Single Resistance Model Research Articles

CO2 and CH4 diffusivities through synthesized ZIF-8 nanocrystals: An experimental and theoretical investigation

CO 2 separation is of paramount importance owing to global warming abatement, as well as sour natural gas sweetening. Mixed matrix membranes (MMMs), containing porous zeolitic imidazolate frameworks (ZIFs), in particular ZIF-8, have drawn noticeable attention due to their favorable separation performance. However, there are evidences of discrepancies in the reported values of gas diffusion coefficients/diffusivities through ZIFs, even for common well-studied gases, such as CO 2 and CH 4 in the literature. These discrepancies might be attributed to the surface/barrier effects, which are intensified by ZIF-8 nanocrystals downsizing. In this paper, an effort has been made to determine the impact of these surface effects on diffusivities of CO 2 and CH 4 through ZIF-8 nanocrystals. To do so, ZIF-8 nanocrystals ( ~ 100 nm), pristine poly(ethylene glycol diacrylate) (PEGDA) membrane, and PEGDA/ZIF-8 mixed matrix membranes (MMMs) were prepared. Gas adsorption/sorption measurements for CO 2 and CH 4 over a temperature range of (308–348) K were conducted. The Maxwell model was applied to obtain gas permeabilities in pure ZIF-8 nanocrystals by employing the measured values of permeabilities through fabricated MMMs. The solubilities in ZIF-8 nanocrystals were found using adsorption isotherms, and the corrected/intracrystalline diffusivities were subsequently obtained using solution–diffusion theory. Moreover, the apparent/extracrystalline diffusivity values, affected by the surface effects, were attained from transient uptake rate measurements, and were compared to the corrected ones. The surface effects were eventually determined via a single-resistance model. • Surface effects of ZIF-8 nanocrystals against diffusion of CO 2 and CH 4 were investigated. • Surface permeabilities of CO 2 and CH 4 in ZIF-8 were obtained in the range of 10 −8 cm s −1 . • Corrected transport diffusivities were corresponding to intracrystalline diffusivities. • Extracrystalline diffusivities were found seven orders of magnitude lower than the intracrystalline diffusivities.

Identification of Internal Parameters of a Mono-Crystalline Photovoltaic Cell Models and Experimental Ascertainment

This paper presents two mathematical models of mono-crystalline solar photovoltaic (PV) cells: (i) the ideal model, and (ii) the single resistance model. An identification algorithm of internal parameters of a photovoltaic cell using electrical characteristics provided by the manufacturer datasheet has been suggested. Several of these parameters are not always provided by the manufacturer. Moreover, influences and variation effects of the temperature and the effective irradiance level has been studied for the proposed models. Obtained simulations have been compared to those provided by JAC M5SF-2 cell’s datasheet. These models has been implemented on Matlab-Simulink and Simpower softwares. Then, the effectiveness of the proposed models has been validated against an experimentally tests under real operating conditions. The setup is based on some sensors: current, voltage, temperature and light sensors. Two Arduino Boards are used to acquire data from sensors and send them to the computer. These results show an acceptable correspondence with the data issued by the manufacturer. Identification algorithms, based on the rated data given by the manufacturer, can thus, be very useful for researchers or engineers to quickly and easily determine the internal parameters of any photovoltaic cell.

Kinetic model for the immobilised biosorbents: Uptake of cationic dyes

Abstract A sorption kinetic model has been developed using concept of Chemically Active Available Binding Sites (CAABS). Dead “ Fomitopsis carnea ” immobilized on polyvinyl alcohol (PVA) matrix has been employed as the immobilized sorbent. Safranin O and Alcian Blue are the representative sorbates. Results indicate that CAABS model described the kinetics with high degree of correlation coefficient ( R 2 ⩾ 0.99) for under different environmental conditions, viz., mixing speed (60, 200 and 500 revolutions per minutes), and biosorbent doses. Student’s t -test also revealed that the predicted data using Chemically Active Available Binding Sites (CAABS) model were significantly correlated with the experimental data. The CAABS model was also compared with well known kinetic models such as Lagergren’s model (first order kinetic model), Single resistance model, Pore diffusion model, and Pseudo-second order kinetic model. The comparative study of these models also confirmed high efficacy of the CAABS model to depict the experimental data.

The role of external and internal mass transfer in the process of Cu2+ removal by natural mineral sorbents

The kinetics of Cu2+ sorption on to zeolite, clay and diatomite was investigated as a function of initial metal concentrations. For consideration of the mass transfer phenomena, single resistance models based on both film and intraparticle diffusion were tested and compared. The obtained results suggested that the rate‐limiting step in Cu2+ sorption strongly depended on the sorbent type, as well as on initial cation concentration. The decrease in external mass transfer coefficients with the increase in initial metal concentrations was in excellent agreement with expressions based on Sherwood and Schmidt dimensionless numbers. The internal diffusivities through zeolite particles were in the range 1.0 × 10−11 to 1.0 × 10−13 m2/min, depending on the Cu2+ concentration and the applied theoretical model.

Contribution of arterial Windkessel in low-frequency cerebral hemodynamics during transient changes in blood pressure

The Windkessel properties of the vasculature are known to play a significant role in buffering arterial pulsations, but their potential importance in dampening low-frequency fluctuations in cerebral blood flow has not been clearly examined. In this study, we quantitatively assessed the contribution of arterial Windkessel (peripheral compliance and resistance) in the dynamic cerebral blood flow response to relatively large and acute changes in blood pressure. Middle cerebral artery flow velocity (MCA(V); transcranial Doppler) and arterial blood pressure were recorded from 14 healthy subjects. Low-pass-filtered pressure-flow responses (<0.15 Hz) during transient hypertension (intravenous phenylephrine) and hypotension (intravenous sodium nitroprusside) were fitted to a two-element Windkessel model. The Windkessel model was found to provide a superior goodness of fit to the MCA(V) responses during both hypertension and hypotension (R² = 0.89 ± 0.03 and 0.85 ± 0.05, respectively), with a significant improvement in adjusted coefficients of determination (P < 0.005) compared with the single-resistance model (R² = 0.62 ± 0.06 and 0.61 ± 0.08, respectively). No differences were found between the two interventions in the Windkessel capacitive and resistive gains, suggesting similar vascular properties during pressure rise and fall episodes. The results highlight that low-frequency cerebral hemodynamic responses to transient hypertension and hypotension may include a significant contribution from the mechanical properties of vasculature and, thus, cannot solely be attributed to the active control of vascular tone by cerebral autoregulation. The arterial Windkessel should be regarded as an important element of dynamic cerebral blood flow modulation during large and acute blood pressure perturbation.

Application of film-pore diffusion model for methylene blue adsorption onto plant leaf powders

In the present work kinetics of methylene blue adsorption onto three low-cost adsorbents namely guava leaf powder (GLP), teak leaf powder (TLP) and gulmohar leaf powder (GUL) was predicted using film-pore diffusion model. The model equations were solved numerically by method of lines using Excel. Initial estimates of mass transfer parameters namely external-film transfer coefficient and internal diffusion coefficient were obtained using single resistance models at temperatures 303, 313 and 323 K and for initial dye concentrations 50, 100, 150 and 200 mg dm −3. Film-pore diffusion model was then used to determine the concentration-independent values of these mass transfer coefficients. Thus, external-film transfer coefficients were found to be in the range of 3 × 10 −6 to 35 × 10 −6 m s −1, 1 × 10 −6 to 8 × 10 −6 m s −1 and 1 × 10 −6 to 11 × 10 −6 m s −1 for guava, teak and gulmohar leaf powders, respectively, in the chosen temperature range. At the same time internal diffusion coefficients were in the range of 0.1 × 10 −12 to 1.9 × 10 −12 m 2 s −1, 0.1 × 10 −12 to 0.6 × 10 −12 m 2 s −1 and 0.2 × 10 −12 to 1.3 × 10 −12 m 2 s −1 for guava, teak and gulmohar leaf powders, respectively. It was evident that film-pore diffusion model could satisfactorily describe kinetics of methylene blue adsorption onto the three low-cost adsorbents used.

TEOM analysis of the equilibria and kinetics of n-hexane and n-heptane adsorption on FCC catalyst/silicalite

A tapered element oscillatory microbalance is used for the measurement of uptake rates of n-hexane and n-heptane on fluid catalytic cracking catalyst and silicalite adsorbent. Investigations are considered over the temperature range of 373 to 513 K , and adsorbate partial pressures up to 0.12 bar . Based on measured adsorption isotherms, and through mechanistic descriptions of the diffusion process, a mathematical model is developed to describe the transient response of the microbalance, and subsequently the kinetics of adsorption and desorption. For example, for the hexane-silicalite system at a temperature of 473 K , the diffusion coefficient at zero-surface coverage is estimated as 2.9×10 −11 m 2/ s , with an activation energy of 17 kJ/ mol . This is consistent with published data based on other transient analysis methods. At relatively low temperatures of operation, i.e. less than 450 K , a single resistance model for mass transfer failed to accurately predict the desorption profiles for hexane on silicalite. As a means of quantifying the observed desorption rates, a dual-resistance model is introduced in which two different diffusion rates are assumed to take place above and below a threshold value of adsorbate concentration. Such a model may be used to account for silicalite phase transitions at high adsorbate loading.

A COMPARATIVE STUDY FOR THE SORPTION OF Cu(II) IONS BY CHITIN AND CHITOSAN: APPLICATION OF EQUILIBRIUM AND MASS TRANSFER MODELS

The sorption of Cu(II) by chitin, a naturally occurring material, and chitosan, prepared from chitin, was investigated and compared. The effect of pH, initial metal ion concentration, particle size, sorbent concentration, and stirring rate on sorption capacity was characterized by measuring the sorption isotherms. Sorption data of chitin and chitosan were best modeled by the Langmuir and Redlich–Peterson isotherms, although they can be modeled by the Freundlich and BET sorption models. Next, batch studies were carried out to identify the rate-controlling steps for Cu(II) sorption. Single resistance models were used in the determination of the external film mass transfer step and the intraparticle diffusion step.

The Adsorption of Pollutants by Peat, Lignite and Activated Chars

The ability of peat, lignite and activated chars made from peat and lignite to adsorb dyes and metals from wastewater and NO 2 from air was investigated. Equilibrium isotherms were determined to assess the maximum adsorption capacity of the adsorbents for the pollutants. Kinetic studies for the adsorption of dyes and metal ions onto the adsorbents were undertaken in agitated batch adsorbers. Mass transport models were tested to predict the concentration decay curves in batch adsorbers. The models tested were single resistance models based on the assumption of a single external mass transfer coefficient and two resistance models which included an internal diffusion coefficient and an external mass transfer coefficient. The surface phenomena which influence the extent and the rate of uptake have been studied. The equilibrium capacity data conform to Langmuir plots. A previously proposed model was used to evaluate the external single resistance mass transfer model and was successfully applied to predict the adsorption of metal ions in single component systems under batch conditions. It has been shown that the assumption of negligible intraparticle diffusion is valid and that external film diffusion is the rate limiting step in describing the adsorption processes at high sorbent loadings. The same type of result is not observed for the adsorption of coloured organic matter onto peat where the sorption processes cannot be successfully modelled by use of a single resistance model and a two resistance model incorporating internal diffusion is required. The surface phenomena which influence the extent and the rate of uptake of NO 2 have been studied. The type of chars produced and the activation processes affect the adsorption. As activation increases, micropore volume and surface area increase and the maximum capacity of the adsorbent increases. Surface area alone is not the only parameter which affects equilibrium uptake.

The influence of film diffusion on cadmium biosorption by marine biomass

The sorption of cadmium by biomass of brown marine alga Sargassum fluitans has been studied in a standard mixed batch reactor at steady-state and transient conditions. Steady-state sorption data over the temperature range of 7 ° C to 60 ° C indicated a higher cadmium uptake at elevated temperatures. Overall adsorption rates also slightly increased with increasing temperature in the range of 20 ° C to 60 ° C. Assuming only a single external mass transfer resistance to adsorption external mass transfer coefficients were determined. Experimental data were compared to a single resistance model for several variable system parameters such as agitation, particle size and sorbent loadings under transient batch conditions. The biosorption system operated at the optimal pH 4.5 with 20 mM Na-acetate buffer. The model reflected the experimental data well only at high sorbent and low metal concentrations, which generally represents batch sorber conditions. Under these conditions, film diffusion appeared to be the rate-controlling step in adsorption. However, at low sorbent concentrations the model could not represent the sorption system behavior due to the likely predominant influence of intraparticle diffusion.

Peat as an adsorbent for dyestuffs and metals in wastewater

The ability of peat to adsorb dyestuffs and metals from wastewaters was investigated. Equilibrium isotherms were determined in order to assess the maximum adsorption capacity of some basic and acidic dyestuffs, and metal ions onto peat, lignite and other adsorbents. Economic evaluations indicated that peat was a particularly attractive adsorbent. Kinetic studies for the adsorption of basic dyes onto peat were undertaken in agitated batch and fixed bed adsorbers. Mass transport models detailed elsewhere were tested and used to predict (a) the concentration decay curve for batch adsorption and (b) the breakthrough curves in fixed bed adsorption. The models tested were single-resistance models and included an estimation of the external mass transfer coefficients.