Liquid Boundary Layer Research Articles

Phosphorus distribution between potassic alkali feldspar and metaluminous haplogranitic liquid at 200 MPa (H2O): the effect of undercooling on crystal–liquid systematics

To evaluate the applicability of P2O5 concentration in potassic alkali feldspar as a monitor of P2O5 in melt for undercooled systems, crystal–melt partitioning for P was evaluated via feldspar growth experiments in P-bearing ((3 wt% P2O5), water-saturated haplogranitic liquids at 200 MPa, with liquidus undercoolings (ΔT) of 25, 50, 100, 200, and 300°C. Increasing undercooling in the range ΔT=25–200°C shows an evolution of crystal morphologies, from euhedral and well-filled individuals at ΔT=25–50°C to radial clusters with increasingly skeletal habit at greater undercooling. Experiments at ΔT=100–200°C also document the development of P- (up to (9 wt% P2O5) and Si-enriched, more alkaline boundary layers adjacent to crystals. Experiments at ΔT=300°C show an additional change in crystallization fabric in which spherulites of skeletal crystals form in open (vapor) space created by the dissolution of bulk silicate, and compositional boundary layers are not observed. We interpret the changes in reaction products at ΔT=300°C to indicate conditions below a glass transition; hence, partition coefficients were not determined for this undercooling. Values of K d(P)Kfs/melt from experiments at ΔT=25–200°C, calculated from pairs of crystal and immediately adjacent liquid compositions (including boundary layers at higher undercooling), are mostly in the range of 0.25–0.55 and show no effective change with increased undercooling. Essentially no change in K d(P)Kfs/melt with undercooling apparently stems from an interplay between boundary layer composition and a change in the substitution mechanism for P in feldspar from AlPSi−2, common in peraluminous to metaluminous liquids near equilibrium, to increasing proportions of ([ ],P)(M+,Si)−1 with increased undercooling. Bulk glass and liquid beyond boundary layers in experiments with significant percentages of crystallization are homogeneous, and show pronounced fractionation primarily due to the removal of an orthoclase component. Because crystallization was still in progress in experiments with ΔT≤200°C, compositional homogeneity in the bulk liquid requires extremely rapid diffusion of most haplogranite components (Na, K, and Al), apparently resulting from chemical potential gradients stemming from the removal of components from the liquid by crystal growth. Similar homogeneity and bulk fractionation in experiments with ΔT=300°C requires rapid diffusive equilibration for the alkalis even at temperatures below an apparent glass transition. Unlike the haplogranite components, P is only concentrated in liquid boundary layers (ΔT≤200°C) or low-density aqueous vapor (ΔT=300°C) adjacent to crystals. Hence, the P2O5 contents of melt inclusions likely are not representative of bulk melt concentrations in significantly undercooled systems (ΔT≤50–100°C).

Separation of Organic Compounds from Surfactant Solutions by Pervaporation. The Influence of a Micellar Phase on Mass Transfer

Abstract Volatile organic compounds (VOCs) can be separated from aqueous micellar surfactant solutions with high efficiency by pervaporation processes using organophilic polymer membranes. This seems to be a surprising result because the transmembrane flux of a VOC strongly depends on its volatility, which is rather low in the presence of a surfactant at concentrations far above the critical micellar concentration. Based on results of equilibrium measurements in micellar systems and pervaporation experiments, a theoretical analysis of the mass transfer is given. It is shown that the mass transfer for VOCs in the liquid boundary layer of a pervaporation membrane in the presence of a micellar phase cannot be described by molecular diffusion processes alone. Obviously, the mass transfer is enhanced considerably by diffusing micelles which transport the solubilized VOC molecules in direction to the surface of the membrane.

Effects of concentration, temperature, and coupling on pervaporation of dilute flavor organics

Pervaporation is a novel method to extract flavor organics from dilute distillates and extracts. Selection of operating conditions and membranes is critical for the process design and scale-up. In the current study, the effects of feed concentration and operating temperature on membrane separation performance were investigated. Four polydimethyl siloxane (PDMS) membranes and one polyoctylmethyl siloxane (POMS) membrane were tested for pervaporation and their separation performances were compared. Flavor loss rate due to evaporation was determined from a batch operation experiment. Experimental study was extended from single component to multicomponent (ethyl butyrate, trans-2-hexenal, benzaldehyde, cis-3-hexenol, phenethyl alcohol, and methyl anthranilate) mixtures that resembled real flavor systems. The total mass transfer resistance was divided into two parts: one in the liquid boundary layer and the other in the membrane. Specific mass transfer driving forces and resistances were defined based on the nonequilibrium thermodynamic formalisms. Using the concentration polarization model, the liquid boundary layer thickness on the feed side and the intrinsic membrane permeance were calculated for various pervaporation systems. The effects of operating conditions and membrane properties on concentration polarization were analyzed. It was concluded that the boundary layer thickness was affected not only by the bulk flow parallel to the membrane surface, but also by the permeation flow perpendicular to the membrane surface. When separation performances of multicomponent systems were compared to those obtained from single component systems, no obvious coupling effects were detected for the pervaporation of dilute multiple flavor organics. It was, thus, concluded that no coupling terms need to be included in the mass transfer equations for dilute flavor pervaporation. Therefore, same flux equations and concentration polarization models can be applied to both single- and multi-component pervaporation systems.

Verification of mass transfer simulation with CFD using highly accurate solutions

Computational fluid dynamics (CFD) is a powerful tool used for a wide range of simulations for industry processes and agricultural operations that typically involve some sort of fluid flows. In this application note, we demonstrated how we employed a commercial CFD package (FLUENT ® 6.0 with GAMBIT ® 2.0) to set up a prediction model of the solute concentration distribution in the liquid boundary layer of a slit pervaporation membrane channel and verified the numerical methodology with the analytical solution to a classic diffusion problem. The general principle of our approach is applicable to any mass transfer simulation with commercial CFD software packages.

Boundary layers of aqueous surfactant and block copolymer solutions against hydrophobicand hydrophilic solid surfaces

The boundary layer of aqueous surfactants and amphiphilic triblock copolymers against flatsolid surfaces of different degrees of hydrophobicity was investigated by neutronreflectometry (NR), grazing incidence small angle neutron scattering (GISANS) and atomicforce microscopy (AFM). Solid substrates of different hydrophobicities were prepared byappropriate surface treatment or by coating silicon wafers with polymer films of differentchemical natures. For substrates coated with thin films (20–30 nm) of deuteratedpoly(styrene) (water contact angle ), neutron reflectivity measurements on the polymer/water interface revealed a waterdepleted liquid boundary layer of 2–3 nm thickness and a density about 90% of the bulkwater density. No pronounced depletion layer was found at the interface of water against aless hydrophobic polyelectrolyte coating (). It is believed that the observed depletion layer at the hydrophobic polymer/waterinterface is a precursor of the nanobubbles which have been observed by AFM at thisinterface.Decoration of the polymer coatings by adsorbed layers of nonionicCmEn surfactants improves their wettability by the aqueous phase at surfactantconcentrations well below the critical micellar concentration (CMC) ofthe surfactant. Here, GISANS experiments conducted on the systemSiO2/C8E4/D2O reveal that there is no preferred lateral organization of theC8E4 adsorption layers.For amphiphilic triblock copolymers (PEO–PPO–PEO) it is found that under equilibriumconditions they form solvent-swollen brushes both at the air/water and the solid/waterinterface. In the latter case, the brushes transform to uniform, dense layers after extensiverinsing with water and subsequent solvent evaporation. The primary adsorption layersmaintain properties of the precursor brushes. In particular, their thickness scales withthe number of ethylene oxide units (EO) of the block copolymer. In the caseof dip-coating without subsequent rinsing, surface patterns of the presumablycrystalline polymer on top of the primary adsorption layer develop upon drying undercontrolled conditions. The morphology depends mainly on the nominal surfacecoverage with the triblock copolymer. Similar morphologies are found on bare andpolystyrene-coated silicon substrates, indicating that the surface patterning is mainlydriven by segregation forces within the polymer layers and not by interactions with thesubstrate.

Numerical Simulation of Concentration Polarization in a Pervaporation Module

A mathematical model was developed to describe mass transfer in a slit flow channel formed by a thin supported membrane at the bottom and an impermeable stainless steel block at the top in a lab‐scale flat sheet pervaporation membrane module. Boundary layer theory was employed to obtain the mass transfer equations governing mass transport in the liquid boundary layer and in the membrane matrix. Equations of the model were solved numerically with computational fluid dynamics (CFD) techniques. The extent of concentration polarization and its impact upon permeation flux rate under different conditions were examined.

Ultrasonic studies of the characteristics of the structural material-heavy liquid metal coolant boundary layer

Ultrasonic studies of the characteristics of the structural material-heavy liquid metal coolant boundary layer

CFD modeling of pervaporative mass transfer in the boundary layer

Modeling mass transfer in the liquid boundary layer accounting for concentration polarization in pervaporation (PV) is particularly challenging since there is no practical way of experimentally determining solute concentration at the membrane surface. We have developed a computational fluid dynamics (CFD) approach to describe not only velocity distribution but also concentration profile in the liquid boundary layer of a slit membrane channel. The satisfactoriness of the numerical methodology used in CFD for obtaining concentration profiles were verified using a classic diffusion problem with its known analytical solution. The overall mass transfer coefficients from the numerical study were also compared with those from the experiment.

Concentration of dilute flavor compounds by pervaporation: permeate pressure effect and boundary layer resistance modeling

Pervaporation experiments with flat sheet PDMS–PVDF composite membranes were carried out at ambient temperature (20–22 °C) to concentrate three flavor compounds (ethyl butyrate, benzaldehyde, and trans-2-hexenal) from dilute aqueous solutions. Due to the different thermodynamic properties (saturated vapor pressure and activity coefficient) of these flavor compounds, the effects of downstream permeate pressure on the organic flux and the enrichment factor varied. The results were correlated with simple mass transfer equations. The organic and water fluxes at different feed flow rates were measured. The feed flow rate had negligible effect on the water flux because of the dilute solute concentration in the feed solution. However, for the organic flux, the significant effect of the feed flow rate proved the existence of a mass transfer boundary layer on the membrane feed side. A concentration polarization model derived from a steady state flux equation was used to calculate the liquid boundary layer thickness on the feed side and the organic mass transfer coefficient in the membrane. Using the resistance-in-series model, the mass transfer resistance of the liquid boundary layer was separated from the mass transfer resistance of the membrane. It was clearly shown in this work that the mass transfer resistance of the boundary layer was controlled by hydrodynamic conditions, while the varying degrees of flavor concentration results were mainly due to the different thermodynamic properties.

Influence of mass transfer and chemical reaction on ozonation of azo dyes

Azo dyes can be only mineralised by chemical oxidation. In this paper the oxidation of Reactive Black 5 (RB 5) and Reactive Orange 96 (RO 96) with concentrations between 35 and 5,700 mgL(-1) (RB 5) and between 20 and 2,050 mgL(-1) (RO 96) was investigated in a lab-scale bubble column. The reactor was modelled for two cases, a completely mixed and a plug flow gas phase. The oxidation rate was influenced by mass transfer for all dye concentrations used. For low dye concentrations mass transfer alone was decisive for the reaction rate showing no enhancement due to chemical reaction, E approximately equal to 1. However, in the region of high dye concentrations, the slope of the ozone concentration profile inside the liquid boundary layer increases more and more with increasing dye concentration as a result of a chemical oxidation. Therefore, the enhancement factor depends on the type and concentration of the azo dyes. For RB 5, a diazo dye, an enhancement factor of E = 5.5 was observed for cd = 2,000 mgL(-1), RO 96, a mono azo dye, with a remarkably higher chemical oxidation rate shows an E = 16 for cd = 2,050 mgL(-1).

Kinetics of In-situ formation of AlN in Al alloy melts by bubbling ammonia gas

In-situ processing of AlN-Al alloy composites by the gas bubbling method was investigated using ammonia as the gaseous precursor in the temperature range of 1373 to 1523 K. The products were characterized using X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray microanalysis. It was found that in-situ formation of AlN reinforcing particles was feasible by bubbling ammonia through aluminum and aluminum alloy melts. The AlN particles formed in situ were small in size and enriched in the top part of the product formed in the crucible. In comparison with the purified nitrogen bubbling gas, using ammonia as the nitrogen precursor enhanced the formation of AlN. Hydrogen gas generated from the dissociation of ammonia is an effective oxygen getter in the system, which can offset the deleterious effect of oxygen impurities and enhance the formation of AlN. The rate of formation of AlN was controlled by the diffusion of nitrogen atoms in the liquid boundary layer. A kinetic model was developed to describe the rate of formation of AlN, which was in excellent agreement with the experimental results. The influence of various processing variables on the rate of formation of AlN were also investigated. The rate of formation of AlN changed little with the content of silicon in the matrix melt, increased slightly with increase in temperature and decrease in nozzle size, and increased significantly with the increasing gas flow rate.

The Origin of Basic-Ultrabasic Sills with S-, D-, and I-shaped Compositional Profiles by in Situ Crystallization of a Single Input of Phenocryst-poor Parental Magma

An attempt is made to develop an in situ crystallization model based on the concept of Soret fractionation to explain the origin of commonly observed S-, D-, and I-shaped compositional profiles in sills formed from a single pulse of phenocryst-poor parental magma. The model envisages that the various compositional profiles observed in sills can be interpreted in terms of different combinations of four principal units—Basal Zone and Layered Series forming the floor sequence, and Top Zone and Upper Border Series constituting the roof sequence. The Basal and Top Zones represent mirror images of the Layered and Upper Border Series, respectively, and therefore are referred to as basal and top reversals. It is proposed that the formation of basal and top reversals takes place through the non-equilibrium Soret differentiation of liquid boundary layers which form as a consequence of the temperature gradient imposed by the cold country rock. In contrast, the Layered and Upper Border Series originate predominantly through the crystal–liquid boundary layers developing in equilibrium conditions. The model permits the production of S-, D-, and I-shaped compositional profiles from the same magma composition. All that is necessary to produce a specific shape of compositional profile is an appropriate temperature gradient imposed by the cold country rock on the liquid boundary layers of a parental magma of a given composition.

The Origin of Marginal Compositional Reversals in Basic-Ultrabasic Sills and Layered Intrusions by Soret Fractionation

Marginal reversals—a common feature of many basic differentiated igneous bodies regardless of their size and bulk composition—are remarkable in being a mirror of the Layered Series. These are distinguished by: (1) an apparent lack of mass balance between the lower part of the marginal reversals, including chilled margins, and the bulk composition of the intrusions; (2) mineral crystallization sequences and (3) mineral compositional trends, which are both essentially the opposite of those in the Layered Series; (4) the cotectic composition of rocks composing the marginal reversals; (5) the capacity to form from both phenocryst-rich and phenocryst-free parental magmas; (6) the capability to develop along the floor, subvertical walls and even the roof of magma chambers. None of the current models of magma chamber evolution can provide an adequate explanation for the characteristic features of the marginal reversals. The problem can be resolved in the context of a model combining Soret diffusion in thin liquid boundary layers at the magma chamber margins and vigorous convection in the main magma body. The key proposal is that the formation of marginal reversals takes place through the non-equilibrium evolution of liquid boundary layers as a result of a temperature gradient imposed by the cold country rock. The fundamental explanation for the mirror image of a marginal reversal is that the non-equilibrium Soret fractionation works in a manner opposite to that of the equilibrium crystal–liquid fractionation that produces the Layered Series.

Profiling concentration gradient in a tubular membrane pervaporation module: a modeling approach

Concentration gradient appears in as flow tube formed by the pervaporation membrane as a result of different diffusion rates of permeating species in the liquid boundary layer and in the membrane matrix. The occurrence of this phenomenon is sometimes considered detrimental to pervaporative separations resulting in decrease in trans-membrane flux. Thus, the ability to describe the concentration gradient in the pervaporation membrane module is highly desirable in process design and optimization. A mathematical model was developed to illustrate the interplay between concentration gradient and the process performance in pervaporation operation. Incorporating pervaporative mass transfer, laminar hydrodynamics, and boundary layer theory, the model allows speedy analysis of the sensitivity of process parameters and concentration gradient upon trans-membrane flux.

Temperature polarization in pervaporation

The incidence of temperature polarization has received considerable attention in membrane processes such as membrane distillation and thermoosmosis but has been much less investigated in pervaporation. Based on a theoretical computation on a case study (pervaporation of water through a dense cellulose acetate membrane), it has been confirmed that this phenomenon is likely to occur frequently, as soon as a thin and permeable membrane is used, with the temperature drop being located essentially in the liquid boundary layer. Experimental investigations on the importance of temperature polarization and its influence on pervaporation flux have been further performed with pure liquids (water and organic compounds) by changing the impeller agitation rate in a batch stirred cell. Different membrane materials (cellulose acetate, Cuprophan, PDMS, PEBA) and various liquids (water, ethanol, butanol, pentanol, ethyl propionate) were investigated in order to point out the influence of either liquid or membrane material physicochemical properties on the temperature polarization effect. A simplified data treatment of the observed results, derived from theoretical computations, is proposed and discussed.

Modelling selective H 2S absorption and desorption in an aqueous MDEA-solution using a rate-based non-equilibrium approach

A rate-based algorithm was used to yield a predictive tool for MDEA gas scrubbing processes. The model adopts the two-film theory, assuming that thermodynamic equilibrium exists only at the gas–liquid interphase, but not in the boundary layers, where temperature and concentration gradients are present. Correspondingly chemical equilibrium among the reacting species in the liquid phase is assumed for the bulk phase, but not for the liquid boundary layer. Mass transfer is modelled using calculated mass transfer coefficients in combination with an enhancement model to account for the chemical reactions. Correlations for geometric data, like hold-up and interfacial area, and for reaction rates are provided to give reliable results. The latter correlations are also used to describe the desorption process, which is calculated with an equilibrium approach, considering the kinetics of CO 2 desorption. The so obtained tool is tested against measurements done recently by Lurgi GmbH at a commercially operated selective MDEA plant in Germany. A closed absorption and desorption loop was build up using Aspen RATEFRAC™, capable of modelling the whole process with all necessary equipment.

Non-degradable microparticles containing a hydrophilic and/or a lipophilic drug: preparation, characterization and drug release modeling

Non-degradable microparticles based on ammonio methacrylate copolymers (Eudragit RS:RL 4:1 blends) containing the hydrophilic drug propranolol HCl and/or the lipophilic drug nifedipine were prepared with an oil-in-water (O/W) and a water-in-oil-in-water (W/O/W) solvent evaporation technique. Both drugs were successfully incorporated separately as well as simultaneously. In all cases, the resulting release rate(s) of the drug(s) was/were found to be controlled over periods of at least 8 h. To elucidate the underlying mass transport mechanisms, the microparticles were thoroughly characterized by X-ray powder diffractometry, differential scanning calorimetry, particle size analysis, and determination of the actual drug loading(s). Analytical solutions of Fick’s second law of diffusion considering non-steady state conditions were used to describe the release of propranolol HCl. Interestingly, the resistance for drug release within the unstirred liquid boundary layers on the surfaces of the microparticles was found to be negligible compared to the diffusional resistance within the polymeric devices. Importantly, the mathematical theories could be used to normalize the experimentally determined in vitro drug release with respect to the microparticle size. Thus, the effect of the type of preparation method (O/W vs. W/O/W) and device composition (polymer blend plus one drug only vs. polymer blend plus drug combination) on the diffusional resistance within the microparticles could be studied. In addition, further insight into the occurring mass transport processes was gained. For example, the time-dependent evolution of the drug concentration profiles within the microparticles upon exposure to the release medium could be calculated. An interesting practical application of the mathematical theories is the possibility to predict the effect of different formulation parameters on the resulting drug release patterns, e.g. the effect of the microparticle size.

Transport of small polar molecules across nonporous polymeric membranes: I. Experimental procedures and data analysis

The transient measurement of concentration profile within the liquid boundary layer close to the membrane interface and the flux of permeating species across the membrane coupled with transient model of membrane allows a more critical evaluation of membrane transport performance. The experimental procedure for transient measurement of pervaporation fluxes and data obtained for the {ethanol–water}/silicone rubber system and experimental set up for transient dialysis measurement by interferometry technique for the same system was described. A detailed analysis of optical effect accounting for the light deflection in a medium of varying refractive index profile was presented. A numerical procedure was described which is capable to handle the transient models consist of highly nonlinear partial differential equations. The potential of recovering the transport model parameters from the interference fringes was tested by using a hypothetical model system. The results obtained confirm that both the diffusive and equilibrium parameters can be recovered from the interference fringes. The possibility of recovering the transport model parameters for the {ethanol–water}/silicon rubber system from dialysis data and using those parameters for predicting pervaporation performance for the purpose of model validation will be described in forthcoming articles.

Modelling of the atomization of a plain liquid fuel jet in crossflow at gas turbine conditions

The penetration and atomization of a plain jet of kerosene fuel in air crossflow were modelled and compared with the experiment at test conditions relevant to lean premixed prevaporized combustion in gas turbines. Tests were conducted at an air velocity of 100 and 75 m/s and an air pressure of 6 and 9 bar at ambient temperature. The fuel nozzle diameter was 0.45 mm and the liquid-to-air momentum flux ratio was between 2 and 18. Measurement techniques employed include time-resolved shadowgraphs, Mie-scattering laser light sheets, and Phase-Doppler-Anemometry. Hence qualitative information on jet disintegration as well as quantitative data regarding jet penetration, fuel placement and dropsize distribution were obtained. The numerical model predicts the jet penetration by treating the liquid fuel jet conceptually as a cylinder deflected by the airflow. Fracture of the liquid column is modelled by a characteristic time criterion. Shear breakup of the liquid column and its fragments is modelled as liquid boundary layer stripping. The engineering model has been implemented as an extension into a 3d CFD-code with Lagrangian particle tracking. Within its application limits, the model fills the gap of lacking droplet initial conditions in numerical spray simulation, while at the same time requiring low computational effort.

Exchange of inorganic phosphate between river waters and bed-sediments.

The kinetics of the release of Soluble Reactive Phosphorus (SRP) in oxic and anoxic conditions and uptake in oxic conditions by contaminated river sediments (River Blackwater in Southern England) were measured using a fluvarium channel operated to mimic environmental conditions. Release rates (from 1 to 10 nmol m(-2) s(-1)) and uptake rates were modeled successfully using a Parabolic equation and Diffuse Boundary Layer model. A SRP release experiment over 61 days showed that large gradients in SRP developed in the porewater as a result of diffusion, sorption, and in-situ generation of SRP in the anoxic zone. This was modeled using a new Triple Zone Model that incorporated diffusion through a liquid boundary layer and sorption/desorption in oxic and anoxic zones. The results highlighted the importance of the oxic zone in controlling the exchange of SRP between the sediment and water column. The model was also applied to explain why the Equilibrium Phosphate Concentration (EPC0) of the sediment measured in oxic conditions was constant (and equal to the value calculated from sorption isotherm measurements) during 2-day release experiments, and also why it increased in the uptake experiments. Measurements in anoxic conditions showed the importance of the sediment temperature in controlling the flux at the interface.