Solutal Convection Research Articles

Effect of a Marginal Inclination on Pattern Formation in a Binary Liquid Mixture under Thermal Stress

Convective motions in a fluid layer are affected by its orientation with respect to the gravitational field. We investigate the long-term stability of a thermally stressed layer of a binary liquid mixture and show that pattern formation is strongly affected by marginal inclinations as small as a few milliradians. At small Rayleigh numbers, the mass transfer is dominated by the induced large scale shear flow, while at larger Rayleigh numbers, it is dominated by solutal convection. At the transition, the balance between the solutal and shear flows gives rise to drifting columnar flows moving in opposite directions along parallel lanes in a superhighway configuration.

Numerical simulation of InGaSb crystal growth by temperature gradient method under normal- and micro-gravity fields

InxGa1−xSb single crystals are to be grown by using a GaSb/InSb/GaSb-sandwich system onboard at the International Space Station (ISS). In order to have a better understanding for the transport phenomena occurring in the melt (solution) of this sandwich system, the dissolution and the growth processes were numerically simulated under a microgravity level of the ISS. Simulations were also performed under the gravitational field of Earth (1g) for comparison. The simulation domain includes the In–Ga–Sb solution (liquid phase) for fluid flow, and heat and mass transfer, and the crucible ampoule (solid phase) for heat transfer. Heat and mass balances were also used at the crystal–solution interfaces to examine the dissolution and growth processes globally. Simulation results showed that, at 1g, dissolution of the GaSb seed was enhanced due to the contribution of solutal natural convection, and the solution saturated faster compared with that under microgravity. Diffusion during growth was dominant at the both gravity levels. The GaSb concentration in the solution under microgravity was slightly affected by the temperature distribution in the ampoule.

Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)–Reynolds (Re)–Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 103 to 105 at Re=1 and 100 for three different fluids of Pr=0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45o. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re2≫1) or mixed convection regime (Gr/Re2∼O(1)) in convection dominated heat transport regime (Pr×Re≳1). Number of steady states are observed to be more in natural convection dominated regime at Re=1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall.

Numerical Simulation of the Effect of the Size of Suspensions on the Solidification Process of Nanoparticle-Enhanced Phase Change Materials

Nanostructure-enhanced phase change materials (NePCM) have been widely studied in recent years due to their enhanced thermal conductivity and improved charge/discharge in thermal energy storage applications. In this study, the effect of the size of the nanoparticles on the morphology of the solid–liquid interface and the evolving concentration field during solidification is reported. Combining a one-fluid-mixture approach with the single-domain enthalpy-porosity model for phase change and assuming a linear dependence of the liquidus and solidus temperatures of the mushy zone on the local concentration of the nanoparticles subject to a constant value of the segregation coefficient, thermal-solutal convection as well as the Brownian and thermophoretic effects are taken into account. A square cavity containing a suspension of copper nanoparticles (diameter of 5 and 2 nm) in water was the model NePCM considered. Subject to a 5 °C temperature difference between the hot (top) and cold (bottom) sides and with an initial loading of the nanoparticles equal to 10 wt. % (1.22 vol. %), the colloid was solidified from the bottom. The solid–liquid interface for the case of NePCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NePCM with particle size of 2 nm, the solid–liquid interface evolved from a stable planar shape to an unstable dendritic structure. This transition was attributed to the constitutional supercooling effect, whereby the rejected particles that are pushed away from the interface into the liquid zone form regions of high concentration thus leading to a lower solidus temperature. Moreover, for the smaller particle size of 2 nm, the ensuing solutal convection at the liquid–solid interface due to the concentration gradient is affected by the increased Brownian diffusivity. Due to size-dependent rejection of nanoparticles, the frozen layer that resulted from a dendritic growth contains regions of depleted concentration. Despite the higher thermal conductivity of the colloids, the amount of frozen phase during a fixed time period diminished as the particle size decreased.

A flow simulation study of protein solution under magnetic forces

We have developed a superconducting magnet system generating magnetic forces able to compensate gravity and suppress convection of diamagnetic protein solution from which protein crystals precipitate. A simulation model has been proposed to elucidate the motion of protein solutions and search for the optimal conditions of the crystal formation process. This model incorporates general, non-uniform magnetic forces as external forces, while the previous models involve only simple, uniform magnetic forces. The simulation results indicate that the vertical component can suppress the convection of protein solution, while the horizontal component induces minimal convection. We, therefore, need to take into account the both components when considering the formation of protein crystals under magnetic forces.

Longwave Marangoni convection in a surfactant solution between poorly conducting boundaries

AbstractWe consider Marangoni convection in a heated layer of a binary liquid. The solute is a surfactant, which is present in both surface and bulk phases; the bulk gradient of the concentration is formed due to the Soret effect. Linear stability analysis demonstrates a well-pronounced stabilization of the layer due to the adsorption kinetics and advection of the surface phase. We derive nonlinear amplitude equations for longwave perturbations in the case of fast sorption kinetics (small Langmuir number) and demonstrate that with increase in the effect of the adsorption, subcritical excitation occurs. In the case of a finite Langmuir number, the weakly nonlinear problem is ill-posed. A physical mechanism of subcritical bifurcation is discussed.

Effects of Dialysate Flow Configurations in Continuous Renal Replacement Therapy on Solute Removal: Computational Modeling

Background/Aims: Continuous renal replacement therapy (CRRT) is commonly used for critically ill patients with acute kidney injury. During treatment, a slow dialysate flow rate can be applied to enhance diffusive solute removal. However, due to the lack of the rationale of the dialysate flow configuration (countercurrent or concurrent to blood flow), in clinical practice, the connection settings of a hemodiafilter are done depending on nurse preference or at random. Methods: In this study, we investigated the effects of flow configurations in a hemodiafilter during continuous venovenous hemodialysis on solute removal and fluid transport using computational fluid dynamic modeling. We solved the momentum equation coupling solute transport to predict quantitative diffusion and convection phenomena in a simplified hemodiafilter model. Results: Computational modeling results showed superior solute removal (clearance of urea: 67.8 vs. 45.1 ml/min) and convection (filtration volume: 29.0 vs. 25.7 ml/min) performances for the countercurrent flow configuration. Countercurrent flow configuration enhances convection and diffusion compared to concurrent flow configuration by increasing filtration volume and equilibrium concentration in the proximal part of a hemodiafilter and backfiltration of pure dialysate in the distal part. In clinical practice, the countercurrent dialysate flow configuration of a hemodiafilter could increase solute removal in CRRT. Nevertheless, while this configuration may become mandatory for high-efficiency treatments, the impact of differences in solute removal observed in slow continuous therapies may be less important. Under these circumstances, if continuous therapies are prescribed, some of the advantages of the concurrent configuration in terms of simpler circuit layout and simpler machine design may overcome the advantages in terms of solute clearance. Conclusion: Different dialysate flow configurations influence solute clearance and change major solute removal mechanisms in the proximal and distal parts of a hemodiafilter. Advantages of each configuration should be balanced against the overall performance of the treatment and its simplicity in terms of treatment delivery and circuit handling procedures.

Asymptotic solution of thermal-solutal capillary convection in a slowly rotating shallow annular pool of two components solution

In order to understand the characteristics of the coupled thermal and solutal capillary convection with the radial temperature gradient in a slowly rotating shallow annular pool with the free surface, the asymptotic solution is obtained in the core region using asymptotical analysis in the limit as the aspect ratio, which is defined as the ratio of the layer thickness to the gap width, goes to zero. The influences of the rotating, Soret effect, solute diffusion coefficient, buoyant force and geometric parameters on fluid flow are analyzed. The results show that when the rotating and the solutal capillary force and the buoyancy induced by the ununiform distribution of solute concentration are not considered, the asymptotic solution is the same as that of the previous work. The influences of the rotating, the buoyancy, solute diffusion coefficient and the geometric parameters on the fluid flow are all small and the coupled thermal and solutal capillary forces play a dominant role in the convection. When the coupled forces are in the same direction, the flow is reinforced, otherwise, the flow is suppressed.

Initiation of Motion in a Fluid with a Free Surface of Small Area

It is generally assumed that the surface of a Newtonian fluid begins to move at any arbitrarily small shear stress. However, specially designed experiments show that under real conditions the fluid flow can be initiated by a particular (threshold) stress, whose value increases rapidly with decreasing surface area of the fluid. At subthreshold shear stresses generated by the surface forces or volumetric flows, the fluid surface remains immovable. Such a behavior of the surface is explained by the existence of an adsorption layer formed by the uncontrolled surface-active impurities contained in the fluid. The composition and amount of impurities absorbed by the surface are dependent on the degree of purification of the fluid and its surface tension value. The most accurate theoretical description of the behavior of a Newtonian fluid in the presence of the adsorption layer can be obtained by introducing a free surface showing the Bingham properties.In this study, we performed a series of experiments in order to analyze the peculiarities of the fluid flow developed under such conditions. As an example, we investigated the appearance of the oscillatory mode of the solutal convection near a stationary bubble. In the experiments, the bubble was placed in a horizontal channel of small cross-section filled with an aqueous solution of a surfactant with non-uniform concentration. As a surfactant, we used several monoatomic alcohols, which made it possible to investigate the influence of their physicochemical characteristics, such as their surface activity and solubility in water. These characteristics affected the frequency of occurrence of the capillary convection near the bubble, convection intensity, the ratio of predominance of the capillary to buoyancy flow times, duration of the oscillatory mode, the threshold stress value, and the relevant critical Marangoni number.

Instability in evaporative binary mixtures. II. The effect of Rayleigh convection

Multi-component mixtures undergoing phase change in the presence of gravity depict instabilities whose physical origins depend upon the heating arrangement. Calculations on evaporative instability in closed systems using the example of low weight alcohols predict that cellular patterns would occur when the system is heated from above provided that the liquid depths are small compared to the vapor depths. The cellular patterns give way to long wavelength modes when the liquid depths are large because the solutal convection is dominant. When heated from below, cellular patterns can always be obtained regardless of the phase depths. Moreover, for this heating arrangement the physics shows thermal dominance at large wave numbers and solutal dominance at small wave numbers.

Lattice Boltzmann Method for Simulation of Solutal Interfacial Convection in Gas–Liquid System

Two approaches based on the lattice Boltzmann method (LBM), the two-BGK (Bhatnagar, Gross, and Krook)-equation LBM and the hybrid LBM–finite-difference method (FDM), were developed for simulations of solutal interfacial convection. Implementations of the gravity/buoyancy and surface tension forces and an interfacial perturbation model, namely, the self-renewal interface model, were proposed for the simulation of interfacial convection, including Rayleigh convection and Marangoni convection, in a gas–liquid mass transfer process. The simulation approaches and model were validated by experimentally measured data via the particle image velocimetry technique for the CO2–ethanol system. The performances of the two simulation methods presented in this paper are discussed.

Steady thermal-solutal capillary convection in a shallow annular pool with the radial temperature and concentration gradients

Using asymptotical analysis, we investigate the characteristics of the coupled thermal and solutal capillary convection with the radial temperature and solute concentration gradients in a shallow annular pool with the free surface. The pool is heated from the outer cylinder with high solutal concentration and cooled at the inner cylinder with low solutal concentration. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the depth to the width of the pool, goes to zero. The comparison with the previous work certifies that the asymptotic solution is right and believable. The influences of the solutal capillary force, the buoyant force, the Soret effect and the geometric parameters on the fluid flow are analyzed.

Solutal Convection in Confined Geometries: Enhancement of Colloidal Transport

We evidence experimentally and theoretically that natural convection driven by solutal density differences in a molecular binary mixture can boost the transport of colloids. We demonstrate that such buoyancy-driven flows have a negligible influence on the gradients that generate them, for moderate Rayleigh numbers in a confined geometry. These flows therefore do not homogenize the binary mixture but can disperse very efficiently large solutes. We illustrate the relevance of such effects thanks to several original experiments: drying of confined droplets, microfluidic evaporation, and interdiffusion in microfluidic flows.

CONTRIBUTIONS OF THE VULCANO EXPERIMENTAL PROGRAMME TO THE UNDERSTANDING OF MCCI PHENOMENA

Molten Core Concrete Interaction (MCCI) is a complex process characterized by concrete ablation and volatile generation; Thermal and solutal convection in a bubble-agitated melt; Physico-chemical evolution of the corium pool with a wide solidification range (of the order of 1000 K). Twelve experiments have been carried out in the VULCANO facility with prototypic corium and sustained heating. The dry oxidic corium tests have contributed to show that silica-rich concrete experience an anisotropic ablation. This unexpected ablation pattern is quite reproducible and can be recalculated, provided an empirical anisotropy factor is assumed. Dry tests with oxide and metal liquid phases have also yielded unexpected results: a larger than expected steel oxidation and unexpected topology of the metallic phase (at the bottom of the cavity and also on the vertical concrete walls). Finally, VULCANO has proved its interest for the study of mitigation solutions such as the COMET bottom flooding core catcher.

Evidence of oscillatory convection inside an evaporating multicomponent droplet in a closed chamber

Visualization of an evaporating binary (ethanol–water) droplet reveals presence of oscillatory internal circulation. The visualization is done by using a laser scattering technique. The oscillatory circulation possibly results from the opposing effect of solutal and thermal Marangoni convection as proposed in some earlier theoretical works. The frequency of this oscillation is measured and the variation of this frequency with the initial concentration of the volatile component (ethanol) is reported.

Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer

Active diffusiophoresis-swimming through interaction with a self-generated, neutral, solute gradient-is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. First, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity on the swimmer and the concentration field. This effect, which we term "reaction induced concentration distortion," strongly influences the particle speed. Building on these insights, we employ irreversible, linear thermodynamics to formulate an energy balance. This approach highlights the importance of solute convection for a consistent treatment of the energetics. The efficiency of swimming is calculated numerically and approximated analytically. Finally, we define an efficiency of transport for swimmers which are moving in random directions. It is shown that this efficiency scales as the inverse of the macroscopic distance over which transport is to occur.

Application of High-Field Superconducting Magnet to Protein Crystallization

A quasi-microgravity environment appears in a high-field superconducting magnet bore where a large magnetic force counterbalances gravity acting on a diamagnetic substance. This suppresses convection of the diamagnetic solution in the crystallization cell placed in the bore from which protein crystals precipitate. A 16 T class superconducting magnet has been developed with a special coil configuration; one of the component coils produces a magnetic field the direction of which is opposite to that of the other coils. Thus, a large magnetic field gradient occurs, creating a magnetic force large enough to levitate water and hinder convection. This magnet system is operated in persistent mode, which is adequate for a rather time-requesting crystallization process of proteins. Preliminary experiments have shown that the protein crystallization process is substantially retarded in the magnetic force field.

OS1-2-6 界面動電現象による流れを解析するための格子ボルツマン法(OS1 マルチスケール現象のシミュレーション技術(2))

We present a coupled lattice Boltzmann (LB) method to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst-Planck equation for the ion concentration, and the Navier-Stokes equation for the flows of the electrolyte solution. One of the features that distinguishes the present method from the existing LB methods for electrokinetic flows lies in the scheme for the Nernst-Planck equation, in which the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator of the LB algorithm. As a validation of the present method, a one-dimensional microchannel is considered, and the simulation results in the steady state are compared with the semi-analytical solution of the model with the Poisson-Boltzmann approximation.

Redox magnetohydrodynamics enhancement of stripping voltammetry of lead(ii), cadmium(ii) and zinc(ii) ions using 1,4-benzoquinone as an alternative pumping species

Differential pulse anodic stripping voltammetry (DPASV) coupled with redox-magnetohydrodynamics (MHD) is used to enhance the anodic stripping voltammetry (ASV) response using a mercury thin film-glassy carbon electrode. The sensitivity increased to at least a factor of two (at 1.2 T) and is facilitated by using 20.0 mmol L(-1) 1,4-benzoquinone as an alternative pumping species to enhance ASV by redox-MHD. The MHD force formed by the cross-product of ion flux with magnetic field induces solution convection during the deposition step, enhancing mass transport of the analytes to the electrode surface and increasing their preconcentrated quantity in the mercury thin film. Therefore, larger ASV peaks and improved sensitivities are obtained, compared with analyses performed without a magnet. The influence of pH, 1,4-benzoquinone concentration, accumulation potential, and time are also investigated. Detection limits of 0.05, 0.09 and 2.2 ng mL(-1) Cd(II), Pb(II) and Zn(II) were established with an accumulation time of 65 s. The method is used for the analysis of Cd(II), Pb(II) and Zn(II) in different water samples, certified reference materials, and saliva samples with satisfactory results.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.