Drainage Velocity Research Articles

Influence of droplet deformability on the coalescence rate of emulsions

In this article the influence of deformation on the coalescence rates of oil-in-water (O/W) emulsions is analyzed. Calculations for doublets and many-particles systems were performed based on a Brownian dynamics algorithm. Extensional and bending energies were included in order to quantify the effect of the changes in the surface geometry on the coalescence rates. Also, the hydrodynamic resistance due to the flat film was included through a correction to the diffusion coefficient in the lubrication limit. Results of two particles calculations were compared with previous analytical evaluations of the coalescence time in absence of highly repulsive barriers [Danov, Langmuir 9, 1731 (1993)]. Lifetime of doublets was calculated as a function of the particle radius from 100 nm to 100 microm. It was found that the doublets lifetime strongly depends on the interplay between the potential of interaction between the droplets and the hydrodynamic resistance. Depending on the repulsive barrier either a monotonous increase of the lifetime with the droplet size or a maximum value is observed. Finally, the evolution of O/W emulsions with a volume fraction of phi=0.10 was studied. For these many-particle systems, the results show a sensitive dependence of the aggregation behavior on the interfacial tension. The procedure reported here allows us to include Derjaguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO forces and the film drainage velocity of many different systems.

Enhanced foam drainage using parallel inclined channels in a single-stage foam fractionation column

A single-stage vertical foam fractionation column was investigated under continuous steady-state experimental conditions. Using a simple power-law expression to describe the drainage velocity through the foam, and in conjunction with continuity arguments, a theoretical framework was developed to analyse the performance of the vertical column. A reduction in the degrees of freedom in the analysis was achieved by using a fixed feed to gas flux ratio to promote a reasonably constant surfactant recovery. It was then possible to measure the process performance by determining the change in the level of enrichment produced from a change in the gas flux, and corresponding change in the feed flux. For a constant recovery, the enrichment is directly proportional to the volume reduction (defined as the ratio of the feed volume processed to foamate volume produced in a given time). The analysis was found to be consistent with experimental data and demonstrated the need to limit the gas flux, and hence the feed flux, to relatively low values in order to produce satisfactory volume reductions, and in turn achieve high enrichment. To overcome this processing constraint, three parallel inclined channels1 (PIC) were used to provide an effective increase in the vessel area, and hence facilitate the release of the entrained liquid within the foam. A significant increase in the volume reduction was obtained using the inclined channel arrangement. For the same processing rate, the PIC column achieved up to a 4 fold increase in enrichment compared to the vertical column. A slight decrease in recovery, however, was observed using the PIC column.

The effect of fine particles on the drainage and coarsening of foam

The effects of coal fly ash dispersed in foams on the coarsening and drainage dynamics are investigated in a free drainage experiment. The growth rate of the bubbles is not significantly changed. The rates of the fluid drainage are significantly slower when powder is present, which cannot be attributed to an increase in the fluid’s viscosity associated with the dispersal of powder. Instead, the drainage process can be effectively modeled by adjusting the permeability parameters that relate the liquid fraction and drainage velocity for two-phase foams; however, the values of the adjusted parameters are considerably larger than those observed and expected for non-particulate foams indicating that new physical mechanisms are at play.

Salt and water balance analysis after adopting controlled drainage in Yinnan Irrigation District, Ningxia, China

AbstractAccording to data collected from a field experiment of controlled drainage in Yinnan Irrigation District, this paper analyses the amount of drainage water and variation of salt and water balance. Compared with traditional drainage, it is found that the volume of drainage water is obviously reduced by controlled drainage. The groundwater table in the controlled drainage areas is 1.8 cm higher than that in the traditional drainage areas. If drainage velocity is used to substitute for the volume of drainage water, the total volume of drainage water drained from controlled drainage areas is on average 50% less than that from traditional drainage areas. At the same time, the volume of underground drainage water decreases by 46%. By analysing the balance between salt and water in the controlled drainage areas, the introduced amount of salt is less than the discharged amount of salt, so salt and water are still kept in good status. Copyright © 2008 John Wiley & Sons, Ltd.

Attempt of a flux‐based evaluation of field capacity

AbstractField capacity is one of the most frequently used soil parameters. According to the original definition, the field capacity is a site‐specific parameter, which is closely connected to soil water flux. Many of the existing procedures for field‐capacity estimation neglect its flux‐based character. In this study, a method and selected results are presented. This allows a better reflection of the unsteady behavior of unsaturated water flow in estimating field capacity. Based on the velocity of the relative internal drainage, a threshold value is defined (field‐capacity threshold) which enables a flux‐based estimation of the field‐capacity value. Furthermore, the direct consideration of the drainage time allows the soil water contents to be estimated for defined internal drainage durations.

Temporal variation of chemical and isotopic signals in major discharges of an alpine karst aquifer in Turkey: implications with respect to response of karst aquifers to recharge

Proper management of karst aquifers requires a better understanding of flow and transport mechanisms in these systems. Flow in karst aquifers is inherently very complex due to the non-linear and non-stationary relationship between recharge and discharge. Information on this relationship has been acquired for a large (1,000 km2), mountainous (>3,500 m asl) karst aquifer with a deep unsaturated zone (>2,000 m) in the Aladaglar mountain range of south-central Turkey. All major discharges from the aquifer, which drain almost all the recharge, have been observed periodically for specific electrical conductivity, tritium and oxygen-18 variations during a period of 12 months. Observations reveal that the system’s response to recharge depends strongly on the competition between the infiltration and drainage velocities. These velocities, which are controlled by variables such as the time of precipitation, time of infiltration, intensity, and continuity of recharge, determine the degree of dominance of different types of flow mechanisms in the aquifer. Bypass, well-mixed and piston flow mechanisms are used to explain the response of the aquifer to the spatio-temporal variations in recharge. It appears that the aquifer switches among these flow mechanisms depending on the prevailing recharge mode and the competition between infiltration and drainage velocities.

Effect of Repeated Induced Airway Collapse During Total Liquid Ventilation

Negative pressure generated during the expiratory phase of total liquid ventilation (TLV) may induce airway collapse. Evaluation of the effect of repeated airway collapse is crucial to optimize this technique. A total of 24 New Zealand White rabbits were randomly divided into four groups. Ventilation was performed for 6 hours with different strategies: conventional gas ventilation, TLV without airway collapse, and TLV with collapse induced in either 75 or 150 sequential breaths. In the treated groups, airway collapse was induced by increasing the perfluorocarbon drainage velocity while maintaining the minute ventilation constant. Airway pressure, gas exchange, and blood pressure were monitored at 30-minute intervals. At the end of the experiment, airway and lung parenchyma specimens were processed for light microscopy. No evidence of fluorothorax was noticed in any of the four groups at autopsy examination. Minimal signs of inflammation were noticed in all airway and lung parenchyma specimens, but no evident structural alteration was visible. Adequate gas exchange and systemic blood pressure were maintained during all the studies. Repeated airway collapse is not associated with structural changes in the respiratory system and does not alter the gas exchange ability of the lungs.

A note on the effects of liquid viscoelasticity and wall slip on foam drainage

A foam drainage model is modified to attempt the description of foams made of viscoelasticliquids (such as polymer solutions). In particular, the standard approach to foamdrainage dominated by viscous dissipation in Plateau borders is modified to takeinto account the elastic forces acting on the fluid within Plateau borders, andslipping of the polymer solution at the walls of Plateau borders. It is shown that,in the case of forced drainage, the resulting differential equations reduce to thesame one obtained in the case of Newtonian liquids, which is satisfied by thewell-known solitary wave solution. According to these results, the fluid elasticity hasno effect on the drainage velocity, while the wall slip assumption is compatiblewith recent observations showing a faster drainage velocity in the forced drainageexperiment.

Continuous Foam Separation of Metals Enhanced by Down-Flowing Surfactant Solution from Column Top

A novel operational mode of foam separation was suggested in this study. In a conventional operation, the separation of a target solute has its own limit because non-target ones exist in the interstitial water between foam and get mixed in the recovered foamate solution. As a countermeasure for this inherent drawback in foam separation, an aqueous surfactant solution was injected into the rising foam bed to enhance a downflow of the interstitial water containing unfavourable solutes. The flow characteristics of the system with and without the injection of a washing solution were investigated in terms of the liquid holdup, ϕ and the drainage velocity, U LD, under various operating conditions. Their correlation was obtained as U LD (cm s −1) = 1.85 ϕ 2 + 0.0005. The application to metal separation was also performed using a nonionic surfactant, polyoxyethylene nonylphenyl ether (PONPE 20), with an affinity to Au(III). The non-specific metal, Cu(II), was effectively washed out from the foam bed, and satisfactory separation of Au(III) was attained.

Linking drainage front morphology with gaseous diffusion in unsaturated porous media: A lattice Boltzmann study

The effect of drainage front morphology on gaseous diffusion through partially saturated porous media is analyzed using the lattice Boltzmann method (LBM). Flow regimes for immiscible displacement in porous media have been characterized as stable displacement, capillary fingering, and viscous fingering. The dominance of a flow regime is associated with the relative magnitudes of gravity, viscous, and capillary forces, quantifiable via the Bond number Bo, capillary number Ca, and their difference, Bo-Ca . Forced drainage from an initially saturated two-dimensional (2D) porous medium was simulated and the resulting flow patterns were analyzed and compared with theoretical predictions and experimental results. The LBM simulations reproduced expected flow morphologies for a range of drainage velocities and gravitational forces (i.e., a range of capillary and Bond numbers). Furthermore, measures of drainage front width as a function of the dimensionless difference Bo-Ca correspond well with scaling laws derived from percolation theory. Effects of flow morphology on residual fluid entrapment and gaseous diffusion were assessed by running LBM diffusion simulations through the partially saturated domain for a range of water contents. The effective diffusion coefficient as a function of water content was estimated for three regimes: stable drainage front, capillary fingering, and viscous fingering. Significant reductions in gaseous diffusion coefficient were found for viscous fingering relative to stable displacement, and to a lesser extent for capillary fingering, indicating that wetting phase distribution with a high degree of fingering in the 2D domain severely restricts connectivity of gas diffusion pathways through the medium. The study lends support for the use of LBM in design and management of fluids in porous media under variable gravity, and enhances the understanding of the role of dynamic fluid behavior on macroscopic transport properties of partially saturated porous media.

Modelling the axial dispersion of particles in froths

The separation achieved through flotation is dependent on the selective attachment of mineral particles to bubble surfaces. However, the majority of solids collected have been attributed to unattached particles. This is due to the release of attached particles from bubble surfaces due to bursting on the top of the froth and coalescence within the froth. The unattached particles move and disperse axially and radially through the interconnected network of liquid channels within the froth, known as Plateau borders. A model has been developed using previous work on the bulk drainage of liquid through froths in addition to a velocity profile equation describing the local variation in liquid velocity over the Plateau border cross-section. These descriptions of the liquid flow on two separate scales are combined with realistic froth structures to form a mathematical description of the liquid flow through the froth which has been used to simulate unattached particle motion. The results have been validated through the replication of liquid and particle froth drainage experiments. This validation confirmed the power law relationship between particle dispersion and apparent liquid drainage velocity. The model was then used to extend experimental results to show the effect of particle size and density on dispersion.

Evolution of glacial flow and drainage during the ablation season

Proglacial discharge is controlled by the geometry of the glacial drainage network and by meltwater processes. The glacial drainage systems of some alpine glaciers have been characterised using a model based on a proglacial discharge analysis. In this paper, we apply high frequency systemic analysis to data collected from the Baounet Glacier (French Alps) during two successive ablation seasons. Our approach is based on an analysis of the evolution of daily recession curves during the ablation period. The observed data are fitted by a single 〈β〉-coefficient dependant recession law. Changes in 〈β〉 are compared to variations in the daily discharge amplitude and the time lag between air temperature and proglacial discharge. The changes in the 〈β〉 values do not appear to be related to changes in the time lag and the amplitude of the daily discharge. There were significant variations in the 〈β〉-coefficient during the two ablation periods studied here even if there was no time lag or the daily discharge amplitude change. High values of 〈β〉 correspond to high drainage velocities; therefore increases in 〈β〉 values can be used as an indicator of the evolution of the glacier’s internal drainage network.

Free Surface Instability and Gas Entrainment during Blast Furnace Drainage

AbstractUnexpected discharge of blast gas in the early stages of castingfrom an ironmaking blast furnace has a signrficant impact on the furnace operations. A physical modelling study was carried out, using both a Hele‐Shaw cell and porous bed, in order to understand the mechanism of the gadliquid interface instability during the hearth drainage. The proposed hypothesis that the early discharge of blast gas is due to the occurrence of “viscous fingers” at the gas/liquid interface was tested. The experimental evidence from both the Hele‐Shaw and packed bed models proved conclusively that viscous fingering did take place and resulted in the premature release of gas. However, viscous fingering occurred when the drainage velocity was an order of magnitude higher than those used for normal blast furnace operation. These conditions can occur due to local variations in the bed permeability, and further experiments were performed to demonstrate this situation.

Evolution of liquid holdup profile in a standing protein stabilized foam.

Evolution of liquid holdup profile in a standing foam formed by whipping and stabilized by sodium caseinate in the presence of xanthan gum when subjected to 16 and 29g centrifugal force fields was measured using magnetic resonance imaging for different pH, ionic strength, protein and xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Foam drainage was slowest at pH 7, lower ionic strength, higher protein and gum concentrations. Foam was found to be most stable at pH 5.1 near the isoelectric point of protein, lower ionic strength and higher protein and xanthan gum concentrations. A predicted equilibrium liquid holdup profile based on a previous model (G. Narsimhan, J. Food Eng. 14 (1991) 139) agreed well with experimental values at sufficiently long times. A proposed model for velocity of drainage of a power law fluid in a Plateau border for two different simplified geometries was incorporated in a previously developed model for foam drainage (G. Narsimhan, J. Food Eng. 14 (1991) 139) to predict the evolution of liquid holdup profiles. The model predictions for simplified circular geometry of Plateau border compared well with the experimental data of liquid holdup profiles at small times. At longer times, however, the predicted liquid holdup profile was larger than the observed, this discrepancy being due to coarsening of bubble size and decrease in foam height not accounted for in the model. A Newtonian model for foam drainage under predicted drainage rates did not agree with the experimental data.

Effects of Particle Free Space on Hearth Drainage Efficiency.

This paper presents an experimental and numerical study of the two-phase flow in a particle packed bed, under conditions related to a blast furnace hearth. In these models, drainage velocities, slag ratio, tapping time, and maximum slag level in hearth are studied. The coke free space formed at tap hole level forms a circumference slag flow and significantly improves the hearth drainage efficiency. When the coke free space surround a part of packed bed, the effect is in proportion to the surrounded packed bed size. Such a nonaxisymmetric coke free space causes the imbalances of tap time and slag ratio.

Transformações Geomorfológicas e Fluviais Decorrentes da Canalização do Rio Itajaí-Açu na Divisa dos Municípios de Blumenau e Gaspar (SC)

Nos anos de 1983 e 1984, o vale do rio Itajaí foi atingido por períodos de grandes enchentes devido à intensa pluviosidade. Visando amenizar os efeitos das águas do rio Itajaí-Açu em Blumenau, realizou-se em 1986 a retificação e alargamento do canal do rio, na divisa dos municípios de Blumenau/Gaspar. Essas intervenções provocaram alterações na dinâmica geomorfológica, principalmente na morfologia da várzea e na hidrodinâmica. A análise das transformações geomorfológicas baseou-se na interpretação de fotografias aéreas de 1981 e 1993 (escala 1/8.000) e em observações e levantamentos realizados no campo. A avaliação da hidrodinâmica fluvial foi realizada pela correlação dos níveis máximos mensais das estações fluviométricas de Blumenau e Indaial, considerando os níveis registrados antes e após o alargamento do rio Itajaí-Açu. Outro processo de avaliação baseou-se no cálculo da linha de água gerada pelo alargamento da seção fluvial, obtida pela expressão de remanso. As transformações geomorfológicas geradas no canal fluvial após a dragagem são as seguintes: formação de bancos arenosos (banco lateral, cordão marginal convexo e banco de confluência), e desencadeamento dos processos de escorregamento na margem esquerda. Em relação à dinâmica fluvial, o alargamento do canal é responsável pelas seguintes transformações: aumento da velocidade de escoamento a montante da obra, que reduziu os níveis máximos mas aumentou a ação erosiva nas margens; a jusante, por sua vez, aumento dos níveis máximos assim como aumento da capacidade erosiva pelo escorregamento das margens devido às acentuadas variações do nível de água.

Influence of Ionic Surfactants on the Drainage Velocity of Thin Liquid Films

The process of thinning of liquid films in the presence of ionic surfactants and background electrolytes is studied. The lubrication approximation is used to obtain the influence of spatial dynamic distribution of the different ions and the electric potential on the mobility of film interfaces and on the additional nonequilibrium part of the electrostatic disjoining pressure. The material properties of the interfaces (Gibbs elasticity and surface viscosity) are taken into account. The bulk and surface diffusivities of ionic species tend to restore the equilibrium and suppress the role of the Gibbs elasticity. The problem is linearized under the assumptions of small deviations of the adsorption and the concentration from their equilibrium values and of small Peclet number. In the case of plane parallel films an analytical solution is obtained. The correctness of the assumptions, widely used in the literature, of constant surface charge, of constant surface potential, and of the quasi-equilibrium approach is discussed. Numerical analysis of the governing equations shows that the ionic surfactants influence the film drainage in two ways. For small surfactants and background electrolyte concentrations the main effect is a reduction in surface mobility, which decelerates the drainage of the film. At high surfactant or salt concentrations the interfaces become tangentially immobile and then dynamic changes in the concentration, adsorption, electric charge, and middle plane potential affect the film thinning due to the change in the nonequilibrium part of the electrostatic disjoining pressure.

A Generalized View of Foam Drainage: Experiment and Theory

A new experimental method is presented using fluorescein dye to determine the spatial and temporal variations of the liquid volume fraction in aqueous foams. This method is used for quantitative studies of liquid redistribution (drainage) in three types of experiments: forced, free, and pulsed drainage. Characteristic quantities, such as the drainage velocity, show power-law dependences on experimental parameters that are inconsistent with traditional foam drainage models based on Poiseuille-type flow in the liquid-carrying channels (Plateau borders) of the foam. To obtain a theoretical description, the foam drainage equation is generalized using an energy argument which accounts for viscous dissipation in both the channels and the nodes (or vertices, which are the junctions of four channels) of the liquid network. Good agreement with results for all three types of drainage experiments is found when using this new model in the limit where the dissipation is dominated by the nodes.

Liquid flow through aqueous foams: from the plateau border-dominated regime to the node-dominated regime.

The velocity of gravity-driven flow through aqueous foams (forced drainage) has been determined by using electrical conductivity measurements in foams made with solutions of different surfactants. There is always a scaling behavior (power law) between the drainage velocity V and the imposed flow rate Q: V approximately Q(alpha), but the alpha coefficient varies between the different surfactant solutions and increases with surface viscosity. An explanation of this behavior will be given in terms of a transition between a node-dominated and a Plateau border-dominated viscous dissipation, for which theory predicts respectively alpha=1/3 and alpha=1/2.

Liquid Flow through Aqueous Foams: The Node-Dominated Foam Drainage Equation

We present an experimental study of forced drainage through a soap foam, where a constant liquid flux at the top of a dry foam produces a downwards traveling wave with a constant velocity and uniform liquid content. The results are not consistent with existing models and we propose a new model, based upon relaxing the condition of wall rigidity throughout the network and emphasizing the importance of viscous damping in the nodes where Plateau borders meet. This model agrees well with the experimentally measured (power-law) scaling behavior of the drainage velocity, and the width of the propagating liquid front, on the imposed flow rate and bubble size. [S0031-9007(99)09185-1]