Second-order slip condition considering Langmuir isothermal adsorption for rarefied gas microflows

Author(s):  
Nam T.P. Le ◽  
Thoai N. Tran ◽  
Minh H. Dang
2021 ◽  
Author(s):  
Nam T. P. Le ◽  
Bang V. Dinh ◽  
Quang L. Dang ◽  
Anh V. Dang ◽  
Y. Q. Nguyen

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Baibhab Ray ◽  
Franz Durst ◽  
Subhashis Ray

Abstract In this investigation, Lfd* and Δp in the entrance region of circular and parallel plate microchannels have been determined for 10−2≤Re≤104 and 10−4≤Kn≤0.2, employing the second-order velocity slip condition at the wall with C1=1 and 0≤C2≤0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and Kfd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both Lfd* and Kfd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.


2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jun Zhang ◽  
Ren-jian Deng ◽  
Bo-zhi Ren ◽  
Baolin Hou ◽  
Andrew Hursthouse

Abstract A novel adsorbent (Fe3O4/HCO) was prepared via co-precipitation from a mix of ferriferrous oxide and a Ce-rich waste industrial sludge recovered from an optical polishing activity. The effect of system parameters including reaction time, pH, dose, temperature as well as initial concentration on the adsorption of Sb(III) were investigated by sequential batch tests. The Sb(III)/Fe3O4/HCO system quickly reached adsorption equilibrium within 2 h, was effective over a wide pH (3–7) and demonstrated excellent removal at a 60 mg/L Sb(III) concentration. Three isothermal adsorption models were assessed to describe the equilibrium data for Sb(III) with Fe3O4/HCO. Compared to the Freundlich and dubinin-radushkevich, the Langmuir isotherm model showed the best fit, with a maximum adsorption capacity of 22.853 mg/g, which exceeds many comparable absorbents. Four kinetic models, Pseudo-first-order, Pseudo-second-order, Elovich and Intra-particle, were used to fit the adsorption process. The analysis showed that the mechanism was pseudo-second-order and chemical adsorption played a dominant role in the adsorption of Sb(III) by Fe3O4/HCO (correlation coefficient R2 = 0.993). Thermodynamic calculations suggest that adsorption of Sb(III) ions was endothermic, spontaneous and a thermodynamically feasible process. The mechanism of the adsorption of Sb(III) on Fe3O4/HCO could be described by the synergistic adsorption of Sb (III) on Fe3O4, FeCe2O4 and hydrous ceric oxide. The Fe3O4/HCO sorbent appears to be an efficient and environment-friendly material for the removal of Sb(III) from wastewater.


2012 ◽  
Vol 16 (5) ◽  
pp. 1506-1509 ◽  
Author(s):  
Ying Mei ◽  
Xiao-Hua Yang ◽  
Ya-Nan Guo ◽  
Jun He ◽  
Rong Jiang ◽  
...  

The objective of this study is to explore the mechanism of phosphorus adsorption in the bioretention media. The phosphorus adsorption characteristics of four media of bioretention are studied by four isothermal adsorption experiments. The result indicate that the maximal adsorption capacity (qm) of phosphorus of the four bioretention media are found to be media I (0.3365 mg/g), media II (0.3302 mg/g), media III (0.2751 mg/g) and media IV 0.8435 mg/g), respectively. The negative values of Gibbs free energy of phosphorus indicate that each of the phosphorus adsorption process by the four bioretention media is a spontaneous process. The mean sorption energies obtained from DR isotherm were 0.0758, 0.0772, 0.0803 and 0.0632 kJ/mol respectively, which indicate the physical nature of the adsorbate/adsorbent interactions. Two kinetic models including pseudo first-order and pseudo second-order equation were selected to follow the adsorption process. The results showed that the adsorption of phosphorus with the four types of bioretention media could be described by the pseudo second-order equation. The media IV was the better media of bioretention with high phosphorus removal capacity.


2000 ◽  
Vol 65 (12) ◽  
pp. 939-961 ◽  
Author(s):  
Menka Petkovska

The concept of higher order frequency response functions (FRFs) is used for the analysis of non-linear adsorption kinetics on a particle scale, for the case of non-isothermal micropore diffusion with variable diffusivity. Six series of FRFs are defined for the general non-isothermal case. A non-linerar mathematical model is postulated and the first and second order FRFs derived and simulated. A variable diffusivity influences the shapes of the second order FRFs relating the sorbate concentration in the solid phase and t he gas pressure significantly, but they still keep their characteristics which can be used for discrimination of this from other kinetic mechanisms. It is also shown that first and second order particle FRFs offter sufficient information for an easy and fast estimation of all model parameters, including those defining the system non-linearity.


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