scholarly journals A frequency quantum interpretation of the surface renewal model of mass transfer

2017 ◽  
Vol 4 (7) ◽  
pp. 170103 ◽  
Author(s):  
Chanchal Mondal ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Frequency Distribution ◽  
Age Distribution ◽  
Gas Absorption ◽  
Bulk Liquid ◽  
Gas Transfer ◽  
Transfer Resistance ◽  
Surface Renewal ◽  
Two Parameter

The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.

scholarly journals A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function

2018 ◽  
Vol 5 (5) ◽  
pp. 172423
Author(s):  
Isabelle R. Horvath ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Wind Speed ◽  
Age Distribution ◽  
Gas Absorption ◽  
Process Time ◽  
Unsteady State ◽  
Dissolved Gas ◽  
Transfer Coefficients ◽  
Wind Speeds

The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady-state conditions. For three different wind speeds used by researchers on air–water heat exchange on the Heidelberg Aeolotron, calculations reveal that the distribution has a sharp peak during the initial moments, but flattens out and acquires a bell-shaped character with process time, with the time taken to attain a steady-state profile being a strong and inverse function of wind speed. With increasing wind speed, the age distribution narrows significantly, its skewness decreases and its peak becomes larger. The mean eddy renewal time increases linearly with process time initially but approaches a final steady-state value asymptotically, which decreases dramatically with increased wind speed. Using the distribution to analyse the transient absorption of a gas into a large body of liquid, assuming negligible gas-side mass-transfer resistance, estimates are made of the gas-absorption and dissolved-gas transfer coefficients for oxygen absorption in water at 25°C for the three different wind speeds. Under unsteady-state conditions, these two coefficients show an inverse behaviour, indicating a heightened accumulation of dissolved gas in the surface elements, especially during the initial moments of absorption. However, the two mass-transfer coefficients start merging together as the steady state is approached. Theoretical predictions of the steady-state mass-transfer coefficient or transfer velocity are in fair agreement (average absolute error of prediction = 18.1%) with some experimental measurements of the same for the nitrous oxide–water system at 20°C that were made in the Heidelberg Aeolotron.

scholarly journals Impact of the Cathode Pt Loading on PEMFC Contamination by Several Airborne Contaminants

Molecules ◽  
2020 ◽  
Vol 25 (5) ◽  
pp. 1060 ◽  
Author(s):  
Jean St-Pierre ◽  
Yunfeng Zhai
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Proton Exchange Membrane ◽  
Cell Voltage ◽  
Proton Exchange ◽  
Catalyst Loading ◽  
Transfer Resistance ◽  
Voltage Loss ◽  
Program Costs ◽  
Exchange Membrane

Proton exchange membrane fuel cells (PEMFCs) with 0.1 and 0.4 mg Pt cm−2 cathode catalyst loadings were separately contaminated with seven organic species: Acetonitrile, acetylene, bromomethane, iso-propanol, methyl methacrylate, naphthalene, and propene. The lower catalyst loading led to larger cell voltage losses at the steady state. Three closely related electrical equivalent circuits were used to fit impedance spectra obtained before, during, and after contamination, which revealed that the cell voltage loss was due to higher kinetic and mass transfer resistances. A significant correlation was not found between the steady-state cell voltage loss and the sum of the kinetic and mass transfer resistance changes. Major increases in research program costs and efforts would be required to find a predictive correlation, which suggests a focus on contamination prevention and recovery measures rather than contamination mechanisms.

Steady State Performance of Activated Carbon Contactors

1991 ◽  
Vol 23 (7-9) ◽  
pp. 1677-1686 ◽  
Author(s):  
U. K. Traegner ◽  
M. T. Suidan
Keyword(s):  
Mathematical Model ◽  
Particle Size ◽  
Activated Carbon ◽  
Steady State ◽  
Surface Diffusion ◽  
Age Distribution ◽  
Carbon Surface ◽  
Transfer Resistance ◽  
Homogeneous Surface ◽  
Component Representation

A mathematical model for the steady state adsorption of pollutants from completely mixed activated carbon contactors is derived in this paper. In order to accurately describe these processes, a sludge age distribution is incorporated for the adsorbent. The resulting mathematical model is solvable analytically using the homogeneous surface diffusion model (HSDM) as a descriptor of intraparticle mass transfer resistance. Various examples are included in this paper to illustrate the use of this new derivation. Effects of particle size, particle size distribution of commercial carbon, surface diffusion coefficients, and solids mass flow rate, on the performance of the completely mixed adsorption system are studied in detail. Examples of multicomponent, competitive adsorption as well as an equivalent single component representation of a target component are discussed.

Capillary waves and air-sea gas transfer

1997 ◽  
Vol 332 ◽  
pp. 341-358 ◽  
Author(s):  
Andrew J. Szeri
Keyword(s):  
Boundary Layer ◽  
Chemical Reaction ◽  
Capillary Waves ◽  
Concentration Boundary Layer ◽  
Bulk Liquid ◽  
Gas Transfer ◽  
Dissolved Gas ◽  
Surface Renewal ◽  
Bulk Fluid ◽  
Concentration Boundary

The effects of capillary waves are considered on the transfer of gas into (or out of) solution through a gas-liquid interface. The bulk liquid is assumed to be otherwise motionless in the analysis of a preliminary problem; in this problem, a concentration boundary layer is developed as a consequence of a first-order chemical reaction that is assumed to deplete the dissolved gas in the liquid. The reaction rate determines the asymptotic thickness of the concentration boundary layer. It is shown that gas transfer through the concentration boundary layer is most enhanced by the presence of capillary waves when there is vigorous removal of dissolved gases by chemical reaction - i.e. when the reaction is fast and the boundary layer is thin. The results of this theory are then measured against gas transfer through a turbulent, sheared interface in the context of a surface renewal model. Here it is the exchange, from time to time, of fluid between the interface and the bulk that leads to the development of a thin concentration boundary layer when the bulk fluid is not saturated with dissolved gas. Capillary waves are shown to thicken the concentration boundary layer at the interface and to increase the rate of gas transfer.

Biofilm morphology in porous media, a study with microscopic and image techniques

1997 ◽  
Vol 36 (1) ◽  
pp. 1-9 ◽  
Author(s):  
John E. Paulsen ◽  
Eirik Oppen ◽  
Rune Bakke
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Practical Importance ◽  
Automated Image Analysis ◽  
Bulk Liquid ◽  
Transfer Resistance ◽  
Essential Information ◽  
Spider Web ◽  
Experimental Apparatus

Biofilm activity, behaviour and our ability to control biofilms depends to a large extent on mass transfer phenomena in the biofilm, at the biofilm-liquid interface and in the bulk liquid. Biofilms respond to changing mass transfer conditions by adjusting morphology, thereby optimising the exchange of matter with their surroundings. Observing biofilm morphology and mass transfer in relevant fluid dynamic conditions can therefore yield essential information to understand and model biofilm behaviour. Lack of such knowledge, as the case is with regards to biofilm behaviour in various porous media, such as sandstone reservoirs, limits our ability to predict biofilm effects. A transparent porous media replica of a sandstone reservoir with cybernetic image processing has been designed to study biofilm related transport phenomena in porous media. The porous medium was inoculated with a mixed bacterial culture and fed a sterile nutrient solution in a once through flow mode. The biofilm was observed by microscopy with automated image analysis. This novel integrated software/hardware cybernetic design allows near real-time, essentially simultaneous, surveillance of several critical sites in the porous network and facilitates selective recording and compilation of observations as a function of the biological activity at each particular site. Biofilm biomass distribution in space and time (morphology and morphological changes) are thereby recorded at a representative selection of sites in the porous structure. Local in-pore flow velocity measurements were carried out by measuring the velocity of suspended particulate matter such as detached cells or clusters of cells. The influence of biofilm morphology on convective mass transport could thereby be observed and recorded. This effect, on a meso scale, was also monitored by sensitive, automated pressure drop measurements across the porous medium cell. Important observations so far include: • Bioweb; the biofilm morphology in porous media is very different from the “classical film”, as it appears more like a spider web where each strand varies in size and shape. • The biofilm maintains a large surface area and minimal biofilm depth, thereby minimising mass transfer resistance between the fluid and the biofilm phase, under the conditions tested. • The biofilm influences the convective flow through pores both locally within pores and effecting the flow distribution between pores. Pores with high initial permeability thereby become less permeable, diverting more flow to less permeable zones in the porous matrix. Large variations in this picture were observed, demonstrating the need for a sophisticated experimental apparatus with high sampling capacity to investigate such an intricate system. The observed biofilm behaviour in porous media has important theoretical and practical implications. Flow diversion and permeability effects are of immediate practical importance, improving the prospects for biological treatment of reservoirs. The information obtained in this study will be applied in mathematical simulations of ground water reservoirs, bioremediation and biological enhanced oil recovery.

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