern composed of the triple point interactions seen in planar detonations, but with cell widths bigger by an order of magnitude due to the streamtube effect. The experimentally gathered visualization data are used to formulate empirical guidelines that can help predict rotating detonation waves’ velocity deficit, height, and combustion strength for a given mass flux through the combustor. It is shown that velocity deficits in rotating detonations are a linear function of the effective perimeter inscribed by the wave, where the lowest deficits of 10% are seen at the highest perimeters, which in turn only manifests at the highest tested flow rates. This finding is linked to similar observations seen in planar detonations in tubes, where two distinct, perimeter-predicated loss mechanisms (one due to heat and momentum losses and the other due to streamtube effect) cause velocity deficits at near-limits conditions.

Dilatancy-driven secondary flows in dense granular materials

Abstract

Numerical Investigation of Soil Arching in Dense Sand

Soil arching is relevant in various engineering applications particularly in cases where there is relative movement between soil and structure. When a portion of the soil mass yields, redistribution of stresses take place between the yielding mass and its surrounding. Several trapdoor experiments have been performed with different improvements and extensions over the past few decades to study soil arching. Numerical modeling of a trapdoor mechanism is performed in this study and the suitability of Hardening Soil constitutive model over the Mohr-Coulomb model has been studied. In the present study, extensive parametric studies were conducted to examine the extent of the zone of influence and zone of yielding. The zone of influence, beyond which there is no influence of soil arching, is bounded by straight lines to form a trapezoidal shape. The dimensions of the influence zone depend on the fill height (H) and trapdoor width (B). The two families of failure surfaces, internal and external, are described and their categorization with respect to the H/B ratio is well explained. Furthermore, the zone of yielding and the region enclosed within limits of influence and failure planes are classified as active and passive zones, considering the dilation and compression in the direction of trapdoor displacement. The equilibrium of stress transfer in soil arching that remained as an unjustified assumption until now is systematically brought out in the present study. The present study also highlights salient characteristics of the plane of equivalent settlement and critical height. The present study throws some light on the need for further understanding of arching in various field applications, such as piled embankments, tunnels, culverts, buried pipelines, excavations supported by contiguous pile walls, and slopes stabilized by a row of piles.

Numerical and Analytical Studies of 3D Effects on Pullout Capacity of Anchor Blocks in Granular Compacted Fill

Generally, geotechnical construction works such as sheet pile walls are designed as plane-strain problems. In many practical cases, even if there is a need to consider 3D effects in the analysis, the designer tends to adopt conservative 2D analysis resulting in uneconomical design. This paper discusses a project in Dubai where sheet pile wall tie backed to anchor block was designed to retain 6.25 m height of compacted fill and account for future excavation considering 3D effect in anchor blocks. Anchor blocks were used to control the initial large deflections (> 50 mm) calculated in the sheet pile. Anchor blocks were analyzed considering 3D effects which resulted in increased pullout resistance (2.3 times) compared to assuming it as plane-strain problem. Simultaneously, numerical analyses were performed and an increase in pullout resistance (1.8 times) was noticed in 3D analysis compared to 2D analysis which confirms the importance of considering 3D effects in analyzing anchor blocks fetching subsequent optimization in anchor block design.

Investigation of heat and mass transfer behavior of mannitol during vial freeze-drying

The vial design feature, such as the base curvature, acts as the primary heat transfer barrier in the lyophilization process. In this study, heat and mass transport characteristics of mannitol (5%) during vial freeze-drying are numerically investigated by including the vial base curvature effects. The influence of the product fill height, chamber pressure, and the vial base curvature on the product temperature, drying time, and mass transfer resistance is analyzed in detail. The diameter of the vial is taken as 15 mm, while the fill height of the product is varied from 3 to 5 mm. The chamber pressure is maintained between 5 and 50 Pa. The results revealed that the product with a 3 mm fill height experienced a 2.5 °C lower temperature than the product with a 5 mm fill height. As opposed to the flat vial predictions, if the vial base curvature effects are considered, the drying time is increased by 1.96 and 3.8 h for the 3 mm and 5 mm fill heights, respectively. The increased drying time is attributed to the reduced direct contact area between the vial and shelf and the vapor entrainment in the gap. The results showed that the dry layer mass transfer resistance contributes to 95% of the total mass transfer resistance; however, the contribution of semi-stoppered vial resistance is 1–2% only.