Convective-diffusive Mass Transfer Research Articles

Identification of mass-transfer coefficient in spatial problem of filtration

A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones. An algorithm of the solution of the corresponding nonlinear singular disturbed inverse problem of "convection-diffusion mass transfer" type is suggested.

Mass transfer to a nanostructured nickel electrodeposit of high surface area in a rectangular flow channel

Nanostructured nickel was electrodeposited on a stainless steel plate. The convective-diffusion mass transfer to this nanostructured electrode was compared to that of a planar, mirror polished solid nickel electrode using the limiting current technique, for the reduction of ferricyanide, hexacyanoferrate (III) ion in an undivided cell. The effect of introducing a turbulence promoter into the electrolyte channel was also evaluated for each electrode under steady state conditions. At a Reynolds number of 700, the product of mass transfer coefficient and active electrode area, kLA for the nanostructured nickel electrode increases over 11 times compared to the mirror polished planar nickel electrode. In the presence of a turbulence promoter, the nanostructured nickel electrode shows an approximately 23 times increase in kLA compared to the planar mirror polished nickel electrode. The dimensionless mass transfer correlations Sh=aRebScdLee are compared to others in the literature.

Fractal nature of acid-etched wormholes and the influence of acid type on wormholes

Abstract Two-scale (Darcy scale and pore scale) continuum wormholing models are built to study the fractal nature of the acid-etched wormholes in acidizing carbonate reservoirs and the influence of acid type on the conditions for wormholes to form. This model considers convection-diffusion mass transfer and reaction on the acid-rock interface, and the fractal dimension of dissolution patterns is calculated using box-counting method. The results show that wormholes are formed when convection and diffusion are equivalent in strength; when convection dominates, uniform dissolution is formed; when diffusion dominates, surface dissolution is generated. For the zones where the porosity is greater than 0.7, the fractal dimensions of the surface dissolution, wormholes and uniform dissolution are 1.46, 1.50 and 1.44, respectively, among which, the fractal dimension of the wormholes is approximate to the experimental results obtained by Daccord and Lenormand (1.60.1). The reaction between weak acid and rocks is controlled by reaction kinetics, the acid-etched wormholes are wide, and more acid is consumed. The reaction between strong acid and rocks is controlled by mass transfer, the acid-etched wormholes are narrow, and less acid is consumed. According to an example calculation, it is found that acidizing treatments should be performed in an isolated short section each time when the horizontal well is long.

Cathodic processes in annular crevices

Mass transfer from the volume of medium within a crevice and conversely is of considerable importance for crevice corrosion. A device is used based on a system of two horizontal coaxial disks, one of which (specimen with an annular crevice) is stationary, and the second (counter disk) rotates. This makes it possible to control hydrodynamic conditions around the stationary disk surface and evaluate quantitatively the rate of convective-diffusion mass transfer towards its surface. Data are obtained for the distribution of liquid flow rate over the depth of a crevice with a prescribed counter disk rotation frequency. It is shown that with an increase in crevice width the more critical value of cathodic process rate at a surface within a crevice remains constant, in spite of an increase in solution convective restoration intensity within a crevice. Under natural convection condition within the volume of solution oxygen distribution over the depth of a crevice is very uneven, and this may lead to occurrence of differential aeration pairs. With induced convection within solution around the mouth of a crevice, the cathodic process of oxygen renewal penetrates into the depth of a crevice and is distributed more uniformly over the surface within a crevice.

Convective‐diffusive mass transfer of agonist and the intracellular calcium response of endothelial cell

Endothelial cell layer regulates several crucial physiological processes of the vascular system. The mechanism of the response of this cell layer to the flow of surrounding fluid is still largely unclear. In the present article, a comparison of the available experimental results for the intracellular calcium ion concentration and theoretical results for the extra-cellular ATP concentration obtained using a convective-diffusive mass transfer model, has been made which supports the mass transfer model for the endothelial cell response to the fluid flow. The experimental results are in excellent agreement with the calculated values assuming the effect of ATP concentration alone.

Characterization of Buffered Electrolytes for Nickel Electrochemical Printing

Electrochemical printing (EcP) is a maskless solid free-form microfabrication process that locally electrodeposits materials in a nonuniform current distribution beneath a rastering microjet electrode. To achieve high spatial resolution, EcP electrolytes are formulated such that ohmic resistance is large compared to the kinetic resistance. Extraordinary electrodeposition rates are common because a microjet electrode placed very close to the substrate delivers high convective-diffusive mass transfer rates. As a result, conventional electrolytes are generally not well suited for EcP. We describe a high-throughput approach for formulating and optimizing electrolytes in EcP, using nickel as a model material that displays interesting complications arising from pH changes driven by the coevolution of hydrogen. Two acetate buffered nickel sulfate electrolytes (pH 3.7 and 4.8) are used to show the interplay of bulk pH and tool operating conditions on overall current efficiency and the formation of complex deposit topographies induced by the local formation of soluble nickel hydroxides. An electrochemical quartz crystal microbalance is used to quantify current efficiencies (up to 45%) at current densities between 2 and . Dense nickel patterns with grain sizes of were electrodeposited at .

Chain-exchange dynamics and kinetics by ATR–FTIR: Effects of shear stress and temperature on high density polyethylene flow

The chain exchange dynamics at a polymer–solid interface were studied using attenuated total reflectance Fourier transform infrared spectroscopy technique (ATR–FTIR) in a rectangular flow channel. The decrease in the deuterated polyethylene (d-PE) absorbance, previously deposited on ZnSe crystal, as a function of time was monitored as it was replaced by molten high-density polyethylene (HDPE). The experiments were carried out at 0.020, 0.023 and 0.028 MPa and at 260, 270 and 280 °C. The chains exchange dynamics are characterized by two flow regimes: the fast flow regime is described by the equation for convective-diffusive mass transfer. In the slower regime, the flowing chains are interacting with the chains physically adsorbed on the ZnSe crystal. The chain exchange was treated as a surface reaction that follows a first-order kinetic. The experimental data were fitting to a single exponential decay function of which parameters, time constant ( k s), absorbance and time at the transition point among fast and slow dynamics were determined. From the kinetics model, it was demonstrated that the chain exchange is a transport-limited process in which, k s decreases with the increasing shear rate ( γ w) and temperature. It is an activated process with an activation energy near to flow activation energy. From the theoretical and experimental angular coefficients of the plot k s versus ( γ w − 1 / 3 ), we conclude that the chains diffusivity near the surface is less than the bulk diffusivity.

Uniform Thin Film Electrodeposition onto Large Circular Wafer Substrates

A wafer-scale electrochemical flow cell specially suited for uniform thin-film electrodeposition is presented. The cell consists of a porous disk injector set parallel and coaxial to a working disk electrode with a narrow separation gap between them. The porous injector was designed to supply a uniform axial flow of electrolyte onto the surface of the working disk electrode. The mass transfer characteristics of the cell and the current distribution on the working disk electrode were studied for various operating conditions, geometric parameters and bath chemistries. The experimental results confirmed the simple scaling properties that were theoretically predicted. It has also been shown that this cell can provide nearly uniform current distribution on the working electrode under conditions of both migration and convective-diffusive mass transfer control. The results indicate that this cell is suitable for uniform thin-film electrodeposition onto large circular wafer substrates.

A STUDY ON THE ZERO FLUX APPROXIMATION IN CONVECTION-DIFFUSION MASS TRANSFER PROBLEMS

A one-dimensional steady state convection-diffusion mass transfer problem (for a binary mixture of components A and B), where the molar flux of component B (J B ) is considerably smaller than the molar flux of component A, is taken under study. A usual approximation for the case, especially if the fluxes are in the opposite direction to each other, is that J B = 0. The error resulting from this assumption, when the naturally-developing Stefan flow or concentration distributions are estimated, is evaluated. A simple analysis shows that if the molar fraction of the almost stagnant component is sufficiently low, the zero flux assumption causes a significant error. Such cases occur, for example, in osmosis and in evaporation near or at boiling point. A corrected Stefan flow equation and a modified mass transport equation for more general than one-dimensional problems, based on the use of a mass transfer coefficient, are presented

Convective-diffusive mass transfer inside complex micro-molds during electrodeposition

During fabrication, local variations in convective-diffusive mass transfer and current distribution can give rise to undesirable variations in material composition for electrodeposited microelectromechanical systems (MEMS). Local transport characteristics are normally difficult to analyze in complex microstructures, especially the convective-diffusive conditions present during device fabrication. To tackle this problem, we have developed an experimental method called Process Archaeology. The general approach involves the electrodeposition of NiFe alloys from an electrolyte formulated to give a local composition that is very sensitive to the local mass transfer rate. Spatially-resolved measurements of the alloy composition and growth rate are accomplished by combining scanning electron microscopy and energy dispersive x-ray spectroscopy. Using a simple inverse problem formulation, these experimentally measured quantities are related to the local convective-diffusive mass transfer coefficient (k) and the local Sherwood number present during fabrication. Here the Sherwood number is defined as Sh=kH/D, where H is the thickness of the lithographic mask and D is the diffusivity of a key transport-controlled species. Electrodeposited microgears are used as a test bed for demonstrating Process Archaeology. Sherwood number images show the wide ranges of mass transfer rates and the complex mixing features present during microgear fabrication, especially in the region downstream of the microgear's central hub.

Invariance relations for laminar forced convection in ducts with slowly varying cross-section

Laminar flow forced convective heat transfer in ducts with slowly varying cross-section is analysed. The analysis is based on a simplifying assumption concerning the velocity field, called the similarity assumption. It is assumed that the axial velocity profile is locally fully developed, irrespective of the variation of the cross-sectional area with axial position. It is shown that in the axisymmetric case (circular tube with varying diameter) for boundary conditions of the first kind the diameter variation has no influence at all on the heat transferred. As in the case of a tube with constant diameter, the degree of temperature equilibration depends only on the Fourier number Fo= πaL Q that is on the ratio of length of the tube, L, to flow rate Q. In the case of a plane channel, however, variations of the channel height 2 H have a pronounced influence on the transfer coefficient. It is shown that the degree of equilibration depends only on the effective Fourier number Fo eff = aB Q ·∫ 0 L dz H(z) . The heat transfer is enhanced by a narrow design of the duct. These results hold for any shape of the axial velocity distribution over the duct cross-section, provided the above-mentioned similarity assumption is justified. By analogy, all foregoing results are also applicable to the convective–diffusive mass transfer in flow through ducts with slowly varying cross-section. The range of validity of the similarity assumption is discussed in a hydrodynamic section. It can be shown that for creeping flow of a Newtonian liquid in an infinite cone or wedge this assumption is a very good approximation to the exact solution of Stokes' equations for cone or wedge angles up to 30°. Apart from Newtonian creeping flow, the assumption might well be applicable in the duct flow of a power-law fluid and in pure elongational flow as encountered in stretching filaments or sheets of liquid, where the axial velocity is constant over the cross-section.

Dynamic Surface Tension and Adsorption/Desorption Kinetics for Polymer Mixtures on Planar Surfaces: II. Under Flow Conditions

The adsorption/desorption kinetics for individual polymers and polymer mixtures of the water-soluble associative polymers with molecular weights of 12, 62, and 100 kg/mol onto a SiO2 planar substrate have been studied by ellipsometry at room temperature under flow conditions. Equations were derived to predict behaviors of the adsorption/desorption kinetics and dynamic surface tension onto planar surface for any times. It is shown that the rate of adsorption/desorption kinetics under nonflow conditions is significantly less than the one under flow conditions due to the convective–diffusive mass transfer to an interface.

High Peclet number mass transfer in the acoustic streaming flow between two concentric cylinders

Local and average convective diffusive mass transfer rates are analyzed numerically for high Peclet number acoustic streaming flow between two concentric cylinders. The streaming flows analyzed are for low to moderate streaming Reynolds numbers, where counter-rotating inner and outer recirculating flow cells exist. Thin concentration boundary layers form at the inner cylinder surface, across the streamline that divides the inner and outer flow cells, and at the outer cylinder surface. The core of each recirculating flow cell contains a well-mixed region of nearly uniform composition. The numerical results are used to develop Sherwood number correlations that relate convective mass transfer rates to dimensionless forms of the oscillation amplitude, oscillation frequency, and physical properties of the system. Numerical results are shown to agree with published experimental results.

An integral-spectral approach for convective-diffusive mass transfer with chemical reaction in Couette flow Mathematical formulation and numerical illustrations

Abstract The convective-diffusive mass transfer problem with chemical reaction in a Couette planar flow has been analyzed in terms of the integralspectral methods originally introduced by Arce et al. (Comput. Chem. Eng. 2(11) (1988) 1103). The problem is solved by inverting the differential model into an integral equation of a Volterra type, in the axial variable, and of the Fredholm type, in the radial coordinate. The kernel of such an integral equation is given by the Green function which does not contain any of the kinetic parameters of the (homogeneous and/or heterogeneous) reaction term. This Green function is computed in terms of the eigenfunctions and eigenvalues of the Sturm-Liouville problem associated with the radial variable. The Sturm-Liouville problem is solved (analytically) by using Airy functions and the final integral equation must be solved by an iteration procedure. Several of the mathematical formulation details are discussed and many numerical examples are presented to illustrate the technique: for example, concentration profiles for systems with heterogeneous (wall) catalytic reactions, homogenous (global) reactions and simultaneous (global and wall catalytic) reactions with kinetics of a general form, i.e. power-law and Langmuir-Hinshelwood types of functions are investigated. The solutions to the class of problems considered here are obtained as particular cases of the general integral equation solution of the differential model discussed in the article. The effects of relevant parameters in the system on the computational algorithm with respect to convergence and (numerical) stability characteristics are discussed.

Convective−Diffusive Mass Transfer with Chemical Reaction in Squeezing Flows

A model for convective-diffusive mass transfer in squeezing flow is formulated and solved. A spatial averaging technique is applied to reduce the 2D problem to a 1D problem. It is assumed that the hydrodynamics is decoupled from the mass transfer and the model is solved using a sequential coupling between the convective velocity field and concentration field equations. To account for the loss of information due to averaging, a closure scheme is developed for the deviations of average values of velocity and concentration. This involves derivation of the equations for the deviations of the respective fields. The effective transport parameters are evaluated in terms of the molecular diffusion coefficient, the average velocity, and the dimensions of the system. The associated eigenvalue problem is solved by using a combination of exponentials and Kummer functions. The concentration profile is then found analytically by a Fourier series expansion of the initial condition. Two specific cases are considered. These include (1) no reaction in the bulk and (2) a linear homogeneous reaction in the bulk. The analysis promotes understanding of the behavior of the mass-transfer problem in, for example, polymer reaction molding.

Dynamic tension behavior of aqueous octanol solutions under constant-area and pulsating-area conditions

Dynamic tension data for 0.3 and 0.6 mM aqueous octanol solutions at 25°C and constant-area conditions were obtained and compared with previous diffusion-controlled and mixed kinetics adsorption models. The results show that tension drops more slowly than predicted by the diffusion-controlled model. The modified Langmuir-Hinshelwood equation in a mixed kinetics model describes the data quite well. Moreover, the same solutions were examined with a pulsating bubble surfactometer at 10–80 cycles min −1, with the bubble radius oscillating between 0.40 and 0.55 mm. The dynamic tension oscillates between a tension maximum γ max > γ e and a minimum γ min < γ e , where γ e is the equilibrium tension. The tension amplitude (γ max - γ min) increases with frequency, because the adsorption process is too slow to follow exactly the area changes. The amplitude decreases with increasing concentration from 0.3 to 3 mM. Phase lags between γ( t) and A( t) and low γ min can be predicted by convective-diffusion mass transfer models at spherical coordinates, or even by simple planar mass transfer models, without considering intrinsic surface rheology effects. Comparisons of pulsating-area tension data with the models indicate that intrinsic adsorption-desorption rates must be considered in the overall rate of adsorption. Certain discrepancies between the model and the data are attributed in part to measurement errors and in part to the use of the Frumkin equation of state for nonequilibrium surface densities. The results are relevant to foam generation and lung surfactants.

Calculation of the aqueous diffusion layer resistance for absorption in a tube: application to intestinal membrane permeability determination.

The single-pass intestinal perfusion technique has been used extensively to estimate the wall permeability in rats. The unbiased membrane parameters can be obtained only when the aqueous resistance is properly accounted for. This aqueous resistance was calculated numerically from a convective diffusive mass transfer model, including both passive and carrier-mediated transport at the intestinal wall. The aqueous diffusion layer resistance was shown to be best described by a function of the form, [formula: see text] where G zeta, P*m, P*c, Km, and Co are, respectively, Graetz number, passive permeability, carrier-mediated permeability, Michaelis constant, and the drug concentration entering the tube. Asterisked are dimensionless quantities obtained by multiplying the permeability constants with R/D, where R and D being radius and drug diffusivity, respectively. A, B, C, D and E were obtained by a least-squares nonlinear regression method, giving values of 1.05, 1.74, 1.27, 0.0659, and 0.377, respectively, over the range of 0.001 less than or equal to G zeta less than or equal to 0.5, 0.01 less than or equal to P*m less than or equal to 10, 0.01 less than or equal to P*c less than or equal to 10, and 0.01 less than or equal to Km/Co less than or equal to 100. This aqueous resistance was found to converge to those calculated from Levich's boundary layer solution in low Graetz range, indicating the correct theoretical limit. Using an iteration method, the equation was shown to be useful in extracting the intrinsic membrane permeability from the experimental data.

Calculation of Transport-Shifted CVD Phase Diagrams

AbstractA non-iterative method is presented for constructing CVD phase diagrams which include the systematic effects of chemical element segregation in mass-transfer controlled flow reactors. Element segregation is shown to substantially shift predicted deposit phase boundaries when the vapor/deposit interface equilibrium is calculated using the local element fractions instead of the feed gas elemental composition, as is usually done. The mass transfer analysis developed here accounts for both Fick and Soret multicomponent diffusion acting across a non-isothermal boundary layer. The gas phase is assumed to be chemically frozen, with local thermochemical equilibrium imposed only at the vapor/deposit interface (as in a cold wall reactor with a hot substrate). As a specific example, this model is applied to the chemical vapor deposition of titanium diboride from TiCl4(g), BC13(g) and H2(g) in an Ar(g) carrier gas for ceramic composite material applications. These calculations, which account for boron and titanium transport via 17 chemical species, are illustrated for a long cylindrical reactor with a resistively heated coaxial fiber deposition substrate and coaxial annular flow. However, the method presented here is general in that both the chemical system and CVD reactor geometry can be changed to any other system of interest, provided: i) adequate themochemical and thermophysical data are available, ii) the deposition rate is vapor transport controlled, and iii) convective-diffusion heat and mass transfer coefficients are estimable.

Mass Transfer at the Wall of a Thin Channel Containing an Expanded Turbulence Promoting Structure

The paper deals with convective diffusion mass transfer at one of the planar walls of a rectangular channel containing turbulence promoters constituted by an inert expanded material. Different expanded structures are studied; particularly the influence of the mesh orientation with respect to the flow direction is put in evidence. The performance obtained with the expanded structures are compared with those observed with a SU‐grid in the same experimental conditions. The results concerning the pressure drop measurements are presented and an empirical mass‐transfer correlation is established for materials having similar geometrical characteristics.

Correlation of thermophoretically-modified small particle diffusional deposition rates in forced convection systems with variable properties, transpiration cooling and/or viscous dissipation

Rational correlations are developed and presented for making engineering predictions of small particle diffusional deposition rates in the presence of thermophoresis, transpiration cooling, viscous dissipation and/or variable fluid properties. We propose and find that the effects of these phenomena on the convective-diffusion mass transfer Stanton number can be simply expressed in the product form: ▪ where the first function accounts for particle transport by convective processes normal to the deposition surface, and the second function accounts for the spatial variability of the thermophoretic drift velocity, as influenced by viscous dissipation (mainly outside of the Brownian diffusion sublayer). Correlations of this particular form, when tested against rigorous numerical boundary layer (BL) calculations, gave average errors of only 7% for all laminar BL cases (0 ⩽ Ma e ⩽ 2; 0.5 ⩽; T w / T e ⩽ 1; 0 ⩽ α T, p Le ⩽ 1.5; B ⩽ 5), and 2% for all turbulent BL cases (0.5 ⩽ T w/T e ⩽ 1; 0 ⩽ α T,p Le ⩽ 1.5; 0.9 × 10 4 ⩽ Re ⩽ 3 × 10 7; B ⩽ 5), respectively.