Effect of surfactants on the rate of solid-liquid mass transfer in packed bubble columns

The effect of sodium lauryl sulphate (anionic) and Triton X-100 (nonionic) on the solid-liquid mass transfer at a gas-sparged fixed bed of copper Raschig rings was studied by measuring the diffusion-controlled dissolution of copper rings in acidified chromate solution. The variables studied were the nitrogen flow rate, the type of surfactant, and the surfactant concentration. It was found that an increase occurs in the solid-liquid mass transfer coefficient with increasing the nitrogen flow rate. Increasing the surfactant concentration was found to decrease the mass transfer coefficient. For a given surfactant concentration, it was found that Triton X-100 reduces the mass transfer coefficient more than sodium lauryl sulphate.     

Mass transfer in electrochemical reactors employing gas evolving mercury pool cathodes

The effect of H₂ evolution on the mass transfer coefficient of the cathodic reduction of potassium ferricyanide at a mercury cathode was studied with the aim of (i) comparing the mass transfer behaviour of a Hg cathode with that of solid electrodes under gas evolving conditions, and (ii) testing the effect of surface active agents on the mass transfer behaviour of a H₂-evolving Hg cathode. For a given H₂ discharge rate the mass transfer coefficient at a mercury cathode was much higher than the value at a solid cathode. The mass transfer coefficient at the H₂-evolving Hg cathode was found to decrease in the presence of Triton X-100 surfactant by an amount ranging from 62.6% to 86.2% depending on H₂ discharge rate and surfactant concentration. A simple mathematical model was formulated to explain the results. The presence of surfactant was found to increase the cell voltage.     

Effect of Some Additives on Mass Transfer Coefficient at a Vibrating Horizontal Screen

The object of the present work is to study the effect of drag-reducing additives like Polyox WSR 301 and sodium lauryl sulfate (anionic surfactant) on the rate of mass transfer at a vibrating horizontal screen, an electrochemical technique which involved measuring the limiting current of the cathodic reduction of potassium ferricyanide. Variables studied were the concentration of polymer and surfactant, frequency of vibration and amplitude of vibration. It was found that a decrease in the mass transfer coefficient occurs in the presence of surfactant which ranged from 3 to 61.8% depending on the concentration of the surfactant. The addition of a Polyox leads to a decrease in the mass transfer coefficient which ranged from 20 to 74.4% depending on the concentration of the polymer.     

Effect of drag-reducing additives on the rate of mass transfer in a parallel-plate electrochemical flow reactor

The effect of polyox and CMC drag-reducing polymers on the rate of mass transfer in a parallel-plate flow cell was studied by measuring the limiting current for the cathodic reduction of potassium ferricyanide in alkaline medium. Reynolds number and polymer concentration were varied over the range 3500–21 000 and 10–200 ppm respectively. Under these conditions it was found that polyox and CMC reduce the rate of mass transfer by a maximum of 42% and 35% respectively.Nomenclature a a constant - C concentration of ferricyanide ion (g mol cm^–3) - D diffusivity of ferricyanide ion (cm²s^–1) - d _e equivalent diameter of the cell (4 x cross-sectional area/wetted perimeter) - F Faraday's constant (96 487 C mol^–1) - I limiting current density (A cm^–2) - K mass transfer coefficient (cm s^–1) - L electrode height (cm) - (Re) Reynolds number (d _e /u) - (Sc) Schmidt number (u/D) - (Sh) Sherwood number (Kd _e/D) - u solution viscosity (poise) - flow rate of the solution (cm s^–1) - Z number of electrons involved in the reaction - solution density (g cm^–3)     

Free convective mass transfer at vertical cylindrical electrodes of varying aspect ratio

A limiting current technique was used for the measurement of the free convection mass transfer rate at entire vertical cylinders with varying aspect ratio. The mass transfer rates at the single surfaces were in good agreement with the mass transfer data in the literature. Mass transfer rates at a combination of a downward-facing horizontal and a vertical surface was controlled by the downward-facing horizontal surface (for cylinder aspect ratios lower than 2). It was found that the entire surface measured mass transfer rate was lower than that predicted by summation of the mass transfer rate at the individual surfaces. An interference factor,f, was introduced for correlation of the total mass transfer data for the full range of cylinders together. The dependence of the interference factor on the aspect ratio of the cylinder (L/r) was established.Nomenclature A ₀ total surface area of cylinder - A _V vertical surface area of cylinder - A _H surface area of horizontal base of cylinder - c _b bulk concentration of copper ion - c _{CuSo 4} bulk concentration of copper sulphate - c _{H 2}SO₄ bulk concentration of sulphuric acid - d cylinder diameter - D diffusion coefficient of copper ion - f interference factor - F Faraday's constant - g gravitational acceleration - I _L limiting diffusion current - k mass transfer coefficient - L cylinder length - L _w characteristic dimension (Weberet al. [2]) - n charge number of copper ion - r cylinder radius - Ra Rayleigh number - Ra _L Rayleigh number based on cylinder length - Sh Sherwood number - Sh _L Sherwood number based on vertical cylinder length - Sh ₀ stagnant medium Sherwood number - T electrolyte temperature Greek symbols density difference between bulk solution and interface - density - dynamic viscosity     

Mass transfer at gas evolving screen electrodes

Mass transfer coefficients at horizontal gas evolving screen electrodes were measured by determining the reduction rate of K₃Fe(CN)₆. The variables studied were: gas discharge rate, number of screens per electrode and distance between screens. The relation between the mass transfer coefficient and H₂ discharge rate was found to be:

The mass transfer coefficient was found to go through a minimum when increasing the number of screens per electrode. Screen spacing has a slight effect on the mass transfer coefficient.Mass transfer coefficients were also measured for the deposition of copper from a copper sulphate solution at a horizontal screen cathode stirred by oxygen evolved at a horizontal anode placed below the cathode. The relation between the mass transfer coefficient and the gas discharge rate was found to be.

Useful application for purposes of cell design is pointed out.     

Mass transfer at rotating finned cylinders

Rates of mass transfer at rotating finned cylinders were studied by an electrochemical technique involving the measurement of the limiting current for the cathodic reduction of potassiun ferricyanide in a large excess of sodium hydroxide. The variables studied were fin height and Reynolds number. The ratio of the fin height to the cylinder diameter (e/d) ranged from 0·0185 to 0·075 while the Reynolds number ranged from 1047 to 10 470. Under these conditions, the mass transfer data could be correlated by the equationJ=0·714(Re)^–0.39(e/d)^0.2 Nomenclature L _L limiting current (A) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the reaction - C ferricyanide concentration (moles cm^–3) - F Faraday's constant - A projected cathode area (cm²) - u dynamic viscosity (g cm^–1 s^–1) - density (g cm^–3) - V peripheral velocity at the rotating cylinder (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm²s^–1) - d cylinder diameter (cm) - e fin height (cm) - J (St)(Sc)^0.664 ColburnJ factor - (Sc) u/(D) Schmidt number - (Re) Vd/u Reynolds number - (St) K/V Stanton number     

Mass transfer at rough gas-sparged electrodes

Rates of mass transfer were measured by the limiting current technique at a smooth and rough inner surface of an annular gas sparged cell in the bubbly regime. Roughness was created by cutting 55°V-threads in the electrode normal to the flow. Mass transfer data at the smooth surface were correlated according to the expression j = 0.126(Fr Re)^–0.226 Surface roughness of peak to valley height ranging from 0.25 to 1.5 mm was found to have a negligible effect on the mass transfer coefficient calculated using the true electrode area. The presence of surface active agent (triton) in the solution was found to decrease the mass transfer coefficient by an amount ranging from 5% to 30% depending on triton concentration and superficial air velocity. The reduction in the mass transfer coefficient increased with surfactant concentration and decreased with increasing superficial gas velocity.Nomenclature a constant - A electrode area (cm²) - C _p specific heat capacity Jg^–1 (K^–1) - C ferricyanide concentration (m) - d _c annulus equivalent diameter, (d _o – d _i) (cm) - d _o outer annulus diameter (cm) - d _i inner annulus diameter (cm) - D diffusivity of ferricyanide (cm²s^–1) - e peak-to-valley height of the roughness elements (cm) - e ⁺ dimensionless roughness height (eu ^*/) - f friction coefficient - F Faraday constant (96 500 Cmol^–1) - g acceleration due to gravity (cm s^–2) - h heat transfer coefficient (J cm^–2 s K) - I _L limiting current (A) - K mass transfer coefficient (cm s^–1) - K thermal conductivity (W cm^–1 K^–1) - V _g superficial air velocity (cm s^–1) - Z number of electrons involved in the reaction - Re Reynolds number (_L V _g d _e/) - J mass or heat transfer J factor (St Sc ^0.66) or (St Pr ^0.66), respectively - St Stanton number (K/V _g for mass transfer and h/C _p V _g for heat transfer) - Fr Froude number (V _g ² /d _e g) - Sc Schmidt number (/D) - Pr Prandtl number (C _p/K) - PL solution density (g cm^–3) - kinematic viscosity (cm²s^–1) - gas holdup - u ^* friction velocity = V _L(f/2) - diffusion layer thickness (cm) - solution viscosity (gcm^–1 s^–1)     

Effect of drag-reducing additives on the rate of mass transfer in diffusion-controlled electrochemical processes

Mass transfer between a rotating cylinder and a solution containing sodium carboxymethyl cellulose polymer, was studied using an electrochemical technique involving the reduction of potassium ferricyanide in a large excess of sodium hydroxide. The Reynolds number and polymer concentration were varied over the ranges 4100–41 000 and 10–500 ppm, respectively. Under these conditions, it was found that polymer addition reduces the mass transfer coefficient by 10–22% depending on Reynolds number and polymer concentration. The mass transfer data in polymer-containing solutions were found to fit the equation (St) = 0.07(Re)^–0.3(Sc)^–0.644.List of symbols I _L limiting current density (A cm^–2) - Z number of electrons involved in the reaction - F Faraday's constant (96 500 C) - K mass transfer coefficient (cm s^–1) - V linear velocity of the cylinder (cm s^–1) - angular velocity (rad s^–1) - D diffusion coefficient (cm² s^–1) - kinematic viscosity (cm² s^–1) - d diameter of the cylinder (cm) - u viscosity of the solution (poise) - density of the solution (g cm^–3) - C concentration (mol cm^–3) - (St) K/V, Stanton number - (Sc) /D, Schmidt number - (Re) d/u, Reynolds number     

Mass transfer at the confining wall of helically coiled circular tubes with gas–liquid flow and fluidized beds

Experiments were conducted to investigate the effect of various dynamic and geometric parameters on mass transfer coefficients in two-phase helically coiled flow systems. Computation of mass transfer coefficients was facilitated by the measurement of limiting current at the electrodes fixed flush with the inner surface of the tube wall. Two flow systems were chosen: a two-phase liquid solid fluidized bed and a two-phase gas–liquid up flow. An equimolar potassium ferrocyanide and potassium ferricyanide solution in the presence of sodium hydroxide was used as the liquid phase. In the fluidized bed, glass spheres and sand of different sizes were employed as fluidizing solids. In two-phase flow system nitrogen was employed as inert gas. The pressure drop in the presence of fluidizing solids in helical coils was found to increase with increase in the pitch of the coil and was maximum for straight tube. The mass transfer coefficients were found to increase with increase in liquid velocity. The mass transfer coefficients in case of gas–liquid flow were found to be independent of liquid velocity and the pitch of the coil, and were largely influenced by gas velocity only. The data were correlated using j_D factor, Helical number, Froude number and Stanton number.     

Numerical evaluation of mass transfer coefficient in stirred tank reactors with non-Newtonian fluid

In fermentation processes, a constant supply of oxygen is fundamental for cell growth. The supply rate is controlled by the volumetric mass transfer coefficient. The literature reports few numerical studies evaluating the volumetric mass transfer coefficient for aerated systems with non-Newtonian fluids in stirred tanks. The aim of this work was to undertake a numerical study of the main hydrodynamic and mass transfer parameters, including average gas hold-up, and power number. Xanthan gum solutions were used to simulated. The simulations were performed with different impeller rotational speeds (600 to 1000 revolution per minute) and specific gas flow rates (0.4 to 1.2 volume of gas per volume of liquid per minute), adopting an Euler-Euler approach and assuming uniform spherical bubbles. The turbulence was simulated with k?ε turbulence model and sst shear stress transport turbulent model. The numerical results were compared with experimental values available in the literature. The results showed good agreement between the numerical and experimental values of gas hold-up, power number, and volumetric mass transfer coefficient. The sst shear stress transport turbulence model provided better results, compared to the standard k?ε model, for simulation of volumetric mass transfer coefficient in a non-Newtonian fluid under the conditions used. Simulations for uniform bubbles with 3 millimeters diameter gave mass transfer coefficient values that were close to the experimental data.     

Effect of drag reducing polymers on the rate of mass transfer in relation to their use as corrosion inhibitors in pipelines under turbulent flow conditions

Rates of mass transfer between a turbulently flowing fluid containing CMC drag reducing polymer and the wall of a tube were measured in the mass transfer entry region using the electrochemical technique. Variables studied were polymer concentration, surface roughness and solution flow rate. Carboxymethyl cellulose (CMC) was found to reduce the mass transfer coefficient by an amount ranging from 15 to 37% depending on the operating conditions. The percentage decrease in the mass transfer coefficient becomes greater with increasing CMC concentration and Reynolds number. CMC was found to reduce the rate of mass transfer at rough surfaces (e ⁺>3) by an amount higher than that at a smooth surface. The possibility of using large polymers as drag reducers and corrosion inhibitors simultaneously in pipelines is indicated.Nomenclature I limiting current (A) - Z number of electrons involved in the reaction - F Faraday's constant - A projected (geometrical) area of the cathode (cm²) - K mass transfer coefficient (cm s^–1) - C concentration of ferricyanide ion (mole cm^–3) - e roughness height (cm) - d tube diameter (cm) - L length of transfer surface (cm) - St Stanton number (K/V) - Re Reynolds number (Vd/u) - Sc Schmidt number (v/D) - e ⁺ dimensionless height (eu ^*/v) - u ^* friction velocity [V(f/2)^1/2] (cm s^–1) - V solution velocity (cm s^–1) - f friction factor - v kinematic viscosity (cm² s^–1) - u viscosity (poise) - density (g cm^–3) - D diffusivity (cm²s^–1)     

Mass transfer behaviour of a fixed bed electrochemical reactor with a gas evolving upstream counter electrode

Mass transfer rates were determined at a horizontal screen cathode stirred by oxygen bubbles evolved at a horizontal anode placed below the screen by measuring the limiting current of the cathodic reduction of ferricyanide ion from alkaline solution. Variables studied were oxygen discharge rate, ferricyanide concentration and number of closely packed screens forming the cathode. For a single screen cathode the data were correlated by the equation: J = 0.249 (Re Fr)^-0.25 The mass transfer coefficient was found to decrease with increasing the number of screens forming the cathode. Implications of the present work for improving the performance of the flow-through packed bed electrochemical reactor were highlighted.     

Mass transfer at packed-bed,gas-evolving electrodes

Mass transfer rates were measured for the cathodic reduction of potassium ferricyanide at a H₂-evolving electrode consisting of a packed bed of spheres. Variables studied were bed height, H₂ discharge rate and ferricyanide concentration. It was found that the mass transfer coefficient (K) is related to the H₂ discharge rate (V) by the equation $$K = aV^{0.325} $$ Bed height and electrolyte concentration were found to have little effect on the mass transfer coefficient. A mathematical model based on the surface renewal theory was formulated to explain the mechanisms of mass transfer at gas-evolving electrodes.     

The effect of a surfactant on mixer—settler operation

A single stage mixer—settler was used to investigate the effect of surfactant on the mass transfer rate in the system water—HNO₃—30 vol.% TBP/dodecane. The interfacial tension of this system first falls then rises with increasing sodium lauryl sulphate (SLS) concentration. The addition of SLS makes the stage efficiency, which is closely related to k_ha, the product of the individual mass transfer coefficient of HNO₃ in the aqueous phase, and average interfacial area per unit volume of mixing chamber, to increase significantly due to an increase in the value of a. A maximum k_ha value of 0.53 litres^?1, a minimum value of interfacial tension, and phase inversion which converted the aqueous phase from continuous to dispersed were observed at around the critical micellar concentration (100 parts 10^?6) of SLS in the system of an aqueous to organic phase ratio of 0.2.     

Mass transfer in electrolytic cells with gas stirring

Mass transfer to wall electrodes was investigated in a circular cell agitated by gas bubbles. Perforated and porous plates were used as gas spargers. Electrodes with varying height and electrolytic solutions having different physical properties were tested. It was found that the enhancing effect of gas bubbles on the mass transfer coefficient is a function of the gas hold-up, irrespective of the velocity of the gas flow and the gas distributor employed. The results were correlated for short mass transfer lengths by the relationship $$Sh = 0.231(ScGa)^{\frac{1}{3}} (L/D_c )^{--0.194 _\varepsilon 0.246}$$ and for fully developed mass transfer by $$Sh_\infty = 0.256(ScGa)^{\frac{1}{3}} \varepsilon ^{0.254}$$      

Mass transfer between rough surfaces and solutions containing drag-reducing polymers

Rates of electrochemical mass transfer were measured between finned rotating cylinders and solutions containing drag-reducing polymers. Variables studied were: Reynolds number, polymer concentration and fin height. Polyox and carboxymethyl cellulose (CMC) were used as drag-reducing polymers with concentrations ranging from 10–100 ppm for polyox and from 10–500 ppm for CMC. Cylinders with longitudinal fins ofe/d ranging from 0·0185–0·075 were used. Reynolds number was varied between 1000–10000. It was found that the presence of fins on the cylinder surface reduces the adverse effect of the polymer on the rate of mass transfer, the higher the fin height the lower is the ability of the polymer to reduce the rate of mass transfer. Mass transfer data for solutions containing polyox were correlated by the equation: (St) = 0.765(Re)^-0.36(Sc)^–0.669(e/d)^0.36 Mass transfer data for solutions containing CMC were correlated by the equation: (St) = 1.704(Re)^–0.36(Sc)^–0.75(e/d)^0.315 List of symbols I _L limiting current density based on the projected area of the electrode (A cm^–2) - K mass transfer coefficient (cm s^–1) - Z number of electrons involved in the electrode reaction - C ferricyanide concentration (mol cm^–3) - F Faraday's constant - u dynamic viscosity (g cm^–1 s^–1) - solution density (g cm^–3) - angular velocity (rad s^–1) - V peripheral velocity (cm s^–1) - D diffusion coefficient of ferricyanide ion (cm² s^–1) - d cylinder diameter (cm) - e fin height (cm) - (Sc) u/(D), Schmidt number - (Re) vd/u, Reynolds number - (St) K/V, Stanton number     

HYDRODYNAMICS AND MASS TRANSFER IN DOWNFLOW BUBBLE COLUMN

Gas holdup, effective interfacial area and volumetric mass transfer coefficient were measured in two and three phase downflow bubble columns. The mass transfer data were obtained using the chemical method of sulfite oxidation, and the gas holdup was measured using the hydrostatic technique. Glass beads and Triton 114 were used to study the effects of solids and liquid surface tension on the gas holdup and the mass transfer parameters a and k_L a . The gas holdup in three phase systems was measured for non-wettable (glass bead) and wettable (coal and shale particles) solids.

The mass transfer data obtained in the downflow bubble column were compared with the values published for upflow bubble columns. The results indicate that in the range of superficial gas velocities (0.002-0.025) m/s investigated, the values of the mass transfer coefficient were of the same order of magnitude as those observed in upflow systems, but the values of interfacial area were at least two fold greater. Also, the results showed that the operating variables and the physical properties had different influences on a and k_L a in the downflow bubble column. Correlations for a and k_L a for the downflow bubble column are proposed which predict the data with adequate accuracy in the range of operating conditions investigated.     

Mass transfer at the gas evolving inner electrode of a concentric cylindrical reactor

Mass transfer coefficients for an oxygen evolving vertical PbO₂ coated cylinder electrode were measured for the anodic oxidation of acidified ferrous sulphate above the limiting current. Variables studied included the ferrous sulphate concentration, the anode height, the oxygen discharge rate and the anode surface roughness. The mass transfer coefficient was found to increase with increasing O₂ discharge rate,V, and electrode height,h, according to the proportionality expressionK V ^0.34 h ^0.2. Surface roughness with a peak to valley height up to 2.6 mm was found to increase the rate of mass transfer by a modest amount which ranged from 33.3 to 50.8% depending on the degree of roughness and oxygen discharge rate. The present data, as well as previous data at vertical oxygen evolving electrodes where bubble coalescence is negligible, were correlated by the equationJ=7.63 (Re. Fr)^–0.12, whereJ is the mass transferJ factor (St. Sc ^0.66).Notation a ₁,a ₂ constants - A electrode area (cm²) - C concentration of Fe²⁺ (M) - d bubble diameter (cm) - D diffusivity (cm² s^–1) - e electrochemical equivalent (g C^–1) - F Faraday's constant - g acceleration due to gravity (cm s^–2) - h electrode height (cm) - I _Fe ²⁺ current consumed in Fe²⁺ oxidation A - I _{o 2} current consumed in O₂ evolution, A - K mass transfer coefficient (cm s^–1) - m amount of Fe²⁺ oxidized (g) - P gas pressure (atm) - p pitch of the threaded surface (cm) - Q volume of oxygen gas passing any point at the electrode surface (cm³ s^–1) - R gas constant (atm cm³ mol^–1 K^–1) - r peak-to-valley height of the threaded surface (cm) - t time of electrolysis (s) - T temperature (K) - solution viscosity (g cm^–1 s^–1) - V oxygen discharge velocity as defined by Equation 3 (cm s^–1) - Z number of electrons involved in the reaction - Sh Sherwood number (Kd/D) - Re Reynolds number (Vd/) - Sc Schmidt number (v/D) - J mass transferJ factor (St. Sc ^0.66) - St Stanton number (K/V) - Fr Froude number (V ²/dg) - Solution density, g cm^–3 - v Kinematic viscosity (cm² s^–1) - bubble geometrical parameter defined in [31] - fractional surface coverage - diffusion layer thickness (cm)     

Mass transfer behaviour of gas-evolving particulate-bed electrode

Rates of mass transfer for the cathodic reduction of potassium ferricyanide at a particulate bed of graphite supported on a horizontal nickel disc were studied under H₂-evolving conditions. Variables studied were: H₂ discharge rate, particle size and bed height. The rate of mass transfer was found to increase to a maximum in the presence of the bed which was about 4.5 times compared to that of the supporting disc. The rate of mass transfer was found to increase with H₂ discharge rate, particle size and bed height. Polarization was measured for beds of different particle size and it was found that the presence of the bed increased polarization especially at relatively high current densities, the increase in polarization was independent of particle size of the bed. Comparison with an O₂-evolving particulate electrode was made and possible practical applications were pointed out.Symbols K mass transfer coefficient (cm s^–1) - V H₂ discharge rate (cm³cm^–2s^–1) - I current consumed in reducing potassium ferricyanide (A) - A supporting disc area (cm²) - F Faradays constant (96 500 C mol^–1) - C Potassium ferricyanide concentration (mol cm^–3) - Z number of electrons involved in the reaction