Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
THE ENERGY MINIMIZATION, FOR THE STUDENTS OF M.PHARM, B.PHARM AND OTHERS USEFUL FOR ACADEMIC TOO. THE PRESENT DATA IS MOST USEFUL FOR PHARMACY PURPOSE.
Molecular Mechanics in Molecular ModelingAkshay Kank
In this slide you learn about the computational chemistry and its role in designing a drug molecule. Also learn concept about the molecular mechanics and its application to Computer Aided Drug Design. difference between the Quantum mechanics and Molecular Mechanics.
THE ENERGY MINIMIZATION, FOR THE STUDENTS OF M.PHARM, B.PHARM AND OTHERS USEFUL FOR ACADEMIC TOO. THE PRESENT DATA IS MOST USEFUL FOR PHARMACY PURPOSE.
Molecular Mechanics in Molecular ModelingAkshay Kank
In this slide you learn about the computational chemistry and its role in designing a drug molecule. Also learn concept about the molecular mechanics and its application to Computer Aided Drug Design. difference between the Quantum mechanics and Molecular Mechanics.
This is a Powerpoint for basic understanding regarding Molecular dynamics and NAMD simulation to providing basic information, schematic representation, to understanding the mechanism or process of molecular dynamics ( MD), and NAMD simulation brief discussion.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This is a Powerpoint for basic understanding regarding Molecular dynamics and NAMD simulation to providing basic information, schematic representation, to understanding the mechanism or process of molecular dynamics ( MD), and NAMD simulation brief discussion.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Dynamic Simulation of a Hybrid Solar and Ocean Thermal Energy Conversion SystemIJRES Journal
Ocean thermal energy conversion (OTEC) is à system in which electricity is produced using small temperature difference of warm surface water and deep cold water in oceans. This paper analyzes the dynamic stability and performance simulation results of a solar and ocean thermal energy conversion (SOTEC) system connected to a power grid through undersea cables. In SOTEC, the temperature of warm sea water was boosted by using a typical low-cost solar thermal collector. The complete system model is established from the dynamics of each subsystem and their interconnections. Specifically, we examine stability and performance of the power system against such disturbance conditions as slow variations of solar radiation and severe three-phase short-circuit fault at the power grid. Simulation results indicate that the design of a power system stabilizer can improve the damping of power system under various disturbance conditions.
Modelling design and control of an electromechanical mass lifting system usin...Mustefa Jibril
In this paper, an electromechanical mass lifter system is designed, analyzed and compare using optimal
and robust control theories. LQR and μ -synthesis controllers are used to improve the lift displacement by
comparison method for tracking the desired step and sinusoidal wave signals input. Finally, the comparison
simulation result prove the effectiveness of the electromechanical mass lifter system with μ -synthesis controller for
improving the rise time, percentage overshoot, settling time and peak value of tracking the desired step displacement
signal and improving the peak value for tracking the desired sinusoidal displacement signal with a good
performance.
Computer simulations of realistic ion channel structures have always been challenging and
a subject of rigorous study. Simulations based on continuum electrostatics have proven to
be computationally cheap and reasonably accurate in predicting a channel’s behavior. In
this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for
KcsA channel and study its steady-state response. SILVACO is a well-established program,
typically used by electrical engineers to simulate the process flow and electrical characteristics
of solid-state devices. By employing this simulation program, we have presented an
alternative computing platform for performing ion channel simulations, besides the known
methods of writing codes in programming languages. With the ease of varying the different
parameters in the channel’s vestibule and the ability of incorporating surface charges,
we have shown the wide-ranging possibilities of using a device simulator for ion channel
simulations. Our simulated results closely agree with the experimental data, validating our
model.
The Effect of High Zeta Potentials on the Flow Hydrodynamics in Parallel-Plat...CSCJournals
This paper investigates the effect of the EDL at the solid-liquid interface on the liquid flow through a micro-channel formed by two parallel plates. The complete Poisson-Boltzmann equation (without the frequently used linear approximation) was solved analytically in order to determine the EDL field near the solid-liquid interface. The momentum equation was solved analytically taking into consideration the electrical body force resulting from the EDL field. Effects of the channel size and the strength of the zeta-potential on the electrostatic potential, the streaming potential, the velocity profile, the volume flow rate, and the apparent viscosity are presented and discussed. Results of the present analysis, which are based on the complete Poisson-Boltzmann equation, are compared with a simplified analysis that used a linear approximation of the Poisson-Boltzmann equation.
A series of siloxane based side chain liquid crystal polymers have been prepared with asystematic variation in spacer length. Nematic liquid crystal polymers possess large optical nonlinearities owing to their large refractive index anisotropy coupled with the collective molecular reorientation. All the polymer exhibited a smectic phase, for which the Nematic -isotropic transition temperature increased as the spacer length increased. Electro-optic measurements are used to evaluate the threshold voltages for this series of polymers. It is found that with increasing spacer length (n) of polymer the threshold voltage is lowered and that the variation of the threshold voltage arises from changes to the intrinsic curvature elasticity rather than to differences in orientational order. A simple model is used to indicate the origion of the effects observed which appear to arise from the constraints offered by the coupling of the mesogenic units to the polymer backbone.
modeling and characterization of mems electrostatic energy harvesterINFOGAIN PUBLICATION
In low-power wireless electronic devices, Energy harvesting generators have received increasing research interest in recent years. This paper describes the design and analysis of electrostatic transduction based MEMS energy harvester. Due to the benefit of a folded beam configuration that can be displace large dimensions and compliant in desired direction and stiffer in orthogonal direction. Since, large displacement of proof mass of energy harvester renders the enhance performance. Hence, the folded beam configuration of harvest has been modeled and designed and optimized the dimension of geometry. FEM simulations using COMSOL were conducted to evaluate the natural frequency and mode shape of the system and compared results with that of analytically calculated values. Spice circuit of harvester has been modeled and performed simulation to evaluate the output power of the harvester in LTSPICE. Parameter analysis was conducted to determine the optimal load and optimal output power.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
A Novel Method for Prevention of Bandwidth Distributed Denial of Service AttacksIJERD Editor
Distributed Denial of Service (DDoS) Attacks became a massive threat to the Internet. Traditional
Architecture of internet is vulnerable to the attacks like DDoS. Attacker primarily acquire his army of Zombies,
then that army will be instructed by the Attacker that when to start an attack and on whom the attack should be
done. In this paper, different techniques which are used to perform DDoS Attacks, Tools that were used to
perform Attacks and Countermeasures in order to detect the attackers and eliminate the Bandwidth Distributed
Denial of Service attacks (B-DDoS) are reviewed. DDoS Attacks were done by using various Flooding
techniques which are used in DDoS attack.
The main purpose of this paper is to design an architecture which can reduce the Bandwidth
Distributed Denial of service Attack and make the victim site or server available for the normal users by
eliminating the zombie machines. Our Primary focus of this paper is to dispute how normal machines are
turning into zombies (Bots), how attack is been initiated, DDoS attack procedure and how an organization can
save their server from being a DDoS victim. In order to present this we implemented a simulated environment
with Cisco switches, Routers, Firewall, some virtual machines and some Attack tools to display a real DDoS
attack. By using Time scheduling, Resource Limiting, System log, Access Control List and some Modular
policy Framework we stopped the attack and identified the Attacker (Bot) machines
Hearing loss is one of the most common human impairments. It is estimated that by year 2015 more
than 700 million people will suffer mild deafness. Most can be helped by hearing aid devices depending on the
severity of their hearing loss. This paper describes the implementation and characterization details of a dual
channel transmitter front end (TFE) for digital hearing aid (DHA) applications that use novel micro
electromechanical- systems (MEMS) audio transducers and ultra-low power-scalable analog-to-digital
converters (ADCs), which enable a very-low form factor, energy-efficient implementation for next-generation
DHA. The contribution of the design is the implementation of the dual channel MEMS microphones and powerscalable
ADC system.
Influence of tensile behaviour of slab on the structural Behaviour of shear c...IJERD Editor
-A composite beam is composed of a steel beam and a slab connected by means of shear connectors
like studs installed on the top flange of the steel beam to form a structure behaving monolithically. This study
analyzes the effects of the tensile behavior of the slab on the structural behavior of the shear connection like slip
stiffness and maximum shear force in composite beams subjected to hogging moment. The results show that the
shear studs located in the crack-concentration zones due to large hogging moments sustain significantly smaller
shear force and slip stiffness than the other zones. Moreover, the reduction of the slip stiffness in the shear
connection appears also to be closely related to the change in the tensile strain of rebar according to the increase
of the load. Further experimental and analytical studies shall be conducted considering variables such as the
reinforcement ratio and the arrangement of shear connectors to achieve efficient design of the shear connection
in composite beams subjected to hogging moment.
Gold prospecting using Remote Sensing ‘A case study of Sudan’IJERD Editor
Gold has been extracted from northeast Africa for more than 5000 years, and this may be the first
place where the metal was extracted. The Arabian-Nubian Shield (ANS) is an exposure of Precambrian
crystalline rocks on the flanks of the Red Sea. The crystalline rocks are mostly Neoproterozoic in age. ANS
includes the nations of Israel, Jordan. Egypt, Saudi Arabia, Sudan, Eritrea, Ethiopia, Yemen, and Somalia.
Arabian Nubian Shield Consists of juvenile continental crest that formed between 900 550 Ma, when intra
oceanic arc welded together along ophiolite decorated arc. Primary Au mineralization probably developed in
association with the growth of intra oceanic arc and evolution of back arc. Multiple episodes of deformation
have obscured the primary metallogenic setting, but at least some of the deposits preserve evidence that they
originate as sea floor massive sulphide deposits.
The Red Sea Hills Region is a vast span of rugged, harsh and inhospitable sector of the Earth with
inimical moon-like terrain, nevertheless since ancient times it is famed to be an abode of gold and was a major
source of wealth for the Pharaohs of ancient Egypt. The Pharaohs old workings have been periodically
rediscovered through time. Recent endeavours by the Geological Research Authority of Sudan led to the
discovery of a score of occurrences with gold and massive sulphide mineralizations. In the nineties of the
previous century the Geological Research Authority of Sudan (GRAS) in cooperation with BRGM utilized
satellite data of Landsat TM using spectral ratio technique to map possible mineralized zones in the Red Sea
Hills of Sudan. The outcome of the study mapped a gossan type gold mineralization. Band ratio technique was
applied to Arbaat area and a signature of alteration zone was detected. The alteration zones are commonly
associated with mineralization. The alteration zones are commonly associated with mineralization. A filed check
confirmed the existence of stock work of gold bearing quartz in the alteration zone. Another type of gold
mineralization that was discovered using remote sensing is the gold associated with metachert in the Atmur
Desert.
Reducing Corrosion Rate by Welding DesignIJERD Editor
The paper addresses the importance of welding design to prevent corrosion at steel. Welding is
used to join pipe, profiles at bridges, spindle, and a lot more part of engineering construction. The
problems happened associated with welding are common issues in these fields, especially corrosion.
Corrosion can be reduced with many methods, they are painting, controlling humidity, and also good
welding design. In the research, it can be found that reducing residual stress on the welding can be
solved in corrosion rate reduction problem.
Preheating on 500oC and 600oC give better condition to reduce corosion rate than condition after
preheating 400oC. For all welding groove type, material with 500oC and 600oC preheating after 14 days
corrosion test is 0,5%-0,69% lost. Material with 400oC preheating after 14 days corrosion test is 0,57%-0,76%
lost.
Welding groove also influence corrosion rate. X and V type welding groove give better condition to reduce
corrosion rate than use 1/2V and 1/2 X welding groove. After 14 days corrosion test, the samples with
X welding groove type is 0,5%-0,57% lost. The samples with V welding groove after 14 days corrosion test is
0,51%-0,59% lost. The samples with 1/2V and 1/2X welding groove after 14 days corrosion test is 0,58%-
0,71% lost.
Router 1X3 – RTL Design and VerificationIJERD Editor
Routing is the process of moving a packet of data from source to destination and enables messages
to pass from one computer to another and eventually reach the target machine. A router is a networking device
that forwards data packets between computer networks. It is connected to two or more data lines from different
networks (as opposed to a network switch, which connects data lines from one single network). This paper,
mainly emphasizes upon the study of router device, it‟s top level architecture, and how various sub-modules of
router i.e. Register, FIFO, FSM and Synchronizer are synthesized, and simulated and finally connected to its top
module.
Active Power Exchange in Distributed Power-Flow Controller (DPFC) At Third Ha...IJERD Editor
This paper presents a component within the flexible ac-transmission system (FACTS) family, called
distributed power-flow controller (DPFC). The DPFC is derived from the unified power-flow controller (UPFC)
with an eliminated common dc link. The DPFC has the same control capabilities as the UPFC, which comprise
the adjustment of the line impedance, the transmission angle, and the bus voltage. The active power exchange
between the shunt and series converters, which is through the common dc link in the UPFC, is now through the
transmission lines at the third-harmonic frequency. DPFC multiple small-size single-phase converters which
reduces the cost of equipment, no voltage isolation between phases, increases redundancy and there by
reliability increases. The principle and analysis of the DPFC are presented in this paper and the corresponding
simulation results that are carried out on a scaled prototype are also shown.
Mitigation of Voltage Sag/Swell with Fuzzy Control Reduced Rating DVRIJERD Editor
Power quality has been an issue that is becoming increasingly pivotal in industrial electricity
consumers point of view in recent times. Modern industries employ Sensitive power electronic equipments,
control devices and non-linear loads as part of automated processes to increase energy efficiency and
productivity. Voltage disturbances are the most common power quality problem due to this the use of a large
numbers of sophisticated and sensitive electronic equipment in industrial systems is increased. This paper
discusses the design and simulation of dynamic voltage restorer for improvement of power quality and
reduce the harmonics distortion of sensitive loads. Power quality problem is occurring at non-standard
voltage, current and frequency. Electronic devices are very sensitive loads. In power system voltage sag,
swell, flicker and harmonics are some of the problem to the sensitive load. The compensation capability
of a DVR depends primarily on the maximum voltage injection ability and the amount of stored
energy available within the restorer. This device is connected in series with the distribution feeder at
medium voltage. A fuzzy logic control is used to produce the gate pulses for control circuit of DVR and the
circuit is simulated by using MATLAB/SIMULINK software.
Study on the Fused Deposition Modelling In Additive ManufacturingIJERD Editor
Additive manufacturing process, also popularly known as 3-D printing, is a process where a product
is created in a succession of layers. It is based on a novel materials incremental manufacturing philosophy.
Unlike conventional manufacturing processes where material is removed from a given work price to derive the
final shape of a product, 3-D printing develops the product from scratch thus obviating the necessity to cut away
materials. This prevents wastage of raw materials. Commonly used raw materials for the process are ABS
plastic, PLA and nylon. Recently the use of gold, bronze and wood has also been implemented. The complexity
factor of this process is 0% as in any object of any shape and size can be manufactured.
Spyware triggering system by particular string valueIJERD Editor
This computer programme can be used for good and bad purpose in hacking or in any general
purpose. We can say it is next step for hacking techniques such as keylogger and spyware. Once in this system if
user or hacker store particular string as a input after that software continually compare typing activity of user
with that stored string and if it is match then launch spyware programme.
A Blind Steganalysis on JPEG Gray Level Image Based on Statistical Features a...IJERD Editor
This paper presents a blind steganalysis technique to effectively attack the JPEG steganographic
schemes i.e. Jsteg, F5, Outguess and DWT Based. The proposed method exploits the correlations between
block-DCTcoefficients from intra-block and inter-block relation and the statistical moments of characteristic
functions of the test image is selected as features. The features are extracted from the BDCT JPEG 2-array.
Support Vector Machine with cross-validation is implemented for the classification.The proposed scheme gives
improved outcome in attacking.
Secure Image Transmission for Cloud Storage System Using Hybrid SchemeIJERD Editor
- Data over the cloud is transferred or transmitted between servers and users. Privacy of that
data is very important as it belongs to personal information. If data get hacked by the hacker, can be
used to defame a person’s social data. Sometimes delay are held during data transmission. i.e. Mobile
communication, bandwidth is low. Hence compression algorithms are proposed for fast and efficient
transmission, encryption is used for security purposes and blurring is used by providing additional
layers of security. These algorithms are hybridized for having a robust and efficient security and
transmission over cloud storage system.
Application of Buckley-Leverett Equation in Modeling the Radius of Invasion i...IJERD Editor
A thorough review of existing literature indicates that the Buckley-Leverett equation only analyzes
waterflood practices directly without any adjustments on real reservoir scenarios. By doing so, quite a number
of errors are introduced into these analyses. Also, for most waterflood scenarios, a radial investigation is more
appropriate than a simplified linear system. This study investigates the adoption of the Buckley-Leverett
equation to estimate the radius invasion of the displacing fluid during waterflooding. The model is also adopted
for a Microbial flood and a comparative analysis is conducted for both waterflooding and microbial flooding.
Results shown from the analysis doesn’t only records a success in determining the radial distance of the leading
edge of water during the flooding process, but also gives a clearer understanding of the applicability of
microbes to enhance oil production through in-situ production of bio-products like bio surfactans, biogenic
gases, bio acids etc.
Gesture Gaming on the World Wide Web Using an Ordinary Web CameraIJERD Editor
- Gesture gaming is a method by which users having a laptop/pc/x-box play games using natural or
bodily gestures. This paper presents a way of playing free flash games on the internet using an ordinary webcam
with the help of open source technologies. Emphasis in human activity recognition is given on the pose
estimation and the consistency in the pose of the player. These are estimated with the help of an ordinary web
camera having different resolutions from VGA to 20mps. Our work involved giving a 10 second documentary to
the user on how to play a particular game using gestures and what are the various kinds of gestures that can be
performed in front of the system. The initial inputs of the RGB values for the gesture component is obtained by
instructing the user to place his component in a red box in about 10 seconds after the short documentary before
the game is finished. Later the system opens the concerned game on the internet on popular flash game sites like
miniclip, games arcade, GameStop etc and loads the game clicking at various places and brings the state to a
place where the user is to perform only gestures to start playing the game. At any point of time the user can call
off the game by hitting the esc key and the program will release all of the controls and return to the desktop. It
was noted that the results obtained using an ordinary webcam matched that of the Kinect and the users could
relive the gaming experience of the free flash games on the net. Therefore effective in game advertising could
also be achieved thus resulting in a disruptive growth to the advertising firms.
Hardware Analysis of Resonant Frequency Converter Using Isolated Circuits And...IJERD Editor
-LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region[5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits.
Simulated Analysis of Resonant Frequency Converter Using Different Tank Circu...IJERD Editor
LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region [5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits. The supported simulation
is done through PSIM 6.0 software tool
Amateurs Radio operator, also known as HAM communicates with other HAMs through Radio
waves. Wireless communication in which Moon is used as natural satellite is called Moon-bounce or EME
(Earth -Moon-Earth) technique. Long distance communication (DXing) using Very High Frequency (VHF)
operated amateur HAM radio was difficult. Even with the modest setup having good transceiver, power
amplifier and high gain antenna with high directivity, VHF DXing is possible. Generally 2X11 YAGI antenna
along with rotor to set horizontal and vertical angle is used. Moon tracking software gives exact location,
visibility of Moon at both the stations and other vital data to acquire real time position of moon.
“MS-Extractor: An Innovative Approach to Extract Microsatellites on „Y‟ Chrom...IJERD Editor
Simple Sequence Repeats (SSR), also known as Microsatellites, have been extensively used as
molecular markers due to their abundance and high degree of polymorphism. The nucleotide sequences of
polymorphic forms of the same gene should be 99.9% identical. So, Microsatellites extraction from the Gene is
crucial. However, Microsatellites repeat count is compared, if they differ largely, he has some disorder. The Y
chromosome likely contains 50 to 60 genes that provide instructions for making proteins. Because only males
have the Y chromosome, the genes on this chromosome tend to be involved in male sex determination and
development. Several Microsatellite Extractors exist and they fail to extract microsatellites on large data sets of
giga bytes and tera bytes in size. The proposed tool “MS-Extractor: An Innovative Approach to extract
Microsatellites on „Y‟ Chromosome” can extract both Perfect as well as Imperfect Microsatellites from large
data sets of human genome „Y‟. The proposed system uses string matching with sliding window approach to
locate Microsatellites and extracts them.
Importance of Measurements in Smart GridIJERD Editor
- The need to get reliable supply, independence from fossil fuels, and capability to provide clean
energy at a fixed and lower cost, the existing power grid structure is transforming into Smart Grid. The
development of a smart energy distribution grid is a current goal of many nations. A Smart Grid should have
new capabilities such as self-healing, high reliability, energy management, and real-time pricing. This new era
of smart future grid will lead to major changes in existing technologies at generation, transmission and
distribution levels. The incorporation of renewable energy resources and distribution generators in the existing
grid will increase the complexity, optimization problems and instability of the system. This will lead to a
paradigm shift in the instrumentation and control requirements for Smart Grids for high quality, stable and
reliable electricity supply of power. The monitoring of the grid system state and stability relies on the
availability of reliable measurement of data. In this paper the measurement areas that highlight new
measurement challenges, development of the Smart Meters and the critical parameters of electric energy to be
monitored for improving the reliability of power systems has been discussed.
Study of Macro level Properties of SCC using GGBS and Lime stone powderIJERD Editor
One of the major environmental concerns is the disposal of the waste materials and utilization of
industrial by products. Lime stone quarries will produce millions of tons waste dust powder every year. Having
considerable high degree of fineness in comparision to cement this material may be utilized as a partial
replacement to cement. For this purpose an experiment is conducted to investigate the possibility of using lime
stone powder in the production of SCC with combined use GGBS and how it affects the fresh and mechanical
properties of SCC. First SCC is made by replacing cement with GGBS in percentages like 10, 20, 30, 40, 50 and
by taking the optimum mix with GGBS lime stone powder is blended to mix in percentages like 5, 10, 15, 20 as
a partial replacement to cement. Test results shows that the SCC mix with combination of 30% GGBS and 15%
limestone powder gives maximum compressive strength and fresh properties are also in the limits prescribed by
the EFNARC.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
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Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
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Attacks on counties – USA
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In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
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https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
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Search and Society: Reimagining Information Access for Radical Futures
International Journal of Engineering Research and Development
1. International Journal of Engineering Research and Development
e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com
Volume 10, Issue 3 (March 2014), PP.41-50
41
Mathematical Modelling and Computer Simulation of Particle
Size Growth in Electrochemical Reactor
*
E. O. Ehirim, and A.A. Ujile
Department of Chemical/Petrochemical and Petroleum Engineering Rivers State of University of Science
and Technology Port Harcourt, Nigeria. PMB 5080.
Abstract:- A mathematical model to describe the effect of increase in bed volume of a three-dimensional
fluidized bed electrode operating under the condition of mass transfer is presented. The process of
electrodeposition within electrochemical reactor results in the increase of particle sizes. This phenomenon
increases the volume of the bed. The model incorporates the pseudo-stationary behaviour in the reactor since the
bed increases in volume due to the particle size growth. The developed differential equations are resolved using
finite difference method. The overpotential distribution and the reaction rate within the reactor are calculated.
The principal results are the effects of the limiting current operation on the superficial displacement with time.
The mathematical modelling shows that the bed expansion is independent of the reactor width, the porosity and
the current densities.
Keywords:- Fluidized bed electrodes, electrochemical reactors, perpendicular configuration, mathematical
modelling and limiting current.
I. INTRODUCTION
Fluidized bed electrodes have been widely used in the removal processes of toxic and pollutant
materials and recovery of heavy metals from industrial effluents. This technique offers direct use of
electrochemical reactors designed to carry out such industrial waste cleaning. Fluidized bed electrodes,
consisting of electrically conducting particles in an electrolyte, behave as three-dimensional electrodes which
are suitable for the design of many electrochemical reactors. Such electrodes provides high rate of mass transfer
and large area per unit volume for electrochemical reactions to occur even in very dilute solutions that need low
current densities. Consequently, fluidized bed electrodes have found their numerous industrial applications, such
as organic electrosynthesis, industrial effluents purification and electrowinning of metals from very dilute
solutions. Generally, the rate of reaction is controlled either by mass transport of chemical species from the bulk
of the solution to the surface of the electrodes or by electrode transfer on the electrode surface. The control is
termed mist if none of these mechanisms is explicit in the system [1, 2]. Generally, in terms of configuration,
fluidized bed electrodes are classified as perpendicular when the electrolyte flow is in the axial direction and the
current flow in the lateral direction and parallel when they are in the same direction. A perpendicular
configuration is preferred being that it offers a better potential distribution (more uniform potential) and high
conversion factor.
*All correspondence should go this author.
Mathematical modelling of electrochemical reactors is utilized for detailed analysis of the systems. One
of the advantages is usually to improve productivity or save costs in investment and operation.
Phenomenological understanding of the system behaviour and performance is usually necessary to carry out
such mathematical simulations. Sometimes such calculations may introduce certain innovations of technical
importance for engineering design and scale up. For the engineering and scale up applications of the fluidized
bed electrode, potential distribution and reaction rate distribution within the system must be investigated and
properly analysed. Some authors have elaborated on models which describe the behaviour of electrochemical
reactors with perpendicular configuration [3-5]. A parallel configuration has been reported by several authors
[6-9]. These authors obtained results which were in agreement with theoretical predictions. The basic
information on how to treat the kinetics involved in the electrochemical engineering systems can be found in
refs [9-10]. A reformulation of the Buttler-Volmer equation, introducing limiting current showed to be
important for the optimization of porous electrode systems with carbon particles because such electrodes
possess high superficial area [10]. It will be interesting to note that for a fluidized bed electrochemical reactor,
the transfer of charge in the dispersed phase takes place by intermittent particle contact and the quality of
transferred chare from one particle to another is proportional to the potential difference between them at
moment of contact [9]. In terms of current efficiency and productivity, fixed beds offer better results, however,
with time, the particles grow, closing the pores and thereby retarding the continuous functioning of the bed.
2. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
42
Fluidized bed electrodes offer an adequate alternative to resolve this difficulty and from the engineering point of
view, easy construction, apart from the possibility of on line removal of particle [7]. Some other distinct
advantages that electrochemical techniques offer relative to other conventional technologies include: energy
efficiency, versatility, environmental compatibility, safety, amenability to automation and selectivity.
The process of electrode position or electrowinning occurring within electrochemical reactor results in the
increase of particle sizes and consequently increases the volume of the bed. This paper aims at developing a
mathematical model capable of predicting the behaviour of a three dimensional fluidized bed electrode
(electrochemical reactor) with perpendicular configuration and in expansion. In addition, this investigation has
an added advantage of assisting in engineering project and scale-up.
The reactor in consideration is fluidized bed electrochemical reactor, with rectangular geometry and
perpendicular configuration operating under limiting current condition. The reactor was modelled with emphasis
on the reaction mechanisms occurring in the system. The analysis done in this investigation is based on
numerical solution (finite difference) of differential balances of mass and electrical charges in the reactor,
thereby permitting a prediction of the over potential distribution in the reactor.
II. MATHEMATICAL MODEL OF THE FLUIDIZED BED
The modelled system shown in figure 1 is a fluidized bed electrochemical reactor with a rectangular
geometry and perpendicular configuration whose thickness, width, and height are marked X,Y and Z
respectively. The bed is composed of very highly conductive non porous particles whose specific surface area is
am, a uniform porosity ε and a thickness X. If the electric current direction is the same as that of the movement
of the positive charges, the current feeder is then located at surface x = L and the reception or the counter
current on the surface x = 0. A superficial velocity of the electrolyte solution u entering the reactor is uniform
along the transversal area. The electrical conductivities of the solid and liquid phases are denominated
respectively by σm and σs.
The formulation of the model is based on the transport equations proposed by Gubulin [1, 2]. These
equations were applied to a two-phase solid-liquid system resulting in the following charge and mass balances:
i. Solid phase mass balance
𝝏
𝝏𝒕
𝟏 − 𝜺 𝑪 𝒌,𝒎 + 𝒅𝒊𝒗 𝟏 − 𝜺 𝑪 𝒌,𝒎 𝑽 𝒌,𝒎 = 𝟏 − 𝜺 𝑹 𝒌,𝒎 (1)
ii. Solid phase charge balance
𝒅𝒊𝒗 𝟏 − 𝜺 𝒊 𝒎 = 𝟏 − 𝜺 𝑭
𝒛 𝒌
𝑴 𝒌
𝒌 𝑹 𝒌,𝒎 (2)
The respective constitutive equations are:
𝐶𝑘,𝑚 𝑣 𝑘,𝑚 = 𝐶𝑘,𝑚 𝑣 𝑚
𝑖 𝑚 = −𝜎 𝑚 𝑔𝑟𝑎𝑑∅ 𝑚
iii. Liquid phase mass balance
𝝏
𝝏𝒕
𝜺𝑪 𝒌,𝒔 + 𝒅𝒊𝒗 𝜺𝑪 𝒌,𝒔 𝒗 𝒌,𝒔 = 𝜺𝑹 𝒌,𝒔 (3)
iv. Liquid phase charge balance
𝒅𝒊𝒗 𝜺𝒊 𝒔 = 𝜺𝑭
𝒛 𝒌
𝑴 𝒌
𝒌 𝑹 𝒌,𝒔 (4)
The constitutive equations for the liquid phase are:
𝐶𝑘,𝑠 𝑣 𝑘,𝑠 = −𝐷𝑘,𝑠
𝑒𝑓
𝑔𝑟𝑎𝑑𝐶𝑘,𝑠 + 𝐶𝑘,𝑠 𝑣𝑠 − 𝑧 𝑘 𝐹𝐶𝑘,𝑠 𝜇 𝑘,𝑠 𝑔𝑟𝑎𝑑𝜙𝑠
𝑖 𝑠 = − 𝐹
𝑧 𝑘
𝑀𝑘
𝑘
𝐷𝑘,𝑠
𝑒𝑓
𝑔𝑟𝑎𝑑𝐶𝑘,𝑠 − 𝜎𝑠 𝑔𝑟𝑎𝑑𝜙𝑠
Where by conservation of mass and charge,
𝟏 − 𝜺 𝑹 𝒌,𝒎
𝒎
𝒌=𝟏 = −𝜺 𝑹 𝒌,𝒔
𝒎
𝒌=𝟏 (5)
𝟏 − 𝜺
𝒛 𝒌
𝑴 𝒌
𝒎
𝒌=𝟏 𝑹 𝒌,𝒎 = −𝜺
𝒛 𝒌
𝑴 𝒌
𝑹 𝒌,𝒔
𝒎
𝒌=𝟏 (6)
The equation for the rate of reaction of the chemical specie k, in the electrolyte is generally written as:
𝑹 𝒌,𝒔 = 𝒂 𝒎
𝟏−𝜺
𝜺
𝒊 𝒌,𝒔
∗
𝑭
𝒛 𝒌
𝑴 𝒌
. (7)
where
𝑖 𝑘,𝑠
∗
= 𝑖 𝑘,𝑠
∗
𝜙𝑠, 𝜙 𝑚 , 𝐶1,𝑠, 𝐶1,𝑠
∗
, … ,
Rk,s and 𝒊 𝒌,𝒔
∗
are, respectively, the rate of reaction of the chemical specie k, per unit volume of the liquid phase
and the rate of reaction for the chemical specie k, in terms of charge transferred per unit area of the liquid phase;
zk is the charge transferred, Mk is the molecular mass of the chemical specie, and F is the Faraday constant
3. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
43
whose value is approximately 96500C/mol. The three-dimensional fluidized bed electrode used for this work is
schematized in Fig. 1.
For the purpose of simplifying the transport equations, we make the following restrictions:
i. Only component k = 1 reacts in the system;
ii. There is no accumulation of the chemical species k > 1, in the liquid phase;
iii. Hydrodynamic and electrochemical operating conditions are kept constant;
iv. In the bulk of the solution, outside the diffusion layer, the effects of diffusion and dispersion are
negligible compared to that of convection, which implies that This implies that 𝒗 𝒌,𝒔 = 𝒗 𝒔
v. The solid phase does not leave the system, or the average velocity of the solid phase is zero which
implies that 𝒗 𝒎 = 𝟎; Then
𝝏
𝝏𝒕
𝟏 − 𝜺 𝑪 𝒌,𝒎 + 𝒅𝒊𝒗 𝟏 − 𝜺 𝑪 𝒌,𝒎 𝑽 𝒎 = −𝜺𝑹 𝒌,𝒔 (8)
𝝏
𝝏𝒕
𝜺𝑪 𝒌,𝒔 + 𝒅𝒊𝒗 𝜺𝑪 𝒌,𝒔 𝑽 𝒔 = 𝜺𝑹 𝒌,𝒔 (9)
𝒅𝒊𝒗 𝜺𝑪 𝒌,𝒔 𝑽 𝒔 = 𝟎, k = 3,4,...,m (10)
𝒅𝒊𝒗 𝟏 − 𝜺 𝒊 𝒎 = −𝜺𝑭
𝒛 𝒌
𝑴 𝒌
𝑹 𝒌,𝒔 (11)
𝒅𝒊𝒗 𝜺𝒊 𝒔 = 𝜺𝑭
𝒛 𝒌
𝑴 𝒌
𝑹 𝒌,𝒔 (12)
𝒊 𝒔 = −𝝈 𝒔 𝒈𝒓𝒂𝒅∅ 𝒔 (13)
𝒊 𝒎 = −𝝈 𝒎 𝒈𝒓𝒂𝒅∅ 𝒎 (14)
Potential Distribution Equations in the Reactor
These equations are simplified and applied to a system of rectangular geometry and perpendicular configuration
as shown in Fig. 1. The suppositions made for the simplification of the above equations are:
1. The potential and the current density are only functions of the variable x,
2. The superficial velocity of the electrolytic solution is sufficiently high to ensure that concentration change
through the through the bed height is insignificant,
3. The porosity and the specific area are kept uniform and do not vary with time during the operation.
4. The operation is isothermal.
With these conditions equations 10 through 16 reduce to
Potential in the solid phase
𝒅 𝟐∅ 𝒎
𝒅𝒙 𝟐 =
𝟏
𝝈 𝒎
𝜺
𝟏−𝜺
𝑭
𝒛 𝒌
𝑴 𝒌
𝑹 𝒌,𝒔 (15)
Potential in the liquid phase
𝒅 𝟐∅ 𝒔
𝒅𝒙 𝟐 = −
𝟏
𝝈 𝒔
𝑭
𝒛 𝒌
𝑴 𝒌
𝑹 𝒌,𝒔 (16)
Boundary Conditions
The boundary conditions in the system in terms of the charge transfer are:
1. At the feeder, practically, all the current is carried by the liquid phase and at the receptor all the current
is by the metallic phase. Therefore,
x = 0;
𝒅∅ 𝒔
𝒅𝒙
= 𝟎 and x = X,
𝒅∅ 𝒎
𝒅𝒙
= 𝟎 (17)
2. If the system operates under constant current, then
x=0;
𝒅∅ 𝒎
𝒅𝒙
= −
𝑰
𝟏−𝜺 𝝈 𝒎 𝑨
(18)
x = X,
𝒅∅ 𝒔
𝒅𝒙
= −
𝑰
𝜺𝑨𝝈 𝒔
(19)
where I is the total current applied and A = AL = Y.L(t) is the lateral area of the bed.
Kinetics of the System
If, in the neighbourhood of the solid phase, exists a boundary layer of width δ, the rate of reaction of
the chemical specie k, in the liquid phase in terms of electron transfer is:
4. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
44
𝒊 𝒌,𝒔
∗
= −𝑭
𝒛 𝒌
𝑴 𝒌
𝑫 𝒌
𝜹
𝑪 𝒌,𝒔 − 𝑪 𝒌,𝒔
∗
(20)
A combination of this equation with equation 7 results:
𝑹 𝒌,𝒔 = −𝒂 𝒎
𝟏−𝜺
𝜺
𝑫 𝒌
𝜹
𝑪 𝒌,𝒔 − 𝑪 𝒌,𝒔
∗
(21)
At the solid-liquid interface, an intrinsic kinetic will always exists and can be represented by the Butler-Volmer
equation given as:
𝒊 𝒌,𝒔
∗
= 𝒊 𝟎 𝒆𝒙𝒑 −
𝜶𝒏𝑭
𝑹𝑻
𝜼 − 𝒆𝒙𝒑
𝟏−𝜶 𝒏𝑭
𝑹𝑻
𝜼 (22)
Where
𝒊 𝟎 = 𝒏𝑭𝒌 𝟎 𝑪 𝒌,𝒔
∗
(23)
A combination with equation 7 results:
𝑹 𝒌,𝒔 = −𝒂 𝒎
𝟏−𝜺
𝜺
𝑴 𝒌
𝑭𝒛 𝒌
𝒊 𝟎 𝒆𝒙𝒑 −
𝜶𝒏𝑭
𝑹𝑻
𝜼 − 𝒆𝒙𝒑
𝟏−𝜶 𝒏𝑭
𝑹𝑻
𝜼 (24)
In these equations, Dk is the diffusion coefficient of the chemical specie k participating in the reaction, n is the
number of electrons involved in the reaction, i0 is the exchange current density, Ck,s and 𝑪 𝒌,𝒔
∗
are the bulk and
superficial concentrations, respectively, 𝜹 is the width of the boundary layer, 𝜶 is the charge transfer coefficient,
and 𝜼 is the surtension in the reactor defined by the relation:
𝜼 = ∅ 𝒎 − ∅ 𝒔 − 𝑬 𝒆𝒒 +
𝑹𝑻
𝒏𝑭
𝒍𝒏 𝑪 𝒌,𝒔
∗
(25)
The process control of the reaction, generally, depends on both the mass and intrinsic kinetic. Eliminating 𝑪 𝒌,𝒔
∗
,
between equations 18 and 21 results:
𝑅 𝑘,𝑠 = −𝑎 𝑚
1−𝜀
𝜀
𝐶𝑘,𝑠
Θ
1+
𝛿
𝐷 𝑘
Θ
;
𝚯 =
𝑴 𝒌
𝒛 𝒌
𝒏𝒌 𝟎 𝒆𝒙𝒑 −
𝜶𝒏𝑭
𝑹𝑻
𝜼 − 𝒆𝒙𝒑
𝟏−𝜶 𝒏𝑭
𝑹𝑻
𝜼 (26)
A close look at equation 26 shows two limiting cases:
i. If 𝛿 → 0, then 1 +
𝛿
𝐷 𝑘
Θ → 1, then equation 26 reduces to
𝑹 𝒌,𝒔 = −𝒂 𝒎
𝟏−𝜺
𝜺
𝚯𝑪 𝒌,𝒔 (27)
ii. If 𝛿 >>0 then 1 +
𝛿
𝐷 𝑘
Θ →
𝛿
𝐷 𝑘
Θ and equation 26 becomes
𝑹 𝒌,𝒔 = −𝒂 𝒎
𝟏−𝜺
𝜺
𝑫 𝒌
𝜹
𝑪 𝒌,𝒔 (28)
If the system is controlled by intrinsic reaction, equation 27 is used and if controlled by mass transfer, equation
28 is used. On the other hand, if none of these is the controlling factor, equation 26 should be used. In this work
we are considering that the system is being controlled by mass transfer. This means that the system is operating
under limiting current condition.
Over potential in the Reactor:
If equation 16 is subtracted from equation 15, the model for the distribution of the surtension in the reactor is
obtained after substituting equation 21:
𝒅 𝟐 𝜼
𝒅𝒙 𝟐 = −𝒂 𝒎
𝟏
𝝈 𝒎
+
𝟏−𝜺
𝜺𝝈 𝒔
𝑫 𝒌
𝜹
𝑭
𝒛 𝒌
𝑴 𝒌
𝑪 𝒌,𝒔 (29)
The respective boundary conditions are
𝒅𝜼
𝒅𝒙 𝒙=𝟎
= −
𝑰
𝟏−𝜺 𝝈 𝒎 𝑨
(30)
𝒅𝜼
𝒅𝒙 𝒙=𝑿
=
𝑰
𝜺𝝈 𝒔 𝑨
(31)
The Model for the Displacement of the Bed Surface
If the electrochemical phenomena are more rapid than the fluid dynamic phenomena of the increase in volume
of the reactor, the process can be considered pseudo-stationary. The equation that predicts the interfacial
displacement, L(t) is given as:
𝒅𝑽
𝒅𝒕
= 𝑨 𝒃
𝒅𝑳
𝒅𝒕
(32)
But
𝑽 =
𝑴 𝒌
𝝆 𝒎 𝟏−𝜺
(33)
Therefore,
𝒅𝑴 𝒌
𝒅𝒕
= 𝝆 𝒎 𝟏 − 𝜺 𝑨 𝒃
𝒅𝑳
𝒅𝒕
(34)
On the other hand, if the reactor operation approximates a steady state operation of an ideal discontinuous
reactor, then
5. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
45
𝒅𝑴 𝒌
𝒅𝒕
≈ −𝜺𝑨 𝑳 𝑹 𝒌,𝒔 𝒙 𝒅𝒙
𝒙=𝑿
𝟎
(35)
Based on Fig. 1, AL/Ab = L/X and equation 31 equal to equation 32, therefore:
𝒅𝑳
𝒅𝒕
= −
𝜺
𝝆 𝒎 𝟏−𝜺
𝑳
𝑿
𝑹 𝒌,𝒔 𝒙 𝒅𝒙
𝒙=𝑿
𝟎
(36)
Since the bed is subject to an expression with time due to the particles growth, the specific surface area am and
the lateral area AL of the bed automatically become time dependent variables. Consequently, if the initial height
of the bed and the initial particle radius are respectively, L0 and r0, then, in any given time, we get:
𝒓 = 𝒓 𝟎
𝑳
𝑳 𝟎
𝟑
(37)
Consequently, for equilateral cylindrical particles used in this investigation, the specific surface area can be
written as:
𝒂 𝒎 =
𝑨 𝒑
𝑽 𝒑
=
𝟑
𝒓 𝟎
𝑳
𝑳 𝟎
𝟑
(38)
Substituting equation 38 in equation 33results:
𝒅𝑳
𝒅𝒕
=
𝟑
𝝆 𝒎
𝑳
𝒓 𝟎
𝑳
𝑳 𝟎
𝟑
𝑹 𝒌,𝒔 𝒙 𝒅𝒙
𝒙=𝑿
𝟎
(39)
Equations 29, 30, 31 and 39 represent mathematical model for a reactor in expansion. The method of
finite difference is implemented on equation 39 after substitution of equation 28 and resolved with the boundary
conditions, 30 and 31. The position of the interface in a given time can be calculated by equation 39, with L = L0
for t = 0. The model is applied to the system where copper is being deposited.
The conductivities σm and σs used in these simulations are respectively, 250.0Ω-1
m-1
and 50.0Ω-1
m-1
.
The simulations were based on a laboratory reactor having initial height of 0.0880252m, and thickness of
0.019m, 0.024m and 0.029m. Copper ion concentration in the electrolytic solution was 508.368g/m3
. The
simulation parameters were the current density, bed porosity, concentration, and position of the superficial
interface of the bed.
III. RESULTS AND DISCUSSION
Fig. 2 Potential distribution of metallic liquid phases for fixed bed reactor ( ε = 0.36)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Reactor width distance
Potentials(V)
Liquid Phase
Metalic Phase
6. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
46
Fig. 3 Potential distribution of metallic and liquid phases for fluidized bed reactor (ε = 0.5)
Figures 2 and 3 show typical potential distributions of metallic and liquid phases in the reactor with bed
porosities of 0.36 and 0.50, respectively, for different values of applied currents. The potentials of the metallic
phase are practically uniform in relation to the liquid phase, probably due to the effect of the higher values of the
electrical conductivities of the metallic phase used in relation to that of the liquid phase.
Fig. 4 Distribution of the over potentials in fixed bed reactor (ε = 0.36) for
different values of the applied current.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Reactor width distance
Potentials(V)
Metalic Phase
Liquid Phase
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
Reactor width distance
OverPotentials(V)
I=2A
I=4A
I=6A
7. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
47
Fig. 5 Distribution of the over potentials in fluidized bed reactor (ε =0.5) for
Different values of the applied current.
Figures 4 and 5 illustrate the overpotential distributions in the reactor for different values of applied
current. The distributions show a negative increase of overpotential for high applied currents. This behaviour
signifies that high current density produces a high reaction rate. Increase in the density of current means
increase in the number of electrons available to react with copper ions present in the solution. It can also be
observed that electrochemical activities are confined to the region close to the receptor or membrane. This
behaviour has been observed in the electrosynthesis of organic products by German and Goodridge [8]. A
comparison of these figures shows that low overpotential values are associated with high bed porosity.
Consequently, fixed-bed reactors are associated with high electrochemical reaction rates in contrast to fluidized
ones.
Fig. 6 Distribution of over potentials for fixed bed reactor (ε = 0.36) for different reactor widths.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-2.5
-2
-1.5
-1
-0.5
0
Reactor width distance
OverPotentials(V)
I=2A
I=4A
I=6A
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
Reactor width distance
Overpotential(V)
R1=0.019m
R2=0.024m
R3=0.029m
8. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
48
Fig. 7 Distribution of over potentials for fluidized bed reactor (ε = 0.5) for different reactor widths
Figures 6 and 7 show the distributions of over potentials for fixed and fluidized beds respectively, for
different reactor widths. Close observation of these figures shows that the higher the porosity, the higher the
values of the overpotentials in both cathodic and anodic regions. These figures also show that the higher the
reactor width, the more cathodic are the overpotentials. These figures demonstrate that the major alterations of
the overpotentials, occur at vicinity of the current feeder or the micro porous diaphragm.
Fig. 8 Distribution of bed expansion over time for various concentrations
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
Reactor width distance
OverPotentials(V)
R=0.019m
R=0.024m
R=0.029m
0 1 2 3 4 5 6 7 8 9 10
x 10
5
1
1.005
1.01
1.015
1.02
1.025
1.03
1.035
Time, (s)
Normalizedbedheight
C1
C2
C3
9. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
49
The displacement or the increase in the bed height with time is illustrated in figures 8 for different
concentrations of C1 = 508.36, C2 = 408.36 and C3 = 308.36, respectively. A notable feature of these
distributions is that the bed growth is proportional to the concentrations. That is, the reactor with a least
concentration experienced least expansion. This result is true since the rate of electrodeposition is proportional
to the local mass density.
IV. CONCLUSIONS
This investigation has theoretically demonstrated the behaviour of a three-dimensional fluidized bed
electrode operating under current limit and pseudo-static conditions as seen in the literatures [3,6,11]. The
electrochemical active regions are situated close to the receptor and about ten percentage of this region is
electrochemically active. The model is capable of predicting the behaviour of a fluidized bed in expansion. It is
important to note that the expansion model is independent of the local porosity, width of the reactor, and the
applied current density. In these simulations, only the reaction of copper was analysed, consequently, the current
efficiency will be 100%. However, experimental investigations have shown that, despite the fact that the
increase in the applied current caused an increased reaction rate, its effect, as far as the efficiencies of current
and energy are concerned, there was no benefit, because, there is always a decrease in both the current and
energy efficiencies as we increase the current density.
Nomenclature
am Specific surface of the solid[m-1
]
AL Lateral area of the bed[m2
]
Ap Particulate phase area[m2
]
Ab Base area of the bed[m2
]
Ck,s Concentration of the chemical specie k in the liquid phase [g/m3
]
𝐶𝑘,𝑠
∗
Concentration of the chemical specie k in the liquid phase on the electrode surface[g/m3
]
Dk Diffusion coefficient of the chemical specie k [m2
/s]
Eeq Equilibrium potential[V]
F Faraday constant[96500C/m
I Current density [A/m2
]
is Liquid phase current density [A/m2
]
im Solid phase current density [A/m2
]
I Total applied current [A]
𝑖 𝑘,𝑠
∗
Reaction rate of the chemical specie k in term s of charge per area [A/m2
]
i0 Exchange current density [A/m2
]
L0 Initial bed thickness [m]
L Bed height at a particular instant [m]
Mk Mass of the copper particles[g]
N Number of electrons
Rk,s Mass rate of reaction of chemical specie k per unit volume of the liquid[g/m3
s]
R Universal gas constant [8.314Jmol-1
K-1
]
r0 Initial particle radius[m]
R Particle radius at a particular instant, t [m]
T Time [s]
T Temperature [K]
U Superficial velocity of the electrolyte [m/s]
vk,s Local velocity of the chemical specie k in the solution bulk [m/s]
vs Average velocity of the solution phase [m/s]
V Bed volume [m3
]
Vp Particle phase volume [m3
]
X Space coordinator[m]
zk Number of transferred charges [-]
10. Mathematical Modelling and Computer Simulation of Particle Size Growth in Electrochemical Reactor
50
Greek Symbols
Α Kinetic constant [-]
η Overpotential[V]
δ Thickness of diffusion layer[m]
ε Porosity [-]
ζm Metal conductivity [Ω-1
m-1
]
ϕm Metal phase potential [V]
ϕs Liquid phase potential [V]
ζs Solution conductivity[Ω-1
m-1
]
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