scholarly journals Modeling of simultaneous ultra filtration and diafiltration with real flux

2005 ◽  
Vol 59 (3-4) ◽  
pp. 66-72 ◽  
Author(s):  
Hela Tokos ◽  
Zoltan Zavargo ◽  
Mirjana Djuric
Keyword(s):  
Mathematical Model ◽  
Time Dependence ◽  
Solute Concentration ◽  
High Concentration ◽  
Constant Flux ◽  
Variable Volume ◽  
Rejection Coefficient ◽  
Ultra Filtration ◽  
Variable Flux

A mathematical model of diafiltration with variable volume is presented in this study. The characteristics of the process were examined, both with constant flux and variable flux. In the case of variable flux, the equations for the flux were taken from the literature, based on different theories. The time dependence of the macro solute concentration, the amount of out-wash liquid, the out-wash degree of the micro solute were studied. The results show that the accomplishment of a high concentration of macro solutes, required more time and out-wash liquid. In order to remove small amounts of micro solutes larger amounts of out-wash liquid must be used. For high degrees of out-washing, the velocity of the process increases and the amount of out-wash liquid decreases. It was observed that the rejection coefficient decreased with macro solute penetration through the membrane causing decrease of the process velocity.

scholarly journals Spreading of chemical substance after its accidental spillage onto the soil surface under unsaturated conditions and variable porosity

2019 ◽  
pp. 41-44
Author(s):  
Olena Kozhushko ◽  
Petro Martyniuk
Keyword(s):  
Mathematical Model ◽  
Soil Moisture ◽  
Soil Profile ◽  
Moisture Transport ◽  
Soil Surface ◽  
Chemical Substance ◽  
High Concentration ◽  
Solute Transfer ◽  
Variable Porosity ◽  
The One

In this paper we study a mathematical model of soil moisture transport with variable porosity. The problem is set for the case of highly concentrated solute spilled onto soil surface. We investigate the way solute transfer, adsorption of contaminant by soil particles and variable porosity influence infiltration of solute into the soil profile. For that purpose, two models are used: a classical one and the one with consideration of mentioned factors. By comparing the results of both models, we established that high concentration of solute causes moisture transport to transpire more slowly, and the pollutant to remain on the soil surface for longer time. Numerical results indicate that porosity can vary considerably under the conditions of intensive contamination with salts.

Modeling the Effects of Mixed Flowing Gas (MFG) Corrosion and Stress Relaxation on Contact Interface Resistance

1993 ◽  
Vol 115 (4) ◽  
pp. 404-409 ◽  
Author(s):  
Shrikar Bhagath ◽  
Michael G. Pecht
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Stress Relaxation ◽  
Contact Resistance ◽  
Time Dependence ◽  
Normal Force ◽  
Operating Temperature ◽  
Contact Interface ◽  
Time Stress ◽  
Over Time

This paper presents the development of an initial, “first-cut”, mathematical model for the prediction of electrical interface reliability trends. The model pertains to gold plated contacts subject to loss of normal force and environmental corrosion with time. Stress relaxation over time and temperature in the base metal of the contact is accounted for. Utilizing the results of Mixed Flowing Gas (MFG) tests, the model can be used to estimate the statistical contact resistance at a particular load (normal force), aging and operating temperature in the class II and III environments. An attempt is made to correlate experimental data with the classical Holm’s equation and to introduce time dependence into the equation. Further work is proposed to correlate results with experimental connector performance data.

Understanding Channel Segregates in Numerical Models of Alloy Solidification: A Case of Converge First and Ask Questions Later

2014 ◽  
Vol 790-791 ◽  
pp. 73-78 ◽  
Author(s):  
Igor Vušanović ◽  
Vaughan R. Voller
Keyword(s):  
Numerical Models ◽  
Solidification Rate ◽  
Grid Cell ◽  
Solidification Process ◽  
Solute Concentration ◽  
Heat Transfer Fluid ◽  
Mushy Region ◽  
High Concentration ◽  
Flow Paths ◽  
Grid Convergence

In static castings of multi-component alloys, visually observable bands of channels, with high solute concentration, can form in the final solidified product. The phenomenological explanation for these formations is that perturbations during the solidification process lead to preferred flow paths in the solid-liquid mushy region. Once these flow paths are initiated, the higher solute liquid that flows in them suppresses the solidification rate and thus provides a mechanism through which the preferred paths can evolve into high concentration channels. Models of solidification that couple heat transfer, fluid and flow and mass transport appear able to predict the formation of these channels. In many cases, however, the formation of these numerical channels is highly dependent on the nature of the numerical calculation. In particular, geometric attributes of the channels is a strong function of the size of the computational grid and in some cases the particular method (code) used. In this work, after discussing what might drive the observed discrepancies in predictions, a grid convergence study is undertaken. This study shows that for the case of a side cooled solidification of a binary (Al-4.5wt%Cu) in a square (40mm x 40mm) domain, it is possible to approach grid converged results of the solution of the standard mixture model for macrosegregation. Achieving this level of convergence requires the use of an explicit time stepping scheme to couple the thermal and solute fields along with a Carman-Kozeny permeability and lever rule microsegregation models. The results indicate that to reach grid convergence the size of a grid cell has to be on the order ~0.25-0.5 mm.

Electrochemical Model for Ionic Liquid Electrolytes in Lithium Batteries

2015 ◽  
Author(s):  
Kisoo Yoo ◽  
Prashanta Dutta ◽  
Soumik Banerjee
Keyword(s):  
Mathematical Model ◽  
Ionic Liquid ◽  
Lithium Ion Battery ◽  
Current Density ◽  
Lithium Batteries ◽  
Specific Capacity ◽  
Lithium Ion ◽  
High Concentration ◽  
Load Current ◽  
Liquid Electrolytes

A mathematical model is developed for transport of ionic components to study the performance of ionic liquid based lithium batteries. The mathematical model is based on a univalent ternary electrolyte frequently encountered in ionic liquid electrolytes used for lithium batteries. Owing to the very high concentration of components in ionic liquid, the transport of lithium ions are described by the mutual diffusion phenomena using Maxwell-Stefan diffusivity. The model is used to study a lithium ion battery where the cations and anions of ionic liquid are mppy+ and TFSI-. The electric performance results predicted by the model are in good agreement with experimental data. We also studied the effect of load current density on the performance of lithium ion battery using this model. Numerical results indicate that low rate of lithium ion transport causes lithium depleted zone in the porous cathode regions as the load current density increases. This lithium depleted region is responsible for lower specific capacity in lithium-ion cells. The model presented in this study can be used for optimum design of ionic liquid electrolytes for lithium-ion and lithium-air batteries.

Mathematical model of variable volume diafiltration with time dependent water adding

2009 ◽  
Vol 26 (7) ◽  
pp. 857-867 ◽  
Author(s):  
A. Takači ◽  
T. Žikić‐Došenović ◽  
Z. Zavargó
Keyword(s):  
Mathematical Model ◽  
Time Dependent ◽  
Variable Volume

scholarly journals Mathematical Modeling of the Pandemic Peak

2022 ◽  
Vol 10 (E) ◽  
pp. 22-26
Author(s):  
Nadezhda Cherkunova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Differential Equations ◽  
Time Dependence

BACKGROUND:  The article examines the history and statistics of the pandemic spread. AIM: The study aimed to  develop a mathematical model reflecting the time dependence of the parameters characterizing the spread of the pandemic. MATERIALS AND METHODS: Differential equations were used to study the spread of the pandemic. RESULTS:  The case, where the coefficients of morbidity and recovery are different is considered. The patterns of change in the number of people susceptible to the disease and the number of infectious patients are revealed as a function of time. Using the developed model, the peak of the pandemic is found, i.e., the time at which the number of infectious patients will be the maximum.

Diffusion of Fluorine at High Concentration in Silicon: Experiments and Models

2004 ◽  
Vol 810 ◽  
Author(s):  
Robert R. Robison ◽  
Antonio F. Saavedra ◽  
Mark E. Law
Keyword(s):  
Time Dependence ◽  
Amorphous Silicon ◽  
Depth Profiling ◽  
Amorphous Region ◽  
High Concentration ◽  
Conventional Furnace

ABSTRACTWe have developed a model for high concentration fluorine diffusion and fluorine diffusion in amorphous silicon. In this context, we define high concentration fluorine to mean fluorine doses above the threshold of amorphization for implantation into silicon, which is approximately 1×1015/cm2 dose. We pre-amorphized with silicon to create a continuous amorphous region, and samples were subsequently implanted with the fluorine conditions of 16keV at 2×1015cm−2 dose, 30keV at 2×1014 cm−2 dose, or 16keV at 8×1015cm−2 dose. Samples were annealed by either conventional furnace or RTA with an N2 ambient for various times at temperatures of 550-750 °C. SIMS was used for depth profiling, and TEM images were also taken of the samples to check for defects and amorphous depth. We then created the model for the data by extending the fluorine model presented in our previous work, and it models the profile motion and the time dependence well. The model is also still capable of describing our previous work and fits it very well.

Internal Flows in Microscopic Polymer Solution Droplets Evaporating on Flat Surfaces

2010 ◽  
Author(s):  
Shohei Yasumatsu ◽  
Narumi Nanri ◽  
Yu Yoshitake ◽  
Koichi Nakaso ◽  
Jun Fukai
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Free Surface ◽  
Polymer Solution ◽  
Local Minimum ◽  
Flow Direction ◽  
Solute Concentration ◽  
Internal Flows ◽  
Initial Solute ◽  
The Mathematical Model

To control the formation process of polymer thin films from polymer solution droplets using inkjet printings, internal flows of the droplets on substrates are studied. In our previous study [1], internal flow of polymer solution droplets receding on a lyophobic surface was experimentally visualized. It was found that the direction of the circulation flow in the droplet depended on the solvent and the initial solute concentration. In particular, the flow direction of polystyrene-anisole solution was reversed as the initial solute concentration increased. In this study, to clarify this reason, the conservation equations of momentum, energy and mass on two-dimensional cylindrical coordinate are numerically solved using a finite element method. The mathematical model considers the free convections derived by the dependencies of the density and surface tension on the solute concentration. As a result, the dependences of the calculated velocities on the initial solute concentration agree qualitatively with the experiments. The mathematical model predicts that double circulation flows appear after a single flow develops at high initial solute concentrations, while double circulations do not develop at low concentrations. It is concluded that the difference between the flow directions investigated experimentally is due to such a change of the flow structure. The distribution of the surface tension on the free surface is also discussed. When a local minimum of the surface tension appears on the free surface, the double circulations develop. According to the result for a low contact angle, the local minimum point shifts toward the axis of symmetry with a lapse of time, and finally erases the double circulations.

scholarly journals Modeling the Kinetics of Potassium Diffusion in Estima Potato under Different Leaching Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
David Adu-Poku ◽  
Selina A. Saah ◽  
Jacob K. Agbenorhevi
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Effective Diffusion ◽  
Solute Concentration ◽  
Operating Conditions ◽  
Optimum Operating ◽  
Gelatinization Temperature ◽  
Satisfactory Description ◽  
Mass Transfers ◽  
Kinetics Of

The diffusion of potassium in potato (Solanum tuberosum) at different leaching conditions was investigated. Two modes of pretreatment of potato samples (cubes and spheres) by preheating to 80°C and leaching at temperatures of 20-80°C were performed using a temperature- and agitation-controlled batch extractor. A Fickian model incorporating the effective diffusion coefficient ( D eff ), partition coefficient ( K ) between the solute concentration in the potato and medium, and mass transfer coefficient ( kl ) was developed to simulate and predict the fraction of potassium leached from the potato at any temperature. Results showed significant reduction in activation energies from 92 to 25.02 kJ/mol for cubes and from 75.02 to 13.40 kJ/mol for spheres culminating in higher extraction rates when samples were preheated to 80°C. The D eff , K , and kl values obtained were in the range of 0.02 − 7.33 × 10 − 9     m 2 / s , 0.63 − 8.00 × 10 − 2 , and 0.01333.00 × 10 − 4     m / s , respectively. The kinetic parameters showed a change in slope or discontinuity in the gelatinization temperature range as a function of temperature, an indication of a change in the diffusional matrix. The optimum operating conditions were 80°C preheating and leaching at temperatures up to 50°C. The proposed mathematical model offered a satisfactory description of both dynamic and equilibrium mass transfers of potassium by adequately predicting the fraction of potassium from potato cubes and spheres. The present findings could be useful in the pretreatment of potato for renal patients.

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