Solute Mass Transport Research Articles

Effects of mass transfer coefficient on pore shape in solid

The shape of a pore resulting from a nucleated bubble entrapped by a solidification front for different mass transfer coefficients is predicted in this work. Mass transfer coefficient associated with different reference concentrations is used to determine different characteristics of solute transfer rate across the cap of the pore or bubble responsible for the pore shape in solid. Pore formation and its shape in solid influence contemporary issues of biology, engineering, foods, geophysics and climate change, etc. This work extends previous models, accounting for mass and momentum transport of solute across a self-consistently determined shape of the bubble cap whose surface is satisfied by physico-chemical equilibrium beyond the solidification front, to study different mechanisms for pore formation. Mechanism of pore formation can be Case 1, which is subject to solute transport from the pore across an emerged cap through the concentration boundary layer on the solidification front into surrounding liquid in the early stage. Cases 2a and 2b are referred to opposite directions of solute transport across a submerged cap in the concentration boundary layer. In contrast to the former, the latter exhibits stronger effects of pore volume expansion on solute gas pressure in the pore than solute transport. The results show that an increase in mass transfer coefficient decreases pore radius and time for bubble entrapment in Case 1. An isolated pore cannot be found in Cases 2a and 2b, since solute concentration at the cap increases and decreases rapidly in the late stage, respectively. The predicted pore shape in solid agrees with experimental data. Mass transfer coefficient associated with solidification rate can be used to control the pore shape, which strongly depends on directions and magnitudes of solute transport.

LTA zeolite monoliths with hierarchical trimodal porosity as highly efficient microreactors for strontium capture in continuous flow

LTA zeolite monoliths (6 mm diameter, 3 cm length) featuring a hierarchical trimodal network of micro-/meso- and macropores (obtained by either controlling the nucleation step of LTA crystallization into nanocrystals or by creating mesopores into micronic crystals by using organosilane surfactant) were used for strontium capture in aqueous medium. LTA monoliths were compared to other LTA zeolite architectures: LTA microcrystals, commercial LTA beads and bimodal micro-/macroporous LTA zeolite monoliths. In batch mode, the presence of mesopores allowed to increase remarkably by a factor 15 the diffusion of ions, whereas macropores had no influence on ions transport. In flow mode, only LTA monoliths featuring flow-through macropores proved suitable as microreactors. The trimodal LTA monoliths were 1000 times more efficient than packed-beds of LTA beads, and 4 times than bimodal (micro-/macroporous) LTA monoliths due to higher rates of diffusion. Trimodal LTA monoliths were able to treat efficiently 4 L of Sr2+ solution (10 mg L−1) with 1 mL of material at a flow rate of 0.5 mL min−1 (or 1 m h−1); ie. 4200 bed volumes (BV) were efficiently treated at a flow rate of 34 BV h−1, with no Sr2+ detectable by ionic-chromatography in the effluent. This result highlights the fact that the multiscale pore architecture engineering of an adsorbent is crucial for process intensification: macropores allow uniform mass transport of solutions with low pressure drop while the generation of mesopores in zeolites leads to faster ionic transport and more efficient crystal use in cation-exchange processes, both in batch and flow modes.

Fabrication of an Induction Heated Gold Microelectrode for SECM Applications

The field of electrochemistry has traditionally focused its efforts on observing and manipulating the variables of current, voltage, concentration and time as means of probing systems of interest. However, over the course of the past several decades implementation of additional parameters has resulted in the development of several new fields including thermo-, photo-, and triboelectrochemistry. Thermoelectrochemistry in particular has attracted much attention since arbitrary temperature changes can provide several key advantages over other methods. First, thermal convection leads to a micro stirring effect which in turn improves the mass transport in solution. Second, reaction kinetics are accelerated. Third, electrode surfaces can be thermally regenerated. Fourth, temperature dependant potential shifts are unique to every species which allows separation of similar analytes thereby enhancing selectivity. Lastly, the combination of these properties leads to a greatly increased signal-to-noise ratio.1 However, using a thermostated (isothermal) cell incurs problems such as destroying thermally unstable compounds, volatilizing components, and shifts in reference electrode potentials. These drawbacks can be avoided with use of electrically heated electrodes (non-isothermal) pioneered by Gründler.2 Briefly, by applying short heating pulses with a high voltage AC frequency to a wire electrode heating is limited to the solution layer directly adjacent to the electrode surface. Therefore, a single cell can house all components of the device without problems. However, these devices are shape- and size-limited, typically employing joule heating of cylindrical wires with a diameter of 25 μm. Microelectrodes are characterized by small dimensions, relatively large diffusion areas, fast steady state achievement, and small voltage drops at fast scanning rates. These features have allowed microelectrodes to have diverse applications such as studies on corrosion, biological/cell chemistry, and kinetic studies at numerous interfaces. Microelectrodes can be used alone or incorporated into scanning electrochemical microscopes (SECM) to measure localized electrochemical systems at the liquid-liquid, liquid-gas, and liquid-solid interface.3 Fabrication of heated disk microelectrodes applicable in scanning probe microscopy techniques are limited to those developed by Baranski.4 Incorporation of a heated microelectrode into a SECM arrangement has been described as Hot-Tip SECM or HT-SECM by Boika.5 Our goal is to develop heated-tip microelectrodes compatible with SECM and other SPM imaging. We report here the fabrication of a novel induction heated gold coated steel microelectrode having a diameter of ≥ 1 μm. Briefly, a small induction coil is placed inside the electrode housing and around the steel electrode body (work piece). The induction coil is connected in parallel with a capacitor and transformer to form an LC-tank resonator. The tank is excited by sine wave (Vrms = 2.0, frequency = 500 kHz-1 MHz) to generate a heating pulse. The heating characteristics of the electrode have been evaluated by cyclic voltammetry (CV), temperature pulse voltammetry (TPV), and open circuit potentials (OCP) using the [Fe(CN)6]3−/ [Fe(CN)6]4−and other redox couples. The electrode appears capable of rapidly heating aqueous solutions to temperatures near the boiling point. Overall the device and system represent a comparatively cost effective and simple approach to prepare heated microelectrodes. [1] Gründler, P. In-Situ Thermoelectrochemistry: Working With Heated Electrodes; Springer: 2015 [2] Gründler, P.; Zerihun T.; Kirbs A.; Grabow H. Anal. Chim. Acta. 1995, 305, 232-240 [3] Bard, A. J. Scanning Electrochemical microscopy; Mirkin, M. V., Ed.; Marcel Dekker: 2001 [4] Baranski, A. S. Anal. Chem. 2002, 74, 1294−1301 [5] Boika, A. PhD. Thesis, University of Saskatchewan, 2010

Preparation of Porous Nanostructures Controlled by Electrospray

Various solid structures were prepared by electrospray technique. In this process, liquid flows out from a capillary nozzle under a high electrical potential and is subjected to an electric field, which causes elongation of the meniscus to form a jet. In our study, by controlling the amount of polyvinyl pyrrolydone in precursor solution, the jet either disrupted into droplets for the formation of spherical particles or was stretched in the electric field for the formation of fibers. During the electrospray process, the ethanol solvent was evaporated and induced the solidification of precursors, forming solid particles. The evaporation of ethanol solvent also enhanced the mass transport of solutes from the inner core to the solid shell, which facilitated fabrication of porous and hollow structure. The network structures were also prepared by heating the collector.

Non-equilibrium thermodynamic model for calcium carbonate supersaturated solutions of high salinity

Based on principles of non-equilibrium thermodynamics, the behavior of calcium carbonate supersaturated solutions of high salinity is studied. For this purpose, these solutions are treated as continuous media whose physicochemical properties change in space and time. Furthermore, by exploiting the Muller–Liu formulation for the second law of thermodynamics, one recognizes which thermodynamic forces are responsible for keeping the \(CaCO_{3}\) supersaturated solutions out of equilibrium. The obtained results suggest that intermolecular interaction forces play an important role in the dynamics of solution, as well as in the mass transport of solutes. Particularly, from the estimated values for the self-diffusion and mutual diffusion coefficients of NaCl(aq), \(CaCl_{2}(aq)\), and \(Na_{2}CO_{3}(aq)\), one discusses whether changes in the concentration of NaCl(aq) may affect the mass transport of \(Na_{2}CO_{3}(aq)\) and \(CaCl_{2}(aq)\) in calcium carbonate supersaturated solutions. The results of this work may be helpful to understand better the influence of diffusive processes and intermolecular interaction forces on the dynamics of calcium carbonate supersaturated solutions of high salinity.

43. Cell-based modeling of mechanical and chemical stress in tissues during cryoprotocols

Since Mazur’s work a half century ago, modeling of the biophysical processes of single cell cryopreservation has been successful in providing a theoretical groundwork for cryopreservation induced damage hypotheses. Important contributions have included both biophysical explanations of osmotic damage during CPA equilibration due to too aggressive or overly conservative equilibration strategies and estimation of cell injury due to intracellular ice formation through simple or complex ice-growth models. Follow up work by Mazur, Liebo and Chu presented the archetypical single cell protocol optimization using modeling, and subsequent investigators have for the most part followed in their footsteps with more sophisticated models of mass transport, cell damage and ice growth. Expanding on this work, a number of investigators have modeled unique damage pathways for cryopreserved tissues, raising important and challenging questions while providing steps towards optimal protocols. Models have included spatially dependent heat and mass transport, solidification fronts, and thermal and mechanical stresses, and a few models have combined tissue level transport with cell level damage estimators in sparsely celled articular cartilage and in simple spherically symmetrical tissue types. Most tissue modeling paradigms are cell unaware until modeling is complete: either cells are ignored in a continuum hypothesis, or are overlaid in a one-way model of tissue level transport to cell interaction. This approach precludes modeling a number of important cryobiological endpoints that are well understood at the single cell level including cell-to-cell mass transport, intercellular ice propagation, and strains on intercellular adhesion. As computational capabilities increase, cell- or agent-based multiscale modeling paradigms are becoming more realistic for understanding cell interactions, growth, and death in vivo. In these models cell interactions with their environment including cell–cell adhesive forces, transport, and growth and death through a number of mechanisms can be modeled in conjunction with classical heat and mass transport of critical solutes. Importantly from the cryobiological perspective, this approach allows modeling of cell-level tissue damage due to osmotic volume regulation, cell-to-cell ice propagation, and excitingly, the impacts of accumulated damage due to the cryopreservation process on post implantation survival at the single cell level via modeling of apoptotic, necrotic and other pathways. Here we summarize classical tissue cryopreservation modeling and successful approaches to individual cell damage modeling and optimization, and present our vision for the future of tissue and organ cryopreservation modeling and optimization.

Generalized method for determining fluoroacidity by electrochemical diffusion coefficient measurement (application to HfF4)

A universal method for fluoroacidity evaluation was developed and based on a mass transport approach: it simply consists in measuring the diffusion coefficient of an electroactive species in various molten media. The reduction behaviour of Hf(IV) ions was investigated in molten fluorides and diffusion coefficients of Hf(IV) ions were measured. Results showed that diffusion coefficients decrease with fluoroacidity, due to the effect of solvent viscosity (which is linked to bridged fluorines). A global approach of mass transport in solution was then proposed, taking into account both solute and solvent. The Schmidt number (Sc) defined as the ratio between solvent viscosity and solute diffusivity was calculated in order to take into account these two parameters. Results showed that Sc increases with fluoroacidity, in a much more sensitive way than D. This universal method can extended to all electroactive species and to all bath fluoroacidity.

Process-scale modelling of microstructure in direct chill casting of aluminium alloys

The mechanical properties of an alloy being related to its microstructure, the understanding of the mechanisms responsible for the grain structure formation in direct chill casting is crucial. However, the grain size prediction by modelling is difficult since a variety of multi-scale coupled phenomena have to be considered. Nucleation and growth of the grains are interrelated, and the macroscopic transport phenomena such as the motion of grains and inoculant particles with the flow impact the nucleation-gowth competition. Thus we propose to study the grain size distribution of a 5182 alloy industrial scale slab of 510 mm thickness, both non-inoculated and inoculated with Al-3Ti-1B, for which experimental grain size measurements are available. We use a volume-averaged two-phase multi-scale model that describes nucleation from inoculant particles and grain growth, fully coupled with macroscopic transport phenomena: fluid flow induced by natural convection and solidification shrinkage, heat, mass and solute mass transport, grains and inoculant particles motion. We analyze the effect of liquid and grain motion as the effect of grain morphology on microstructure formation and we show in which extent those phenomena are responsible for the grain size distribution observed experimentally. The effect of the refiner level is also studied.

Whispering gallery mode resonators for rapid label-free biosensing in small volume droplets.

Rapid biosensing requires fast mass transport of the analyte to the surface of the sensing element. To optimize analysis times, both mass transport in solution and the geometry and size of the sensing element need to be considered. Small dielectric spheres, tens of microns in diameter, can act as label-free biosensors using whispering gallery mode (WGM) resonances. WGM resonances are sensitive to the effective refractive index, which changes upon analyte binding to recognition sites on functionalized resonators. The spherical geometry and tens of microns diameter of these resonators provides an efficient target for sensing while their compact size enables detection in limited volumes. Here, we explore conditions leading to rapid analyte detection using WGM resonators as label-free sensors in 10 μL sample droplets. Droplet evaporation leads to potentially useful convective mixing, but also limits the time over which analysis can be completed. We show that active droplet mixing combined with initial binding rate measurements is required for accurate nanomolar protein quantification within the first minute following injection.

Reaction and Mass Transport Simulations by LBM in Electrolyte of Aqueous Lithium-Air Battery

The aqueous lithium–air battery receives much attention because of its high theoretical energy density; however, it is necessary to clarify the reaction and mass transport of the electrolytic solution in efforts to obtain much higher current density. In this study, numerical simulation employing the lattice Boltzmann method realized coupled simulation of transport phenomena of Li+ and O2 in the discharge process. The numerical results suggest the importance of supplying the electrolyte with sufficient O2 to achieve discharge with high current density. The results of simulation indicate that a high-pressure O2 supply and increased area of the air/electrolyte interface are effective solutions to realizing discharge with high current density.

A rotating disk study of the photocatalytic oxidation of p-nitrophenol on phosphorus-modified TiO2 photocatalyst

After discussing the general aspects of photocatalytic oxidation of organic compounds in aqueous solutions and the application of the rotating disk theory to (photo)catalytic phenomena, we report the oxidation of p-nitrophenol (PNP) on illuminated phosphorus modified TiO2 (P-TiO2) and TiO2 photocatalysts under controlled hydrodynamic conditions. We found that the performance of the oxygen transfer reaction can be described considering mass transport in solution and surface reaction according to Langmuir–Hinshelwood kinetics. From analysis of the dependence of the reaction rate on the rotation rate, we obtained the apparent organic–photocatalyst adduct interaction constant K, the rate constant k of the surface reaction between adsorbed PNP and hydroxyl radicals, and the diffusion coefficient D of PNP in solution. The results showed that degradation of PNP using P-TiO2 and UV light was readily possible, with reaction half-lives significantly lower than those obtained using pristine TiO2 photocatalyst.

Reaction and Mass Transport Simulations By LBM in Electrolyte of Aqueous Lithium-Air Battery

The aqueous Lithium-air battery receives much attention because of its large theoretical energy density; however, clarification of reaction and mass transport of electrolytic solution is necessary toward practical use [1]. In this study, Lattice Boltzmann Method (LBM) was made to realize coupled simulation of transport phenomena of Li+ and O2 under discharge process. The numerical results suggested the importance of supplying sufficient O2 in the electrolyte to achieve high current density discharge.Structure of aqueous Lithium-air battery and calculation area are shown in Fig. 1. In this study, we focused on mass transport in the electrolyte (1M LiCl aq) and employed two-dimensional calculation area. Through the calculation, constant Li+ flux was set on the end of anode side. O2 concentration at the end of cathode side (air/electrolyte interface) was defined as saturation solubility (8.45×10-6 g/cm). Periodic boundary condition in the y direction of the computational domain was imposed. Shape of the carbon porous layer was simplified and three rectangles were set as electrode. O2 and Li+ are consumed on the electrode surface along with the discharge reaction. Ion transport and electric potential distribution were simulated by LBM with using two-dimensional 9 velocities (2D9Q) model [2] and considering the effect of electric field.Figure 2 shows the results of concentration distribution of Li+ and O2 in 0.1 mA/cm2 discharge process. It was found that sufficient Li+ is supplied for all of electrode surface during discharge process. On the other hand, the distribution of O2 shows quite low concentration.Since the O2 concentration in the electrolyte decreases significantly with the discharge, we focus on the relationship between local reaction rate on the electrode and O2 concentration. Figure 3 indicates x-directional distributions of them at y = 30 mm (see Fig. 1).In case of 0.1 mA/cm2 (see Fig. 3(a)), the O2 concentration near the anode side is reduced to less than 50% of the solubility; however, the O2 is supplied to three of electrodes. As a result, discharge reaction occurs at all electrode surfaces and then local reaction rate shows pulsed shape distribution because reaction occurs on the electrode surface.When the current density is increased to 0.5 mA/ cm2, O2 concentration decreased remarkably near the air/electrolyte interface as shown in Fig.3 (b). O2 concentration is almost zero in the Anode side (0 < x <570 mm). Supplied amount of O2 is seriously insufficient for discharge reaction in this calculation model because the O2 solubility is quite small in the electrolyte, and distance from air/electrolyte interface to electrode is far. As a result, the most of O2 is consumed at the electrode close to air interface and the reaction rate is significantly high. Thus, all of the electrodes are not used efficiently.The presented results indicate that O2 supply from the air/electrolyte interface became insufficient and it defined critical current density of the battery. Supplying sufficient O2 in the electrode surface by increasing the air interface is one of the effective solutions. The use of high-pressure O2 is also an important method in achieving the high current density because O2 solubility in the electrolyte can be increased by pressure control. Acknowledgement The authors would like to thank Prof. Imanishi from Mie University for his assistance with the experimental study of aqueous Lithium-air battery.

First-Passage-Time Kinetic Monte Carlo Simulation of Nucleation and Growth in Electrodeposition

Nucleation and growth are the fundamental processes in electrochemical phenomena, which are influenced by many factors in solution and electrode surface. Important issues in electrochemical engineering such as controlling dendrite formation or single crystal production must be considered based on the understanding of nucleation process since precursors of large scale structures of deposited films are expected to appear in the early stage of nucleation.Kinetic Monte Carlo (KMC) method is widely used to study electrodeposition and crystal growth, which are categorized as “diffusion-reaction system”. This system consists of many diffusing particles (reactants). When two (or more) particles collide with each other, some reaction occurs. In crystal growth, for example, the reactants are adatoms deposited on crystal surface and the reaction is the nucleation as a result surface diffusion. KMC method is a direct and commonly used simulation method for diffusion-reaction systems. The direct KMC method, however, becomes inefficient when the concentration of the reactants becomes low and a large number of hops have to be simulated before a reaction occurs. In order to overcome this problem, a first-passage-time KMC (FPKMC) method has been developed by Oppelstrup, et. al. [1] In the FPKMC method, an area is assigned to each particle which includes only one reactant, and an analytical solution is used to derive the distribution function of the first-passage time which is defined as the time when the particle reaches the boundary of the area for the first time. A particle is moved to the boundary of the area following the FPT distribution function skipping many hops. The FPKMC is an efficient and exact method to realize fast simulation of diffusion-reaction systems. In the work of Oppelstrup et. al., a continuous diffusion model is used to derive the FPT distribution function. [1, 2] Bezzola et. al. extended the FPKMC method to a discrete lattice to simulate crystal growth. [3, 4] In Bezzola’s work, solution is not explicitly included in the model.The purpose of the present work is to study the nucleation and growth in the electrochemical systems by developing the hybrid method of FPKMC and ordinary KMC methods. The reactants are metal ions which are electrodeposited on the electrode surface. The nucleation occurs when the surface adatoms collide after surface diffusion. The mass transport of ions in solution is also taken into account. The surface diffusion and nucleation, which are the time-consuming part of the simulation, are simulated by the FPKMC method. The mass transport and reaction in solution are simulated by the ordinary KMC method. We first confirmed that the computing time is greatly reduced by applying FPKMC compared to conventional KMC method. Using the hybrid method, we study the correlation between the microscopic nucleation process and the resulting large scale crystal structure. The influence of solution structure on nucleation and growth is also discussed.

Mass transfer of a neutral solute in porous microchannel under streaming potential

The mass transport of a neutral solute in a porous wall, under the influence of streaming field, has been analyzed in this study. The effect of the induced streaming field on the electroviscous effect of the fluid for different flow geometries has been suitably quantified. The overall electroosmotic velocity profile and expression for streaming field have been obtained analytically using the Debye-Huckel approximation, and subsequently used in the analysis for the mass transport. The analysis shows that as the solution Debye length increases, the strength of the streaming field and, consequently, the electroviscous effect diminishes. The species transport equation has been coupled with Darcy's law for quantification of the permeation rate across the porous wall. The concentration profile inside the mass transfer boundary layer has been solved using the similarity transformation, and the Sherwood number has been calculated from the definition. In this study, the variation of the permeation rate and solute permeate concentration has been with the surface potential, wall retention factor and osmotic pressure coefficient has been demonstrated for both the circular as well as rectangular channel cross-section.

Seeking effective dyes for a mediated glucose–air alkaline battery/fuel cell

A significant level of power generation from an abiotic, air breathing, mediated reducing sugar–air alkaline battery/fuel cell has been achieved in our laboratories at room temperature without complicated catalysis or membrane separation in the reaction chamber. Our prior studies suggested that mass transport limitation by the mediator is a limiting factor in power generation. New and effective mediators were sought here to improve charge transfer and power density. Forty-five redox dyes were studied to identify if any can facilitate mass transport in alkaline electrolyte solution; namely, by increasing the solubility and mobility of the dye, and the valence charge carried per molecule. Indigo dyes were studied more closely to understand the complexity involved in mass transport. The viability of water-miscible co-solvents was also explored to understand their effect on solubility and mass transport of the dyes. Using a 2.0 mL solution, 20% methanol by volume, with 100 mM indigo carmine, 1.0 M glucose and 2.5 M sodium hydroxide, the glucose–air alkaline battery/fuel cell attained 8 mA cm–2 at short-circuit and 800 μW cm–2 at the maximum power point. This work shall aid future optimization of mediated charge transfer mechanism in batteries or fuel cells.

Modeling mass transfer using surface morphology in full-scale reverse osmosis membrane processes

The influence of surface characteristics on membrane process performance is considered significant and is not well understood. Current mass transport models generally assume constant mass transfer coefficients (MTCs) based on a homogeneous flat surface. This study evaluated membrane mass transfer by incorporating surface morphology into a diffusion-based model assuming that the MTCs are dependent on the thickness variation of the membrane’s active layer. Concentration polarization is also affected by this nonuniform surface property and was incorporated into the model. A simulation was performed using parameters from a full-scale 4.5 million gallon per day brackish water reverse osmosis membrane process. The process was simulated by modeling one thousand uniform slices of the membrane channel and the permeate water quality was determined locally through a finite difference approach. It was determined that solute mass transport is controlled by diffusion in the nonhomogeneous thinner regions (membrane valleys) of the active layer. This nonuniform surface affected the concentration polarization layer, where more solutes tended to accumulate within the valleys than on the ridges. Prediction of the permeate total dissolved solids concentration was accurate, ranging between 5 and 15%, as measured as an average percent difference between predicted and actual values.

Solute transport with longitudinal and transverse diffusion in temporally and spatially dependent flow from a pulse type source

Molecular transverse diffusion through unsteady and heterogeneous medium is accounted for in solute mass transport originating from a uniform pulse-type stationary point-source. The corresponding two-dimensional advection–dispersion equation with variable coefficients is solved by the explicit finite difference method. The heterogeneity of the medium is described by a position dependent linear non-homogeneous expression for velocity with unsteady exponential variation with time. Variation of the dispersion parameter due to heterogeneity is considered proportional to square of the velocity. Results are compared to analytical solutions reported in the literature and good agreement is found. The explicit finite difference method is shown to be effective and accurate for solving the related two-dimensional advection–dispersion equation with variable coefficients in semi-infinite media, which is especially important when arbitrary initial and boundary conditions are required.

Effects of non-Newtonian power law rheology on mass transport of a neutral solute for electro-osmotic flow in a porous microtube.

Mass transport of a neutral solute for a power law fluid in a porous microtube under electro-osmotic flow regime is characterized in this study. Combined electro-osmotic and pressure driven flow is conducted herein. An analytical solution of concentration profile within mass transfer boundary layer is derived from the first principle. The solute transport through the porous wall is also coupled with the electro-osmotic flow to predict the solute concentration in the permeate stream. The effects of non-Newtonian rheology and the operating conditions on the permeation rate and permeate solute concentration are analyzed in detail. Both cases of assisting (electro-osmotic and poiseulle flow are in same direction) and opposing flow (the individual flows are in opposite direction) cases are taken care of. Enhancement of Sherwood due to electro-osmotic flow for a non-porous conduit is also quantified. Effects if non-Newtonian rheology on Sherwood number enhancement are observed.

A Microscopic Multiphase Diffusion Model of Viable Epidermis Permeability

A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯epi, and partition coefficient, K¯epi/w, for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes—water, L-glucose, and hydrocortisone—covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes.

Development of a transient model for the desalination of sea/brackish water through reverse osmosis

ABSTRACT Mathematical models that adequately represent steady state and transient behaviour of desalination process comprising of equalisation tank, reverse osmosis (RO) system using a constant rate of transfer of diffusing substance per unit area of the cylinder surface and a potable water tank system are developed. A solute mass transport model is solved using the partial differential equation parabolic elliptical numerical technique using Crank–Nicholson method is inbuilt. Solution of this model shows decline in the permeate flux in the RO membrane. The theoretical transient and steady state models are compared with experimental results. The comparison shows that both the transient and steady state models are matching with the experimental results. A Transfer function model has also been developed to represent input–output relations. The decrease in flux in the RO membrane was compared with the experimental results.