Layer Mass Transfer Resistance Research Articles

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.

Mechanism of Condensation Enhancement by Corrugated Low Finned Tubes in Presence of Noncondensable Gas

Corrugated tubes are the most convenient reinforcement techniques to enhance intube condensation. In this paper, the average condensation heat transfer coefficients inside the corrugated low finned tube and smooth tube were firstly introduced. The distribution of local heat transfer coefficient was presented at lower and higher inlet noncondensable gas mass fractions. The results show that the major heat transfer resistance is the thermal resistance of liquid film at lower inlet gas fraction. So the mechanism of condensation enhancement by corrugated low finned tubes is the increase of liquid film condensation coefficient. But at higher inlet gas fraction gas layer mass transfer resistance becomes the control thermal resistance. The spiral ribs inside corrugated low finned tube can thinner not only the gas layer thickness but also the liquid film thickness. The mechanism of condensation enhancement is the increase of both gas layer and liquid film condensation coefficient.

Kinetics of Water Vapor Sorption in Wood Cell Walls: State of the Art and Research Needs

Water vapor sorption is the most fundamental aspect of wood-moisture relations. It is directly or indirectly related to the physical properties of wood and the onset of wood-damage mechanisms. While sorption properties of cellulosic materials have been utilized since antiquity, the time-dependent transition from one moisture content to another (i.e., sorption kinetics) has received much less attention. In this critical review, we present the state-of-the-art of water vapor sorption kinetics in wood. We first examine different experimental methods that have been used to measure sorption kinetics, from the quartz helix vacuum balance beginning in earnest in the 1930s, to automated sorption balances used recently. We then give an overview of experimental observations and describe the physical phenomena that occur during the sorption process, which potentially govern the following kinetics: boundary layer mass transfer resistance, heat of sorption, cell wall diffusion, swelling, and polymer mobility. Finally, we evaluate theoretical models that have been proposed for describing sorption kinetics, considering both experimental data and the physical processes described in the previous section. It is clear that no previously developed model can phenomenologically describe the sorption process. Instead, new models are needed. We conclude that the development of new models will require more than simple gravimetric measurements. In addition to mass changes, complementary techniques are needed to probe other important physical quantities on multiple length scales.

Oxygen gain analysis for proton exchange membrane fuel cells

Oxygen gain is the difference in hydrogen fuel cell performance operating on oxygen-depleted and oxygen-rich cathode fuel streams. Oxygen gain experiments provide insight into the degree of oxygen mass-transport resistance within a fuel cell. By taking these measurements under different operating conditions, or over time, one can determine how oxygen mass transport varies with operating modes and/or aging. This paper provides techniques to differentiate between mass-transport resistance within the catalyst layer and within the gas-diffusion medium for a polymer-electrolyte membrane fuel cell. Two extreme cases are treated in which all mass transfer limitations are located only ( i) within the catalyst layer or ( ii) outside the catalyst layer in the gas-diffusion medium. These two limiting cases are treated using a relatively simple model of the cathode potential and common oxygen gain experimental techniques. This analysis demonstrates decisively different oxygen gain behavior for the two limiting cases. For catalyst layer mass transfer resistance alone, oxygen gain values are limited to a finite range of values. However, for gas-diffusion layer mass transfer resistance alone, the oxygen gain is not confined to a finite range of values. Therefore, this work provides a straightforward diagnostic method for locating the prominent source of mass transfer degradation in a PEMFC cathode.

A validated model for the simulation of protein purification through affinity membrane chromatography

A mathematical model is proposed for the description of protein purification through membrane affinity chromatography. The model describes all the three stages of the chromatographic cycle and takes into account convection, axial dispersion and binding reaction kinetics in the porous membrane matrix, while boundary layer mass transfer resistance is shown to be negligible. All the model parameters have a precise physical meaning which enables their evaluation through separate experimental measurements, independent of the chromatographic cycle. Model testing and validation has been performed with experimental chromatographic cycles carried out with pure IgG solutions as well as with complex mixtures containing IgG 1, using new affinity membranes. The comparison between model calculations and experimental data showed good agreement for all stages of the affinity cycle. In particular, for loading and washing steps binding kinetics was found so fast that adsorption equilibrium was sufficient to describe the observed behavior; as a result, the model simulations are entirely predictive for the adsorption and washing phases. On the contrary, in the elution step the reaction rate is comparable to that of the other simultaneous transport phenomena. The model is able to predict the performance of chromatographic purification of IgG from complex mixtures simply on the basis of the parameter values obtained from pure IgG solutions.

Product mass transfer resistance directly determined during freeze-drying cycle runs using tunable diode laser absorption spectroscopy (TDLAS) and pore diffusion model

The pore diffusion model is used to express the dry layer mass transfer resistance, , as a function of the ratio re/τ, where re is the effective pore radius and τ is the tortuosity factor of the dry layer. Using this model, the effective pore radius of the dry layer can be estimated from the sublimation rate and product temperature profiles measured during primary drying. Freeze-drying cycle runs were performed using the LyoStar II dryer (FTS Systems), with real-time sublimation rate profiles during freeze drying continuously measured by tunable diode laser absorption spectroscopy (TDLAS). The formulations chosen for demonstration of the proposed approach include 5% mannitol, 5% sucrose, 5% lactose, 3% mannitol plus 2% sucrose, and a parenteral nutrition formulation denoted VitaM12. The three different methods used for determination of the product resistance are: (1) Using both the sublimation rate and product temperature profiles, (2) using the sublimation rate profile alone, and (3) using the product temperate profile alone. Unlike the second and third methods, the computation procedure of first method does not need solution of the complex heat and mass transfer equations.

Study of mass and heat transfer in the osmotic evaporation process using hollow fibre membrane contactors

In this work, the mass and heat transfer in the osmotic evaporation process was studied using a hollow fibre membrane contactor. A calcium chloride dihydrate solution (2.8–6 M) was circulated in the fibres and a sucrose solution (20% and 45%, w/w) in the shell side of the module. The respective mass transfer correlations were determined using a single-step methodology involving the mass and heat transfer equations, simultaneously: S h t = 2.66 R e t 0.25 S c t 0.33 ( d / l ) 0.33 and S h s = 15.4 R e s 0.92 S c s 0.33 ( d / l ) . The correlations are valid for Reynolds numbers between 0.5 and 45 and are in agreement with that obtained for liquid–liquid extraction and gas absorption. It was observed that the mass transfer resistance in the fibres could be easily minimized, even when high driving forces are applied. Regarding the shell side boundary layer mass transfer resistance, it can be significant when processing concentrated sucrose solutions (50% of the overall resistance for a 61% (w/w) sucrose concentration). The temperature profile was calculated using a model, which combines the heat and mass transfer equations. Although the temperature gradient through the boundary layers was not significant, the temperature difference between the membrane interfaces can be important for high driving forces, it reached almost 3 °C when using a 6 M CaCl 2 solution. The mass and heat transfer model was also used to calculate the water flux and the overall mass transfer coefficient during the concentration process of a sucrose solution. The values predicted are in agreement with the experimental results for the range of Reynolds and Schmidt numbers studied.

Ultrafiltration of W/CO2 Microemulsions in Ceramic Membranes

Water‐in‐CO2 (W/CO2) reverse microemulsions stabilized with 1100 Da poly(ethylene glycol)‐poly(propylene glycol)‐poly(ethylene glycol) block copolymer were recovered using an ultrafiltration ceramic membrane in a custom high‐pressure cross‐flow separation unit. Viscosity‐corrected liquid CO2 flux (298 K) through the membrane was investigated as a function of time and surfactant concentration to determine the cake layer mass transfer resistance. Rapid CO2 flux decline was observed with increasing surfactant concentration, denoting cake layer buildup on the membrane surface. For instance, at 0.09 and 0.55 wt% surfactant, the ratio of cake resistance to membrane resistance was 0.4 and 3.8, respectively. Based on our previous work, the reverse‐micelles retain their aqueous core and are not altered during filtration. Ultimately, inorganic membrane separations can reduce energy consumption associated with compression/expansion cycles typically used in CO2‐based processes.

Dissolution of Wollastonite in a Packed Bed Contactor

In a packed-bed reactor grains of the calcium silicate mineral wollastonite dissolved incongruently. A silicon-rich residue layer appeared to form on the grain surfaces and this quickly limited the overall rate of mineral dissolution. Approximately 54% of the silicon associated with the dissolved calcium was retained on the grains and about 46% went into solution with the calcium. As the amount of Ca dissolved per unit area of grain surface approached approximately 0.5μmol∕cm2 the effluent concentration of Ca decreased to a value that was significantly less than the equilibrium concentration (approximately 300μmol∕L) and the effluent pH decreased from approximately 10 to slightly greater than the influent value of 6.8. The effluent Ca and Si concentrations were effectively predicted by a finite difference model that used layer-by-layer calculation of a residue layer mass transfer resistance (for the Ca ion) acting in series with an extraparticle mass transfer resistance. The effluent pH was predicted using chemical equilibrium calculations and the assumption that the dissolved Si controls the proton balance across the column.

Rapid determination of dry layer mass transfer resistance for various pharmaceutical formulations during primary drying using product temperature profiles

Mass transfer resistance of the dry layer during the primary drying phase of a lyophilizaton cycle is probably the most important factor affecting maximum product temperature and drying time. Product resistance parameters should be determined for each formulation because of their dependence of formulation composition and concentration. The purpose of this study was to determine the dry layer mass transfer resistance, using a simple and rapid method, for various pharmaceutical formulations during primary drying in a laboratory dryer, using monitored product temperature profiles. The mathematical tools used for the determination were a primary drying simulation program in conjunction with Powell's optimization algorithm. For each formulation studied, primary drying was performed using a shelf temperature of −15 or −20 °C and the chamber pressure controlled at 100 mTorr (0.1 Torr). The product temperature profiles ( T b) during primary drying were recorded and became the input data for the parameter estimation. The normalized product resistance, R pN, as a function of the dry layer thickness, ℓ , can be described by: R pN = R 0 + A 1 ℓ / ( 1 + A 2 ℓ ) , where the constants R 0, A 1 and A 2 are product resistance parameters of water vapor through the dry layer. Even when the parameter A 1 was negative, indicating that product temperature atypically decreased over time, the dry layer product resistance parameters of the various pharmaceutical formulations could be rapidly and successfully determined using the proposed approach. The product resistance equation obtained in this work for 5% marmitol, expressed as R pN = 0.0002025 + 20.23 ℓ , is similar to that obtained by Pikal [Pikal, M.J., 1985. Use of laboratory data in freeze drying process design: heat and product resistance parameters and the compute simulation of freeze drying. J. Parent. Sci. Technol. 39, 115–138.] using the microbalance method, expressed as R pN = 1.40 + 16.0 ℓ . The product resistance values obtained for the 3% lactose–LDH formulation are also very close to those obtained by (Milton, N., Pikal, M.J., Roy, M.L., Nail, S.L., 1997. Evaluation of manometric temperature measurement as a method of monitoring product temperature during lyophilization. PDA J. Pharm. Sci. Technol. 51, 7–16.) for 5% lactose using the MTM (manometric temperature measurement) method. With the obtained values of the parameters R 0, A 1, and A 2, simulations can be performed to determine the maximum product temperature and the drying time during primary drying. As such, optimum cycle parameters can be determined to avoid collapse of the product. The proposed approach requires only accurately measured product temperature profiles, easily obtained in a laboratory dryer.

Correlation of laboratory and production freeze drying cycles

The purpose of this study was to develop the correlation of cycle parameters between a laboratory and a production freeze-dryer. With the established correlation, key cycle parameters obtained using a laboratory dryer may be converted to those for a production dryer with minimal experimental efforts. In order to develop the correlation, it was important to consider the contributions from the following freeze-drying components: (1) the dryer, (2) the vial, and (3) the formulation. The critical parameters for the dryer are the shelf heat transfer coefficient and shelf surface radiation emissivity. The critical parameters for the vial are the vial bottom heat transfer coefficients (the contact parameter K cs and separation distance ℓ v), and vial top heat transfer coefficient. The critical parameter of the formulation is the dry layer mass transfer coefficient. The above heat and mass transfer coefficients were determined by freeze-drying experiments in conjunction with mathematical modeling. With the obtained heat and mass transfer coefficients, the maximum product temperature, T bmax, during primary drying was simulated using a primary drying subroutine as a function of the shelf temperature and chamber pressure. The required shelf temperature and chamber pressure, in order to perform a successful cycle run without product collapse, were then simulated based on the resulting values of T bmax. The established correlation approach was demonstrated by the primary drying of the model formulation 5% mannitol solution. The cycle runs were performed using a LyoStar™ dryer as the laboratory dryer and a BOC Edwards™ dryer as the production dryer. The determined normalized dried layer mass transfer resistance for 5% mannitol is expressed as R pN = 0.7313 + 17.19 ℓ, where ℓ is the receding dry layer thickness. After demonstrating the correlation approach using the model formulation 5% mannitol, a practical comparison study was performed for the actual product, the lactate dehydrogenase (LDH) formulation. The determined normalized dried layer mass transfer resistance for the LDH formulation is expressed as R pN = 4.344 + 10.85 ℓ. The operational templates T bmax and primary drying time were also generated by simulation. The cycle run for the LDH formulation using the Edwards™ production dryer verified that the cycle developed in a laboratory freeze-dryer was transferable at the production scale.

Optimization of the Freeze-Drying Cycle: A New Model for Pressure Rise Analysis

The principal aim of this study was to evaluate the Pressure Rise Analysis (PRA) method as a nonintrusive method for monitoring the product temperature during primary drying of the freeze-drying process of model pharmaceutical formulations. The principle of this method, based on the MTM method initially published by Milton et al.1 consisted in interrupting rapidly the water vapor flow from the sublimation chamber to the condenser chamber and by analyzing the resulting dynamics of the chamber total pressure increase. A new physical model, named PRA model, based on elementary heat and mass balance equations and on constitutive equations expressing the elementary fluxes, was proposed and validated in this study for interpreting the experimental pressure rise data. It was possible to identify very precisely the values of some key parameters of the freeze-drying process such as the ice sublimation interface temperature, the mass transfer resistance of the dried layer and the overall heat transfer coefficient of the vial. The identified ice front temperatures were compared with experimental data obtained from vial bottom temperatures measured by thin thermocouples during freeze-drying runs of 5% w/v mannitol solutions. These two sets of data were found consistent with a maximum difference of no more than 2°C. The dried layer mass transfer resistance increased linearly as a function of its thickness, and the values were coherent with the few literature data published for this system. The method also led to reliable values of the vial overall heat transfer coefficient of approximately 20 Wm−2 K−1 in accordance with the published data for this type of vials and these experimental freeze-drying conditions.

Film and intraparticle mass transfer during the adsorption of metal ions onto bone char

The sorption of three metal ions, namely, copper, cadmium, and zinc, onto bone char has been studied in terms of equilibrium and rate studies. Equilibrium studies have been analyzed using the Langmuir isotherm equation and the maximum sorption capacities for the metals were 0.477, 0.709, and 0.505 mmol g −1 bone char for cadmium, copper, and zinc ions, respectively. The kinetic experimental data were used to analyze the effect of external film boundary layer and intraparticle mass transfer resistance on the sorption process and its significance. Four methods of determining the external film transport coefficient were developed and tested; three utilized experimental data to obtain the coefficient and the fourth method was completely empirical. The three experimentally based models give very similar results and consequently similar values of the deviation error values, whereas the error values for the empirical correlation were greater than these three values. The results also demonstrated that the methods for determining the film coefficient could be integrated into more complex diffusion-transport models such as film–intraparticle diffusion processes.

Mass transfer rate limitation effects on partitioning tracer tests

Partitioning tracer tests are often used to quantify the amount of non-aqueous phase liquid (NAPL) present in a porous medium. Results from such tests are usually interpreted by using models that assume local equilibrium exists between the NAPL and the aqueous phase or by using a moment method to solve for the fraction of the pore space occupied by the NAPL. We investigated the transport of partitioning alcohol tracers through heterogeneous sand porous medium systems containing a stationary trichloroethylene (TCE) phase for a range of aqueous phase velocities. NAPL saturations were quantified using a non-destructive X-ray absorption methodology. Experimental results were simulated using a numerical solution to an advective–dispersive model in which mass transfer between the NAPL and the aqueous phase was approximated using a dual-resistance approach consisting of a boundary layer mass transfer resistance and a diffusional resistance within the NAPL. The numerical model agreed well with the experimental data, and moment analysis yielded reasonable estimates of actual NAPL saturations.

Recovery of VOCs from surfactant solutions by pervaporation

Surfactant-based processes are emerging as promising technologies to enhance conventional pump-and-treat methods for remediating soils contaminated with nonaqueous phase liquids (NAPLs), primarily due to the potential to significantly reduce the remediation time. In order to reuse the surfactant, thereby making the process more economical, the NAPLs must be separated from the surfactant solution. Pervaporation was identified as a potential technology for removing volatile NAPLs from surfactant solutions. Initial tests with 1,1,1-trichloroethane (TCA) in an aqueous solution of the non-ionic surfactant Triton X-100 showed that the surfactant had a negligible effect on both flux and selectivity at concentrations of up to four times the critical micelle concentration (4×CMC). Further tests with a 40×CMC surfactant solution yielded moderately lower TCA fluxes and selectivities than comparable aqueous solutions without surfactant. The reduced pervaporation performance at higher surfactant and TCA concentrations were found to result from two effects: (1) increases in the viscosity of the solution, which increases the liquid-side boundary layer mass transfer resistance and (2) partitioning of TCA into the micelles, thereby reducing the effective extramicellar concentration. Despite these reductions in performance, pervaporation was found to be quite capable of removing this volatile NAPL from the surfactant solutions.

The Sampling Rates of Diffusive Samplers Measured in the Laboratory and in Simulated Use as Personal Samplers

This study investigated the effect of the speed and direction of air movement and the presence of the human body on sampling rate by changes in the boundary layer mass transfer resistance of samplers. The mass transfer resistance of a modified commercial diffusive sampler was measured mounted on a mannequin and compared with the mass transfer resistance of a sampler in an unobstructed airstream. The latter condition is the normal manner in which diffusive samplers are calibrated, while the former is more representative of field use. Results of the analysis are generalized in terms of dimensionless parameters. The presence of the mannequin produced boundary layer mass transfer resistances from 0.8 to 10 times that of samplers in unobstructed airflow for the range of air speeds and incidence angles studied. Illustrating the impact of the mannequin's presence on sampling performance, the sampling rate for m-xylene at 25°C and 1 atm would range from 0.390 to 0.514 cm3/sec, or ± 13.7% of the midrange value. The range of the boundary layer mass transfer resistance was most pronounced at low air speeds. A speed in excess of 70 cm/sec was necessary to keep the difference between the sampling rates of the mannequin-mounted sampler and the sampler in unobstructed airflow less than 10%.These results suggest that the mass transfer resistance during sampler calibration should be as close as possible to that encountered during sampling.

The Sampling Rates of Diffusive Samplers Measured in the Laboratory and in Simulated Use as Personal Samplers

This study investigated the effect of the speed and direction of air movement and the presence of the human body on sampling rate by changes in the boundary layer mass transfer resistance of samplers. The mass transfer resistance of a modified commercial diffusive sampler was measured mounted on a mannequin and compared with the mass transfer resistance of a sampler in an unobstructed airstream. The latter condition is the normal manner in which diffusive samplers are calibrated, while the former is more representative of field use. Results of the analysis are generalized in terms of dimensionless parameters. The presence of the mannequin produced boundary layer mass transfer resistances from 0.8 to 10 times that of samplers in unobstructed airflow for the range of air speeds and incidence angles studied. Illustrating the impact of the mannequin's presence on sampling performance, the sampling rate for m-xylene at 25°C and 1 atm would range from 0.390 to 0.514 cm3/sec, or ± 13.7% of the midrange value. The range of the boundary layer mass transfer resistance was most pronounced at low air speeds. A speed in excess of 70 cm/sec was necessary to keep the difference between the sampling rates of the mannequin-mounted sampler and the sampler in unobstructed airflow less than 10%.These results suggest that the mass transfer resistance during sampler calibration should be as close as possible to that encountered during sampling.

Optimization of multicomponent pervaporation for removal of volatile organic compounds from water

Optimal operation of a hollow fiber membrane module for pervaporative removal of multicomponent volatile organic compounds (VOCs) from wastewater was studied. A shell-and-tube heat-exchange ttype of hollow fiber module was considered for treatment of a wastewater containing toluene, trichloroethane (TCE) and methylene chloride. Three kinds of membranes, i.e., poly (dimethylsiloxane) (PDMS), polyether- block-polyamides (PEBA) and polyurethane (PUR) membranes, were studied. A mathematical model of the module was developed. The flux equations of the model were derived using mass transfer coefficient as described in our previous study. A cost model of the system was used to study the effect of different process and design variables on annual treatment cost. The effects of multicomponent feed mixtures, liquid boundary layer mass transfer resistance, and downstream pressure on the module performance and process economics were studied. A multidimensional optimization technique was used to determine the operation conditions for minimum cost. The sensitivity of the operation cost with respect to different process variables was also studied. The annual treatment cost was found to be relatively insensitive to the downstream pressure in the low pressure iange (for example, 0–2000 Pa for toluene removal, 0–3000 Pa for TCE removal and 0–1500 Pa for methylene chloride removal). The optimal downstream pressure increased with the increase of Henry's law constant of the compounds. The capital cost was found to be dominant in the total treatment cost at laminar flow regime, while the operating cost is diminant cost at turbulent flow regime.

Correlation of mass transfer rates for a diffusive sampler with air speed and incidence angle

An accurate measurement of a gas concentration in air by diffusive sampling requires knowing the sampling rate. Both the boundary layer between turbulent ambient air and the sampler and the stagnant air layer inside the sampler impose resistance to the transport of analyte into the sampler. As the boundary layer mass transfer resistance is a function of the air speed and direction of the air movement, the sampling rate also depends on these variables. By the procedure developed here, the boundary layer mass transfer resistance was accurately measured as a function of wind speed and direction, and from these data a basic correlation with dimensionless parameters describing mass transfer was obtained. Deviation of air incidence angle and speed during sampling from the calibration conditions may produce a small positive bias, probably not in excess of 10%. Random variation of incidence angle and air speed while the sampler is in use may also contribute to the variability of this sampling method.

Effect of boundary layer mass transfer resistance in the pervaporation of dilute organics

Pervaporation separation of dilute aromatic organic solutes is investigated. For the given hydrodynamic conditions, the mass transfer boundary layer resistance is found to contribute significantly to overall solute transport. The boundary layer effect is experimentally investigated by studying the variation of solute permeability with membrane thickness. In theory, the resistance-in-series concept is used to derive an equation for the variation of observed permeability with membrane thickness. The permeability coefficient is defined based on the general flux equation expressed in terms of the chemical potential driving force. Selectivity relationships for various conditions are also established. Further, an attempt has also been made to reconcile the seemingly different pervaporation expressions employed by various investigators. The current study, thus, seeks to emphasize the importance of the boundary layer resistance in studying the transport of organic solutes by pervaporation through a membrane with a high selectivity and/or permeability.