Solute Concentration Field Research Articles

An analytical model for local-nonequilibrium solute trapping during rapid solidification

Updated version of local non-equilibrium diffusion model (LNDM) for rapid solidification of binary alloys was considered. The LNDM takes into account deviation from local equilibrium of solute concentration and solute flux fields in bulk liquid. The exact solutions for solute concentration and flux in bulk liquid were obtained using hyperbolic diffusion equations. The results show the transition from diffusion-limited to purely thermally controlled solidification with effective diffusion coefficient DLNDMb→0 and complete solute trapping KLNDM(v)→1 at v→vDb for any kind of solid-liquid interface kinetics. Critical parameter for diffusionless solidification and complete solute trapping is the diffusion speed in bulk liquid vDb. Different models for solute trapping at the interface with different interface kinetic approaches were considered.

Porosity and permeability changes in sedimentary rocks induced by injection of reactive fluid: A simulation model

Summary Numerical programs for simulating flow and reactive transport in porous media is essential for predicting reservoir properties related to CO 2 sequestration performance, subsurface storage and risk assessment. In this paper we solve the Navier Stokes’ equation using finite difference method, on a simulated porous rock structure, to study the velocity distribution of fluid flowing through it under a constant pressure gradient. A reactive solute carried through the fluid is allowed to interact with the minerals in the rock. This chemical reaction dissolves the mineral which changes the rock structure thus affecting its flow properties. These changes of flow properties are studied with variation in reactive solute concentration and pressure field. The different mechanisms of dissolution responsible for the variation of flow properties for the different parameters is predicted. Before the onset of homogeneous dissolution, variation in porosity follows a power-law behaviour with change in permeability when the latter is scaled by the concentration of the reactive species. The simulation results are compared with available experimental data and found to give a reasonable match.

Investigation on Mechanism of Faceted Cellular Array Growth in International Space Station

An in situ observation experiment of faceted cellular growth was carried out using transparent organic alloy, salol - t-butyl alcohol, in microgravity conditions on the International Space Station. The temperature and solute concentration fields in the vicinity of the solid-liquid and the growth rate were simultaneously measured by microscopic interferometers.

Confined drying of a complex fluid drop: phase diagram, activity, and mutual diffusion coefficient

We describe a drying setup where a liquid drop of a molecular mixture is confined between two circular plates and left to evaporate in a controlled manner. The direct observation of the drying kinetics in such a confined geometry, which includes the measurement of the volume of the drop against time and the monitoring of a series of nucleation events, permits the reconstruction of a rough phase diagram for the case of an aqueous triblock copolymer solution. Accurate estimations of the phase boundaries are obtained thanks to spatially-resolved Raman spectroscopic measurements of the temporal evolution of the solute concentration field within the drop. The comparison of such measurements with a theoretical model describing the drying kinetics of binary mixtures [L. Daubersies and J. B. Salmon, Phys. Rev. E, 2011, 84, 031406] yields estimations of the activity of the solution and of its mutual diffusion coefficient against the solute concentration.

Preparation of the chitosan containing nanofibers by electrospinning chitosan–gelatin complexes

AbstractElectrospinning is an interesting technique, which provides a facile and an effective mean in producing nonwoven fibrous materials; however, for producing nanofibers, investigation of the electrospinning conditions is very important. In this study, chitosan, gelatin, and their polyelectrolyte complexes (PECs) were electrospun to prepare nonwoven nanofibrous mats. The concentrations of chitosan and gelatin solutions and electric field (kV/cm) were optimized. The solutions were then blended in different ratios (0–100%) to get electrospun nanofibrous mats. Solution concentration and electric field showed pronounced effect on the electrospinnability and fiber diameter of these systems. Mostly large beads coexisted with the fibers were observed for chitosan at 1 wt% solution concentration, which then showed good electrospinnability at 2 wt% (nanofiber diameter was 145 and 122 nm at 15 and 20 kV/10 cm, respectively), whereas gelatin showed no electrospinnability below 15 wt% solution concentration and a homogenous fibers network at 15 wt% (149 nm at 20 kV/10 cm). The morphology and diameter of chitosan–gelatin PEC nanofibers varied with the chitosan/gelatin ratio. The crystallinity of chitosan was also observed to reduce with electrospinning and addition of gelatin. POLYM. ENG. SCI. 50:1887–1893, 2010. © 2010 Society of Plastics Engineers

Front Tracking Based Macroscopic Calculations of Columnar and Equiaxed Solidification of a Binary Alloy

The paper explores the potential of a recently developed special front tracking method in the identification of the interface between columnar and equiaxed structures formed during a binary alloy solidification, driven by thermosolutal convection. The method, based on theoretical and experimental dendrite tip kinetics, is capable of directly distinguishing between the columnar mush and the undercooled liquid/equiaxed region developing ahead of the dendrite tip curve. A new numerical model and its computational algorithm are proposed, where the classical Eulerian volume averaged description of the transport processes is coupled with the Lagrangian front tracking method on a fixed control-volume grid. Having thus distinguished zones of different dendrite structures, distinct simulation models are used within each of the zones, e.g., the Darcy’s porous medium model in the stationary dendrite region, and a model of slurry with floating dendrites in the equiaxed part of the mush. The calculated temperature and solute concentration fields are compared with the relevant results of the classical enthalpy-porosity model, for an example problem of Pb-48 wt % Sn alloy solidification driven by diffusion and thermosolutal convection. And a good match with both solutions is exhibited. A preliminary validation study is also presented by comparing the available experimental data with the model predictions. Possible reasons for some observed discrepancies between the calculations and the experimental findings are discussed. Finally, the proposed front tracking approach is used to address the question of the impact of dendrites floating in the liquid on the flow pattern and macrosegregation in the solidifying alloy.

Non-equilibrium dynamics of an active colloidal “chucker”

We report Monte Carlo simulations of the dynamics of a "chucker," a colloidal particle that emits smaller solute particles from its surface, isotropically and at a constant rate k(c). We find that the diffusion constant of the chucker increases for small k(c), as recently predicted theoretically. At large k(c), the chucker diffuses more slowly due to crowding effects. We compare our simulation results to those of a "point particle" Langevin dynamics scheme in which the solute concentration field is calculated analytically, and in which hydrodynamic effects arising from colloid-solvent surface interactions can be accounted for in a coarse-grained way. By simulating the dragging of a chucker, we obtain an estimate of its apparent mobility coefficient which violates the fluctuation-dissipation theorem. We also characterize the probability density profile for a chucker which sediments onto a surface which either repels or absorbs the solute particles, and find that the steady state distributions are very different in the two cases. Our simulations are inspired by the biological example of exopolysaccharide-producing bacteria, as well as by recent experimental, simulation and theoretical work on phoretic colloidal "swimmers."

Effect of membrane permeability on capsule substrate adhesion: Computation using immersed interface method

A two-dimensional thin-walled capsule of a flexible permeable membrane is adhered onto a rigid planar substrate under adhesive forces (derived from a potential function). The capsule and the surrounding environment are filled with a diluted binary solution of different solute concentrations. The Stokes flow problem is solved by the immersed interface method (IIM) with equal viscosities for enclosed and surrounding fluid of the capsule. The numerical results obtained are verified against two simplified theoretical solutions with reasonable concurrence. The osmotic inflation of the adhered capsule is studied systematically as a function of solute concentration field and the membrane permeability properties. Our findings indicate that contact length shrinks in dimension and deformation decreases as capsule inflates. Also the equilibrium contact length does not depend on the hydraulic conductivity of the membrane as theoretically expected. Further numerical investigations show that the inflation and detachment of the initially adhered capsule depend significantly on the solute diffusive permeability and the reflection coefficient of capsule membrane.

Mesoscopic Simulation of Dendritic Growth Observed in X-ray Video Microscopy During Directional Solidification of Al–Cu Alloys

A mesoscopic model is developed to simulate microstructures observed in situ by X-ray video microscopy during directional solidification of Al–Cu alloys in a Hele–Shaw cell. In the model, a volume-averaged species conservation equation is solved to obtain the solute concentration and solid fraction fields, and an analytical stagnant film model is used to predict the motion of the dendrite envelopes. The model is carefully validated in several test cases. Then, the model is applied to simulate the columnar dendritic microstructures observed in the X-ray video microscopy experiments for two different alloy compositions. Reasonable agreement is found between the measured and predicted dendrite envelope shapes, solid fractions, and solute concentration fields. The predicted size of the mushy zone and the extent of the undercooled melt region ahead of the columnar front agree well with the in situ experimental observations. The simulation results show quantitative agreement with the internal solid fraction variations measured from the radiographs. The present model is also able to realistically simulate a primary dendrite trunk spacing adjustment that was observed in one of the experiments. Overall, the present study represents the first successful validation of a solidification model using real time, in situ data from an experiment with a metallic alloy. Considerable additional research is needed to account in the model for the effect of gravity driven melt convection.

Optimal solute transport in heterogeneous aquifer: coupled inverse modelling

Characterisation of transmissivity heterogeneity is critical for groundwater flow and solute transport. The heterogeneity of transmissivity is studied through variogram-based techniques. Conventionally, the parameters in variogram are obtained by fitting measurements to a theoretical variogram. However, conditioning to the sampled geological variables neglects the effects of observed concentration data. This paper presents a coupled inverse modelling system conditioning to both types of measurement. The results of a hypothetical two-dimensional steady flow indicated that the description of transmissivity and solute concentration field was improved when both measured transmissivity data and solute concentration data were combined in the coupled inverse modelling system.

Influence of Forced/Natural Convection on Segregation During the Directional Solidification of Al-Based Binary Alloys

We analyzed the columnar solidification of a binary alloy under the influence of an electromagnetic forced convection of various types and investigated the influence of a rotating magnetic field on segregation during directional solidification of Al-Si alloy as well as the influence of a travelling magnetic field on segregation during solidification of Al-Ni alloy through directional solidification experiments and numerical modeling of macrosegregation. The numerical model is capable of predicting fluid flow, heat transfer, solute concentration field, and columnar solidification and takes into account the existence of a mushy zone. Fluid flows are created by both natural convection as well as electromagnetic body forces. Both the experiments and the numerical modeling, which were achieved in axisymmetric geometry, show that the forced-flow configuration changes the segregation pattern. The change is a result of the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. In a forced flow, the pressure difference along the front drives a mush flow that transports the solute within the mushy region. The channel forms at the junction of two meridional vortices in the liquid zone where the fluid leaves the front. The latter phenomenon is observed for both the rotating magnetic field (RMF) and traveling magnetic field (TMF) cases. The liquid enrichment in the segregated channel is strong enough that the local solute concentration may reach the eutectic composition.

Deformation and osmotic swelling of an elastic membrane capsule in Stokes flows by the immersed interface method

Abstract Although permeable and deformable capsules are found in many applications in biological and industrial systems, studies on computational modeling of these capsules are still rather lacking. In this work, the osmotic swelling of a deforming capsule immersed in a diluted binary solution of a non-electrolyte solute under Stokes flows is simulated using the immersed interface method (IIM). The approximate jump conditions for solute concentration are calculated with the use of the Kedem–Katchalsky relations. The capsule membrane is considered to be either semi-permeable or fully permeable, and the material of capsule membrane is assumed to be Neo-Hookean. The employed properties of fluid and membrane lie in the range of a typical biological system. The numerical validation tests indicate that the present calculation procedure has achieved good accuracy in modeling the swelling and deformation of permeable capsules. The capsule swelling (with mass transfer across the membrane) and deformation are tested for different solute concentration fields and membrane permeability properties. Our numerical investigations show that the initial solute concentration field and the membrane permeability properties have much influence on the swelling/deformation of a permeable capsule under Stokes flows.

Studies of mist deposition for the formation of quantum dot CdSe films

Films of CdSe(ZnS) colloidal nanocrystalline quantum dots (NQDs) were deposited on bare silicon, glass and polymer coated silicon using mist deposition. This effort is a part of an exploratory investigation in which this deposition technique is studied for the first time as a method to form semiconductor NQD films. The process parameters, including deposition time, solution concentration and electric field, were varied to change the thickness of the deposited film. Blanket films and films deposited through a shadow mask were created to investigate the method's ability to pattern films during the deposition process. The differences between these deposition modes in terms of film morphology were observed. Overall, the results show that mist deposition of quantum dots is a viable method for creating thin, patterned quantum dot films using colloidal solution as the precursor. It is concluded that this technique shows very good promise for quantum dot (light emitting diode, LED) fabrication.

Effects of some electrospinning parameters on morphology of natural silk‐based nanofibers

AbstractNatural silk, from Bombyx mori solutions were electrospun into nanofibers, with diameters ranged from 60 to 7000 nm. The effects of electrospinning temperature, solution concentration and electric field on the formation nanofibers were studied. Optical and scanning electron microscope were used to study the morphology and diameter of electrospun nanofibers. It was observed that the nanofibers became flattened with ribbon‐like shape with increasing the electrospinning temperature. The nanofiber diameter increases with the increase in the concentration of silk solution at all electrospinning temperature. With increasing the voltage of electric field at 50°C, morphology of the nanofibers changes from ribbon‐like structure to circular cross section. Referring to the literature the probable mechanism responsible for the change of morphology is pointed out. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Comparison of laboratory-scale solute transport visualization experiments with numerical simulation using cross-bedded sandstone

Using a slab of Massillon Sandstone, laboratory-scale solute tracer experiments were carried out to test numerical simulations using the Advection–Dispersion Equation (ADE). While studies of a similar nature exist, our work differs in that we combine: (1) experimentation in naturally complex geologic media, (2) X-ray absorption imaging to visualize and quantify two-dimensional solute transport, (3) high resolution transport property characterization, with (4) numerical simulation. The simulations use permeability, porosity, and solute concentration measured to sub-centimeter resolution. While bulk breakthrough curve characteristics were adequately matched, large discrepancies exist between the experimental and simulated solute concentration fields. Investigation of potential experimental errors suggests that the failure to fit solute concentration fields may lie in loss of intricate connectivity within the cross-bedded sandstone occurring at scales finer than our property characterization measurements (i.e., sub-centimeter).

Phase-field modeling of solute precipitation and dissolution

A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase-field simulations were carried out assuming first order reaction (dissolution/precipitation) kinetics. In contrast to solidification processes controlled by a temperature field that is continuous across the solid/liquid interface (with a discontinuous temperature gradient), precipitation/dissolution is controlled by a solute concentration field that is discontinuous at the solid/liquid interface. The sharp-interface asymptotic analysis of the phase-field equations for solidification [A. Karma and W.-J. Rappel, Phys. Rev. E 57, 4323 (1998)] has been modified for precipitation/dissolution processes to demonstrate that the phase-field equations converge to the proper sharp-interface limit. The mathematical model has been validated for a one-dimensional precipitation/dissolution problem by comparison with the analytical solution.

Formation of Ultra-Thin Quantum Dot Films by Mist Deposition

Films of CdSe colloidal semiconductor quantum dots were deposited on several substrates including bare silicon, silicon dioxide, aluminum, and ITO coated glass using mist deposition. The process parameters, including deposition time, solution concentration, and electric field, were varied to change the thickness of the deposited film. Blanket films and films deposited through a shadow mask were created to investigate the method's ability to pattern films during the deposition process. Smooth films were formed with thicknesses from about 39 nm, or 7 monolayers, to a single layer. The results show that mist deposition of quantum dots is a viable method for creating thin quantum dot films.

3D macrosegregation simulation with anisotropic remeshing

The article presents a three-dimensional coupled numerical solution of momentum, mass, energy and solute conservation equations, for binary alloy solidification. The interdendritic flow in the mushy zone is assumed to obey the Darcy's law. Microsegregation is governed by the lever rule, assuming local equilibrium at phase interfaces. The resulting energy and solute advection–diffusion equations are solved using the Streamline-Upwind/Petrov–Galerkin (SUPG) finite element method. A SUPG-PSPG velocity-pressure formulation is applied for the momentum equation. The full algorithm was implemented in the 3D code THERCAST, together with an anisotropic remeshing method. Two applications have been considered: a small ingot of Pb-48wt%Sn alloy and a large steel ingot. The numerical results of these two cases are presented with the evolution of temperature, liquid velocity, and solute concentration fields during solidification. To cite this article: S. Gouttebroze et al., C. R. Mecanique 335 (2007).

Mass Transfer Limitations at Crystallizing Interfaces in an Atomic Force Microscopy Fluid Cell: A Finite Element Analysis

Although atomic force microscopy (AFM) has emerged as the preeminent experimental tool for real-time in situ measurements of crystal growth processes in solution, relatively little is known about the mass transfer limitations that may impact these measurements. We present a continuum analysis of flow and mass transfer in an atomic force microscope fluid cell during crystal growth, using data acquired from calcium oxalate monohydrate (COM) crystal growth measurements as a comparison. Steady-state flows and solute concentration fields are computed using a three-dimensional, finite element method implemented on a parallel supercomputer. Steady-state flow results are compared with flow visualization experiments to validate the model. Computations of the flow field demonstrate how nonlinear momentum transport alters the spatial structure of the flow with increasing flow volume, altering mass transport conditions near the AFM cantilever and tip. The simulations demonstrate that the combination of solute depletion from crystal growth and mass transfer resistance lowers the solute concentration in the region between the tip and the crystal compared with the solute concentration at the inlet of the AFM cell. For example, using experimentally measured growth rates for COM, the solute concentration in this region is 3.1% lower than the inlet value because the solute consumed by crystal growth beneath the AFM tip cannot be replenished fully due to mass transport limitations. The simulations also reveal that increasing the flow rate through the cell does not affect this difference significantly because of the inherent shielding by the AFM tip in proximity with the crystal surface. Models such as the one presented here, used in conjunction with AFM measurements, promise more precise interpretations of measurement data.

Relation between Pore Sizes of Protein Crystals and Anisotropic Solute Diffusivities

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.