Spherical Diffusion Model of Interspecies Hydrogen Transfer in Steady-State Methanogenic Reactors

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2389-2392 ◽  
Author(s):  
D. P. Smith
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Diffusion Model ◽  
Hydrogen Concentration ◽  
Hydrogen Transfer ◽  
Solution Concentration ◽  
Bulk Solution ◽  
Transfer Resistance ◽  
Concentration Difference ◽  
Spherical Diffusion

A previously developed spherical diffusion model of interspecies molecular hydrogen transfer was applied to a mathematical model of ethanol and propionate methanogenesis in a dispersed-growth, continuously stirred tank reactor (CSTR). Steady-state methanogenesis at a 0.10 day−1 space velocity required a hydrogen concentration difference of 1.12 × 10−5 aim (8.4 × 10−12 moles/cm3) between the surface of the propionate organisms and the bulk solution. The total difference in hydrogen concentration between source organism and sink organism Ihydrogenotrophic methanogenstwas 2.1 × 10−5 atm (1.6 × 10−11 moles/cm3). Steep gradients in hydrogen concentration existed only at close proximity to the bacterial spheres, with hydrogen concentration approaching bulk solution concentration at distances greater than 10 microns. Small hydrogen gradients and the bulk solution concentration prevailed through the majority of the reactor aqueous volume. Overall, the incorporation of hydrogen mass transfer resistance into the mathematical model had only a slight effect on hydrogen partial pressure, organic substrate levels, and bacterial mass concentrations predicted by the steady-state solution.

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.

The interaction between stirring and osmosis. Part 1

1980 ◽  
Vol 101 (4) ◽  
pp. 843-861 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Steady State ◽  
Physiological Model ◽  
Solute Concentration ◽  
Standard Theory ◽  
Bulk Solution ◽  
Dimensionless Number ◽  
Governing Parameter ◽  
Concentration Difference ◽  
Permeable Membrane ◽  
Wide Range

When pure solvent is separated from a solution of non-zero concentration Cb by a semi-permeable membrane, permeable to solvent (water) but not to solute, water flows osmotically across the membrane towards the solution. Its velocity J is given by J = PΔC, where P is a constant and ΔC is the concentration difference across the membrane. Because the osmotic flow advects solute away from the membrane, ΔC is usually less than Cb, by a factor γ which depends on the thickness of and flow in a concentration boundary layer. In this paper the layer is analysed on the assumption that the stirring motions in the bulk solution, which counter the osmotic advection, can be represented as two-dimensional stagnation-point flow. The steady-state results are compared with those of the standard physiological model in which the layer has a given thickness δ and the osmotic advection is countered only by diffusion. It turns out that the standard theory, although mechanistically inadequate, accurately predicts the value of γ over a wide range of values of the governing parameter β = PCbδ/D (where D is the solute diffusivity) if δ is given by \[ \delta = 1.59\bigg(\frac{D}{\nu}\bigg)^{\frac{1}{3}}\bigg(\frac{\nu}{\alpha}\bigg)^{\frac{1}{2}}, \] where ν is the kinematic viscosity of the fluid and α is the stirring parameter. The final approach to the steady state is also analysed, and it is shown to be achieved in a time scale (D/ν)1/3/αk′ where k′ is a dimensionless number whose dependence on β is computed. Moreover, if β exceeds a certain critical value (≈ 10), the approach to the steady state is not monotonic but takes the form of a damped oscillation (in practice, however, β is unlikely to rise significantly above 1). The theory is extended to the case where the solute concentration is non-zero on both sides of the membrane and in that case it is shown that J is bounded as β → ∞.

scholarly journals Efficacy of a Phosphate-Charged Soil Material in Supplying Phosphate for Plant Growth in Soilless Root Media

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Young-Mi Oh ◽  
Paul V. Nelson ◽  
Dean L. Hesterberg ◽  
Carl E. Niedziela
Keyword(s):  
Plant Growth ◽  
Solution Concentration ◽  
Bulk Solution ◽  
P Deficiency ◽  
Soil Material ◽  
Hydrous Oxides ◽  
Acceptable Range ◽  
Root Media ◽  
Phosphate Fertilization ◽  
Phosphate Leaching

A soil material high in crystalline Fe hydrous oxides and noncrystalline Al hydrous oxides collected from the Bw horizon of a Hemcross soil containing allophane from the state of Oregon was charged with phosphate-P at rates of 0, 2.2, and 6.5 mg·g−1, added to a soilless root medium at 5% and 10% by volume, and evaluated for its potential to supply phosphate at a low, stable concentration during 14 weeks of tomato (Solanum esculentumL.) seedling growth. Incorporation of the soil material improved pH stability, whether it was charged with phosphate or not. Bulk solution phosphate-P concentrations in the range of 0.13 to 0.34 mg·dm−3were associated with P deficiency. The only treatment that sustained an adequate bulk solution concentration of phosphate-P above 0.34 mg·dm−3for the 14 weeks of testing contained 10% soil material charged with 6.5 mg·g−1P, but initial dissolved P concentrations were too high (>5 mg·g−1phosphate-P) from the standpoint of phosphate leaching. The treatment amended with 10% soil material charged with 2.2 mg·g−1P maintained phosphate-P within an acceptable range of 0.4 to 2.3 mg·dm−3for 48 d in a medium receiving no postplant phosphate fertilization.

scholarly journals Carbon cycle at steady state in an ocean. Simulation using a box diffusion model.

1990 ◽  
Vol 16 (6) ◽  
pp. 1195-1202
Author(s):  
Atsushi Inaba ◽  
Yuji Shindo ◽  
Hiroshi Komiyama
Keyword(s):  
Steady State ◽  
Carbon Cycle ◽  
Diffusion Model ◽  
Ocean Simulation

CC-CV charge protocol based on spherical diffusion model

2011 ◽  
Vol 18 (2) ◽  
pp. 319-322 ◽  
Author(s):  
Lian-xing Li ◽  
Xin-cun Tang ◽  
Yi Qu ◽  
Hong-tao Liu
Keyword(s):  
Diffusion Model ◽  
Spherical Diffusion

scholarly journals Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
M. V. Barbarossa ◽  
M. Polner ◽  
G. Röst
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Temporal Evolution ◽  
Disease Outbreaks ◽  
Population Level ◽  
Coupled System ◽  
Disease Outbreak ◽  
Periodic Disease ◽  
Evolution Of Immunity

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

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 The mathematical stability study for the system of the CoO(OH) – overoxidized polypyrrole composite synthesis in the presence of fluor ions

2016 ◽  
Vol 16 ◽  
pp. 13-17
Author(s):  
V. Tkach ◽  
S.C. De Oliveira ◽  
R. Ojani ◽  
P.I. Yagodynets ◽  
U. Páramo-García
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Bifurcation Analysis ◽  
Stability Theory ◽  
Stability Study ◽  
Linear Stability Theory ◽  
Monotonic Instability ◽  
Overoxidized Polypyrrole ◽  
Polypyrrole Composite ◽  
Steady State Stability

The potentiostatic synthesis of CoO(OH) – Overoxidized polypyrrole composite in the presence of fluor ions has been investigated mathematically. The corresponding mathematical model was described and analyzed by means of linear stability theory and bifurcation analysis. The steady-state stability requirements, like also oscillatory and monotonic instability conditions are derived.Mongolian Journal of Chemistry 16 (42), 2015, 13-17

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