Terms Of Dimensionless Numbers Research Articles

Interchangeable modular design and operation of photo-bioreactors for Chlorella vulgaris cultivation towards a zero-waste biorefinery

This study explores diverse cultivation modes for Chlorella vulgaris within a biorefinery at pilot scale that produces both biodiesel by transesterification of waste frying oils and syngas by gasification of organic wood waste. Given microalgae's comparatively modest biofuel yield relative to principal biorefinery products, the microalgae cultivation process is designed on the biofuels production rates. Liquid and gaseous waste streams are recycled inside the biorefinery: crude glycerol is mixed with wood to enhance the quality of syngas, wastewater is fed to microalgae so as flue gas. Also, the oil extracted from microalgae contributes to produce biodiesel and the waste cells are gasified.Considering that the optimal fit for each cultivation mode varies with the shape of the reactor, we propose a modular approach to assemble them in batteries of tubular, bubble flow, and airlift reactors, and present an operating design criterion that can fulfill the mass balance of the plant by adding/transforming the number of units inside the different batteries. Methods to adjust the operating conditions and control the operating parameters are also discussed.The designed configurations were operated recycling nominal waste streams of about 30 L d−1 of wastewater and 90 Nm3 h−1 of flue gas. Results confirm that the most advantageous one, in terms of volume per recycled waste streams, is a battery of 16 airlift reactors, operating in mixotrophic mode, with growing rate of 0.427 d−1, yield of 3.06, glycerol conversion 39 %, CO2 removal 64 % of inlet 6–10 %(mol) concentration. The same nominal waste streams can also be managed by 40 tubular reactors in almost heterotrophic conditions coupled with 12 bubble columns in autotrophic conditions; working respectively at growing rates of 0.395 d−1 and 0.362 d−1 and yields of 2.94 and 2.84. The battery of tubular reactors reached a glycerol conversion of 45 % and the array of bubble columns removed about 51 % of inlet 12–20 %(mol) CO2 concentration. A complete comparison is reported also in terms of dimensionless numbers and pumping/mixing requirements.

A new practical approach to design a Phase Change Material-Water longitudinally finned tube heat exchanger

Phase change materials have demonstrated interesting advantages in solar energy storage systems to produce domestic hot water although more efficient heat exchangers are required. Among the different exchanger typologies, longitudinally finned exchangers are widespread. However, according to scientific literature, there is a lack of analytical models able to estimate the thermal power transferred by this kind of exchangers easily. This paper shows a practical and easy to apply analytical model that has been built for that type of exchangers. Thus, based on a change of the solution given by Heisler and Gröber for an infinitely long cylinder, this new analytical approach characterises the thermal energy discharged in terms of dimensionless numbers. The adjustment of the analytical model was achieved from the results provided by a CFD numerical model which was previously validated from experimental data. 544 numerical simulations of the system were carried out varying the Biot number and a surface factor number from 1 to 100 and 3 to 15, respectively. An analytical equation that estimates the energy discharged is provided as a function of Fourier, Biot, and Stefan numbers and the surface factor number, related to the exchanger geometry. An average value of the root mean square error smaller than 4% indicates that the proposed model is sufficiently accurate and might be used in the design stages of this kind of devices. A further validation of the analytical model against experimental observations will be carried out in a future stage of model development.

Experimental study of heat transfer coefficient in heat exchanger reactors with square millimetric zigzag channels

Heat transfer performances of compact heat exchanger reactors were experimentally characterized and measurement uncertainties were evaluated using the derivation method. Prototypes presenting two kinds of process channel configurations (zigzag and straight channels) with square cross-section were investigated, from 2 mm to 4 mm depth. Water or glycerol-water mixture were used as the process fluid, cooled by water as the utility fluid. Reynolds number ranged between 15 and 7300 and Prandtl number between 3.1 and 115. From the measurements of the fluid temperatures and flow rates, local heat transfer coefficients were calculated. In zigzag channels, it ranged from 760 to 15,000 W.m−2.K−1, with an average uncertainty of 15.7%. With water as the process fluid, the heat transfer coefficients in zigzag channel were 2 to 5 times higher than in straight channel. The experimental data were then used to establish a correlation for the Nusselt number in the zigzag channels as a function of the channel geometry, the fluid properties and flow rates expressed in terms of dimensionless numbers. The average relative difference between experimental and calculated values was 9.1%. Finally, the consistency of the correlation was confirmed by comparison with data obtained in a previous work based on CFD.

Understanding dense granular flow from first principles

Preventing natural disasters like avalanches or landsides, optimising powder-based industrial processes or predicting the flow of sand on planetary surface, are exemplary applications that would benefit from a universal model for a better understanding of granular rheology. Due to the high densities and shear rates involved, the derivation of constitutive equations from first principles is notoriously difficult. Here, we will present such a theoretical approach, the Granular Integration Through Transients (GITT) formalism. Starting from the microscopic equations of motion, GITT yields quantitative predictions for the flow curves of granular fluids at high density and shear rate. GITT predicts Newtonian, shear thinning, and shear thickening regimes depending on density and shear rate. We will present experiments in a fluidized bed rheometer that confirm the rheological regimes and can be evaluated quantitatively in terms of GITT. We will discuss a phenomenological version of GITT that makes the qualitative behaviour understandable in terms of dimensionless numbers. With this we can derive the mu(I)-rheology that has been proposed as an empirical law for granular flow and show that it is a special case of GITT for specific flow conditions.

Absorption of Carbon Dioxide into n‐Butanol and Ethyl Acetate in a Column with Structured Packing

AbstractA recently developed and efficient absorption contactor was evaluated, using alternative physical absorption liquids that are more economical, environmentally friendly, easier to recycle, untested and have lower energy requirements compared to commercial absorption solutions for capturing carbon dioxide. For this purpose, CO2 was captured using n‐butanol and ethyl acetate in an originally designed structured packed column. Mass transfer coefficients were determined at different gas and liquid velocities. The results are correlated in terms of dimensionless numbers, such as ShL = 0.01283ReG1.4ReLScL1/3, with a regression coefficient of 0.992.

Experiments in free falling and downward cocurrent annular flows – Characterization of liquid films and interfacial waves

Falling liquid films and downward cocurrent flows in rounded shape pipes have been experimentally studied during the last decades, estimating the evolution of its major characteristics. The most important variables during the formation and growth of surface waves in falling downward flows have been measured using conductance probes.The main objective of the current research paper is to study the dependency of the characteristics of the thin liquid layer for downward cocurrent annular flows. The GEPELON experimental facility consists of a vertical pipe with 3.8 m of useful test length. Two pipe diameters have been analysed in this experimental study, 42 and 30 mm, in which the range covered by the liquid Reynolds number varies between 570 and 8500 and 800–7900 respectively, while the gas Reynolds numbers vary from 0 to 7.9·104 and from 0 to 1.1·105 respectively for the mentioned pipe diameters. Up to five conductance probes have been placed along the pipes test sections to capture the liquid film thickness fluctuations along time at different distances of the pipe entrance for both developing and fully developed regions.After the study and analysis of the experimental data, the central point of this paper has been the development of new correlations for the liquid film thicknesses and the two major properties of the interfacial waves. Their adjustment procedure has been carried out in terms of dimensionless numbers, aiming to provide more general relationships. In particular, the magnitudes that characterise the interface behavior have been measured, particularly film thicknesses, average disturbance wave amplitudes, and disturbance wave frequencies for each boundary condition.An additional part of the document contains an extensive comparison between the results obtained in this study and the data and expressions of other authors. It has been confirmed the significant dispersion existing among different researchers, especially when analysing variables related to the interfacial waves. This highlights the lack of knowledge in some aspects even today. The different correlations proposed have been calculated based on the best fit of the data from all the series of experiments carried out in this study. Comparisons of the behaviour of these correlations with data from other researchers have also been included.

Fluid-Structure Interaction in Coronary Stents: A Discrete Multiphysics Approach

Stenting is a common method for treating atherosclerosis. A metal or polymer stent is deployed to open the stenosed artery or vein. After the stent is deployed, the blood flow dynamics influence the mechanics by compressing and expanding the structure. If the stent does not respond properly to the resulting stress, vascular wall injury or re-stenosis can occur. In this work, a Discrete Multiphysics modelling approach is used to study the mechanical deformation of the coronary stent and its relationship with the blood flow dynamics. The major parameters responsible for deforming the stent are sorted in terms of dimensionless numbers and a relationship between the elastic forces in the stent and pressure forces in the fluid is established. The blood flow and the stiffness of the stent material contribute significantly to the stent deformation and affect its rate of deformation. The stress distribution in the stent is not uniform with the higher stresses occurring at the nodes of the structure. From the relationship (correlation) between the elastic force and the pressure force, depending on the type of material used for the stent, the model can be used to predict whether the stent is at risk of fracture or not after deployment.

Numerical approximation to the effects of the atmospheric stability conditions on the dispersion of pollutants over flat areas

Using the Computational Fluid Dynamics technique (CFD), we explored the effects of the atmospheric stability conditions on the dispersion of solid and gas-phase pollutants emitted from an area source located on a flat region. As an application, the dispersion of pollutants emitted from roads located on flat terrains was considered. Toward that end, we set up a model that describes the dispersion of air pollutants in a small region (< 1 km long) near the ground surface (< 250 m high). It consists of a neutrally stratified model modified to account for the atmospheric stability effects by imposing the near-ground stratification through the Monin–Obukhov similarity theory and the k–ε turbulence model adjusted for each atmospheric stability condition. Using this model, we simulated the dispersion of pollutants emitted from the road and plotted the resulting downwind concentrations in terms of dimensionless numbers. Results from our CFD-based model were highly correlated (R2 > 0.95) with the SF6 concentrations measured downwind a line source of this trace gas by the U.S. National Oceanic Atmospheric Administration in 2008 under different conditions of atmospheric stability. Numerical and experimental results showed that, under any of the stability conditions explored, the near-road pollutant concentrations are highly correlated (R2 > 0.87) to the concentrations observed under neutral conditions. When the atmosphere is extremely stable, those concentrations were up to 12 times higher than those observed under neutral conditions. We report the constant of proportionality obtained for every stability condition.

Numerical study on molten pool dynamics and solute distribution in laser deep penetration welding of steel and aluminum

To shed new light on the molten pool behavior and transmission mechanism during the laser welding of dissimilar metals, a 3D transient numerical model was developed in this study. The fluid flow, heat transfer, keyhole evolution, and mass transport between two dissimilar metals were studied. The volume of fluid (VOF) method was used to track the free surface. The effects of recoil pressure and surface tension on the keyhole wall were mainly considered. The effects of convection, diffusion, and keyhole formation on the mass transfer were also considered. The relative importance of convection and conduction and the effects of various driving forces on the convection in the molten pool were analyzed in terms of dimensionless numbers. The results showed that the maximum temperature and liquid flow velocity of the molten pool slightly fluctuate at the peak value after the molten pool enters the quasi-steady state, and the stability of the keyhole depends on the dynamic balance between the recoil pressure and the surface tension. Because of the influence of the formation mechanism of the keyhole, the weld zone contained significant amounts of aluminum elements. The results also showed that the welding parameters significantly affect the transition layer thickness and element distribution, which is closely related to the weld quality. The numerical simulation results correspond well with the experimental results. This study provides new insights into the weld pool dynamics in the laser welding of dissimilar metals and can help guide the selection of the welding parameters.

A first principles framework to predict the transient performance of latent heat thermal energy storage

Thermal energy storage (TES) is increasingly recognized as an essential component of efficient Combined Heat and Power (CHP), Concentrated Solar Power (CSP), Heating Ventilation and Air Conditioning (HVAC), and refrigeration as it reduces peak demand while helping to manage intermittent availability of energy (e.g., from solar or wind). Latent Heat Thermal Energy Storage (LHTES) is a viable option because of its high energy storage density. Parametric analysis of LHTES in terms of dimensionless numbers is highly desired as a tool to model LHTES systems. One approach is to develop a model equation so as to minimize the error between the model and data obtained from experiments or simulations. While this approach can produce an accurate correlation applicable within the range of data used for its creation, it does not provide physical understanding of the rate-limiting process controlling the transient behavior of the device. In this paper we present an alternative approach whereby the potential rate-limiting processes are identified from first principles and then the key process is determined as a function of time as a LHTES device is charged. For example, in a simple geometry, the melt-fraction can be expected to vary linearly in time if the heat transfer rate is limited by natural convection of the phase changing material and we show it scales with the PCM Grashof number asGrp1 and PCM Prandtl number asPrp(1∕3). On the other hand, if surface area of solid PCM limits the heat transfer rate, the melt fraction increases asymptotically to reach full melting. The existence of these linear and asymptotic regions and theGrp1Prp1∕3 shape of the melt fraction curve is verified using our database of 64 simulations. Of practical importance in designing LHTES devices is the melt fraction at which the heat transfer rate ceases to be limited by convection, after which the heat storage rate deteriorates. For our geometry, this is found to be about 90%. This test case of our methodology shows the value of our approach, that predicting heat storage rate based on the rate-limiting physical phenomenon as a function of time is an effective approach to modeling LHTES devices.

Effect of Surface Tension on Hydrodynamics and Mass Transfer Coefficient in Airlift Reactors

AbstractThe hydrodynamics and volumetric mass transfer coefficient play important roles in the design and scale‐up of airlift reactors. The effect of surface tension on hydrodynamics and volumetric mass transfer coefficient in internal loop airlift reactors was investigated. With reduction of the surface tension of the fluid, the hydrodynamic parameters raised, namely, gas phase holdup, flow regime transition point, and interfacial area, whereas the bubble diameter as well as the liquid velocity decreased and the volumetric mass transfer coefficient increased. Empirical correlations are proposed for gas‐phase holdup and volumetric mass transfer coefficient in terms of dimensionless numbers and can be applied in the design of airlift reactors.

Efficiency Prediction of Centrifugal Pump Using the Modified Affinity Laws

Abstract This research is a continuation of efforts aimed at establishing the modified affinity laws for viscosity to predict the pump performance directly from a plot in terms of dimensionless numbers, i.e., flow coefficient, Reynolds number, head coefficient, and efficiency. The group has earlier proposed modified head coefficient affinity law. This work proposes and validates a similar efficiency plot that completes the set of modified affinity laws that include all the input and output parameters for a specific pump design and type. A wide range of viscosities and flow rates are considered for CFD analysis to have a comprehensive set of data that includes enough data points to comment on both the laminar and turbulent flow cases categorized based on the hydraulic Reynolds number (2300). Initial analysis shows some inconsistency based on laminar versus turbulent simulation model selection which is addressed in the latter part of this work. In general, two curves can be constructed for laminar and turbulent flow cases. These curves have different axes parameters (exponents of the dimensionless numbers) depending on the plot being for a laminar or a turbulent flow case. Validation with established experimental data shows good agreement in terms of the variation of axes parameters (their exponents) depending on the pump type for a single suction impeller and a double suction impeller pump. The distinction between laminar and turbulent flow cases is found to be applicable to established experimental data as well.

Determination of gas film mass transfer coefficient in a packed bed reactor for the catalytic combustion of hydrogen

The overall kinetics of catalytic combustion of hydrogen in air is decided by the contribution of the different resistances offered in individual steps such as external diffusion, internal diffusion and surface reaction. To estimate the contribution of external mass transfer resistance, empirical correlations in terms of dimensionless numbers viz., Sherwood number, particle Reynold's number, and Schmidt number are used in general. The Schmidt number for hydrogen in air is approximately 0.2 and most of the mass transfer correlations in packed bed reactors are valid for Schmidt number higher than 0.6, which corresponds to that of water vapour in the air. The external mass transfer correlations applicable for hydrogen-air system are scarce. In the present study, the external mass transfer effects were decoupled from internal diffusion and intrinsic reaction by conducting experiments with different particle Reynolds numbers in a packed bed batch reactor with complete recycle. Further, the system is theoretically modeled and the external film mass transfer coefficients were estimated at different particle Reynold's numbers using experimental data. Based on the experimental data, a new mass transfer correlation has been proposed to determine the gas film mass transfer coefficient of hydrogen in the air in packed bed reactors, in terms of conventional dimensionless numbers i.e., Sherwood number, Schmidt number, and particle Reynolds number. Further, the contribution of external mass transfer resistance on the overall reaction kinetics was also estimated.

An experimental and numerical study of air pollution near unpaved roads

Aiming to advance in the understanding of pollutant dispersion near roads, we measured, simultaneously, vehicle traffic, meteorological parameters, and 24-h average concentration of particulate matter (TSP, PM10, and PM2.5) at several locations downwind two unpaved roads, located on a flat region without any other relevant source of pollutants. We also implemented on a commercial software of computational fluids dynamics (CFD) an air quality model to simulate the dispersion of particles and gas-phase pollutants emitted from roads. Numerical results of monthly and daily averages of total suspended particles (TSP) concentrations showed high correlation with experimental measurements (R2 > 0.94). We found, numerically and experimentally, that the plots of pollutant concentrations vs distance to the road edge converge into a single curve when they are expressed in terms of dimensionless numbers. Profiles of vertical concentration sketch an exponential function at the road edge, an S shape downwind and a flat shape far from the road. Particle size distribution fits a Rosin-Rammler function with average diameter of ~ 7 μm. This distribution remains unaltered downwind the road, which implies that at any location within 1.5 km from the road, PM10 and PM2.5 concentrations are a constant fraction of TSP concentration. Experimental data confirmed this observation. Previous results can be used to determine the size of the area impacted by roads, identify mitigating and adaptive countermeasures, and to improve the accuracy of vehicular emission factors.

Hemodynamic Quantitative Analysis Based on Doppler Ultrasound for Arteriovenous Shunt Stenosis Screening

Clinically, arteriovenous shunt (AVS) stenosis results in turbulent and pulsatile flow because of high resistance and pressure within a narrowed space inside a stenotic access. Palpation and ultrasound methods are primarily used (first-line examination) to rapidly screen the risk of the degree of stenosis (DOS). Therefore, quantitative hemodynamic analysis involving Doppler ultrasound is performed in patients suffering from AVS stenosis and undergoing long-term hemodialysis. Doppler ultrasound with a center frequency of 7.5 MHz can provide substantial resolution and sensitivity to the measurement of blood flow velocity within a range of depth of 20.0-30.0 mm and a scan diameter of 10.0 mm. A hemodynamic method is used to analyze blood flow through a hemodialysis access in terms of dimensionless numbers. In this study, velocities were measured using Doppler ultrasound at three specific sites in vessels, namely, arterial anastomosis, loop, and venous anastomosis sites. Dimensionless numbers, such as supracritical Reynolds numbers, critical peak Reynolds numbers, and resistive indices, are determined in accordance with parallel conditional expression-based rules to create decision trees for the rapid screening of the DOS at the abovementioned specific sites. For the enrolled subjects, results demonstrate that noninvasive hemodynamic analysis with Doppler ultrasound measurements and parallel decision trees has potential for the efficient screening of the DOS in patients suffering from AVS stenosis and undergoing long-term hemodialysis. Experimental results also indicate that the hit and true-positive rates of the proposed screening method in clinical indication are higher than those of the machine learning method.

Heat transfer analysis during mixed-mode solar drying of potato cylinders incorporating shrinkage: Numerical simulation and experimental validation

Heat transfer analysis during mixed-mode solar drying of foodstuff is crucial in food industries now-a-days as better understanding of the phenomena will assist in suitable design and optimization of the drying process parameters. In the present work, natural convection mixed-mode solar drying experiments were carried out with potato cylinders of varying diameters (8, 10 and 13mm) with a fixed length of 50mm. The convective heat transfer coefficient, hcon was evaluated without and with the incorporation of shrinkage effect in the mathematical model. The results predicted that consideration of sample shrinkage led to an overestimation of average values of convective heat transfer coefficient, h¯con by 55.72–61.86% for the investigated samples. It was also observed that the moisture content and sample diameter had a notable influence on heat transfer coefficient. Heat transfer correlations in terms of dimensionless numbers were developed for each sample diameter by an equation of the form Nu=C(Ra)n. The uncertainty in the average value of hcon was found to lie in the range of 1–3%. A finite element based COMSOL Multiphysics software was used to develop a numerical model to project the transient sample temperature during the drying process. The predicted sample temperatures considering shrinkage were in close agreement with the experimental results showing lower values of statistical errors.

The rising motion of spheres in structured fluids with yield stress

The rising of spherical bodies in structured fluids with yield stress is studied. The system is a suspension of hydrogenated castor oil colloidal fibers in a surfactant micellar solution. The fiber network confers to the fluid a viscoelastic behavior, with a well-defined yield stress, which increases with increasing fiber concentration. Various fluids with different fiber contents are prepared and rheologically characterized. A home-made time-lapse photography setup is used to monitor the time evolution position of the spherical particles, and the rising motion of both hollow spheres and air bubbles, in the diameter range 65–550 μm, is measured. The experiments last as long as several weeks, corresponding to significantly low measured velocities. Finite element simulations are performed to support the experimental data, assuming both interfacial slip and no slip conditions. The fluid dynamic phenomenon is studied and discussed in terms of dimensionless numbers, such as yield ratio, Bingham number, and Stokes drag coefficient. The results are novel for the system (suspending medium and hollow spheres) and for the covered Bingham number range, which is extended over three orders of magnitude in comparison with already available literature results. Our values provide quantitative data of the mechanical properties (i.e., yield stress value) at very low shear rates, in a prohibitive range for a traditional rheometer, and agree with the macroscopic rheological response. Moreover, the important role of the power law index n of the Herschel-Bulkley model, used to fit the data, has been highlighted. Our results, based on a Bingham-like fluid, are compared with the experimental data already available with Carbopol, treated as a Herschel Bulkley fluid with n = 0.5. The results could have important implications in the fabric and personal care detergency, a technological area where many fluids have composition and show rheological properties similar to those considered in the current work.

Impact of Electrolyte Viscosity on Redox Flow Battery Performance

Due to their inherent scalability and long operational lifetimes, redox flow batteries (RFBs) have shown promise as grid-level energy storage systems that enable the integration of intermittent renewable energy sources and the improvement of non-renewable energy processes on the grid.1 However, additional cost reductions are required to reach proposed capital cost targets for widespread commercial implementation.2 While multiple efforts have focused on discovery and development of next-generation materials for RFBs, fewer studies have systematically investigated the impact of the physical properties of electrolytes on cell performance. This is particularly relevant as many new electrolyte formulations push towards higher concentrations and incorporate new redox structures (e.g., macromolecules), which improve capacity and reduce cost, but also result in higher viscosities and greater property variation as a function of state-of-charge. These factors are expected to strongly influence cell performance. Specifically, engineering an efficient, cost-effective reactor depends on mitigation of resistive losses, several of which depend on electrolyte viscosity, and this dependence has yet to be fully characterized within a RFB. Here, we use a single-electrolyte flow cell configuration3, coupled with a model iron-based electrolyte, to probe the impact of electrolyte viscosity on RFB losses. Through the use of glucose as a chemically and electrochemically inert solution thickener, we investigate polarization as a function of electrolyte viscosity, electrolyte flowrate, and flow field geometry. Experimental data is combined with an one dimensional porous electrode polarization model to extract ohmic, kinetic, and mass transfer contributions to cell resistance. Of particular interest are mass transfer rates in RFBs, which are rarely quantified, thus the observed trends in mass transfer coefficient are correlated in terms of dimensionless numbers (e.g., Reynolds, Schmidt) in a traditional power-law format. This study aims to link electrolyte properties and cell performance and to provide a scalable descriptions of mass transfer in RFBs. Acknowledgments The authors acknowledge the financial support of the Joint Center for Energy Storage Research, which was formed under the Office of Basic Energy Sciences within the Department of Energy. We thank A. Helal and G. H. McKinley for rheological guidance and aid in viscosity measurements. We also thank M. Z. Bazant for use of milling equipment to fabricate flow fields used in this work.

Corrosion rate determination of vessel walls agitated by double impeller and gas sparging

AbstractRecently, multiple impeller gas sparged vessels have found wide application in many industries, such as food, pharmaceuticals, and biofuels. In this study, the rate of diffusion-controlled corrosion of the wall of nitrogen gas sparged-double impeller agitated vessel was studied by the dissolution of copper wall in acidified dichromate solution technique. The variables studied were the impeller rotation speed, the superficial gas velocity, and the clearance between the two impellers. The results were reported in terms of dimensionless number depicting the process conditions, Re, Sc, and the impeller clearance. For the agitated vessel, the corrosion rate correlation was ${\rm{CR}} = 1.6\; \times \;{10^{\; - \;16}}{\rm{R}}{{\rm{e}}_{{\rm{Ag}}{\rm{.}}}}^{0.668}{\left( {{{{C_2}} \over H}} \right)^{0.183}}{\rm{S}}{{\rm{c}}^{0.33}}.$ For the condition: 2800&lt;ReAg.&lt;19,600, 0.19&lt;C2/H&lt;0.58 and Sc=960, with an average deviation of ±2.9%. For the agitated sparged vessel, the data were correlated by ${\rm{CR}} = 2.5\; \times \;{10^{\; - \;15}}{\rm{R}}{{\rm{e}}_{{\rm{Ag}}{\rm{.}}}}^{0.134}{\rm{Re}}_{{\rm{Sp}}{\rm{.}}}^{{\rm{0}}{\rm{.381}}}{\rm{S}}{{\rm{c}}^{0.33}}.$ For the condition: 2800&lt;ReAg.&lt;19,600, 370&lt;ReSp.&lt;1855 and Sc=960, with an average deviation of ±6.7%. These results show that, under these conditions, the rate of corrosion of agitated vessels is controlled by the rate of agitation and the clearance between the impellers. However, when gas sparging is introduced, the rate of corrosion is much more influenced by the gas flow rate, whereas the effect of the clearance between the impellers nearly disappears.

Phase transfer catalysis in a microchannel: Paradoxical effect of transition from kinetic control to mass transfer control

The high surface area per unit volume available in microfluidic devices has led to their use in process intensification of mass transfer limited reactions. The commonly observed flow regimes parallel and slug flows, play a major role in determining the performance of these systems. The strong internal circulations and high interfacial area per unit volume makes the slug flow regime a preferred regime for mass transfer limited reactions. The reaction between benzyl alcohol and sodium hypochlorite to yield benzaldehyde via phase transfer catalysis (PTC) is chosen as a test reaction system. Batch experiments were carried out at three different pH values viz. 10.4, 8.4 and 7.4. The rate of reaction decreased as the medium became alkaline. A mathematical model where the species in the aqueous phase is considered to be in equilibrium was developed. In the slug flow regime of the microchannel the yield of the reaction is found to increase with an increase in organic phase residence time at high pH. The yield however decreased with residence time at low pH. This paradoxical behavior is attributed to a shift in the system from the kinetic control regime to a mass transfer control regime. The effect of residence time, mass transfer time and reaction time on the test reaction is analyzed in this work. Criteria in terms of dimensionless numbers have been proposed to determine if a system is kinetically controlled or mass transfer controlled.