Constant Flux Conditions Research Articles

A model for the spreading and compaction of two-phase viscous gravity currents

Two-phase viscous gravity current theory has numerous applications in the natural sciences, from small-scale lava, sedimentary and glacial flows, to large-scale flows of partially molten mantle. We develop the general equations for two-phase viscous gravity currents composed of a high viscosity matrix and low viscosity fluid for both constant volume and constant flux conditions. A loss of fluid phase is taken into account at the current's upper boundary and corresponds to the degassing of a lava flow or loss of water in sedimentary flows. As the current spreads, its surface increases and fluid loss is facilitated, which modifies the mixture density and viscosity and thus the current's shape; hence spreading of the flow affects fluid loss and vice-versa. Our results show that two-phase gravity currents retain and transport the fluid out to large distances, but the fluid is almost entirely lost within a region of finite radius. This ‘loss radius’ depends on the flow's volume or flux, fluid and matrix properties as well as on the size of fluid parcels or matrix permeability. Application to lava flows shows that degassing occurs over a large area, which affects gas release and transport in the atmosphere.

Characterisation of membrane fouling deposition and removal by direct observation technique

The understanding of fouling mechanisms in membrane processes is commonly inferred via flux and rejection performances. Using direct observation (DO) allows the non-invasive, in situ, visualisation and quantification of fouling deposition and the removal from hollow fiber membranes in real time. While the advantages of the DO technique have been described previously, in this work, the effects of crossflow velocities and backwashing on particle deposition and removal are quantified under constant flux conditions. The foulant resistances are monitored along with the cake height during membrane filtration and cleaning. By measuring the cake height non-invasively, the DO technique reduces some of the assumptions required to estimate the specific cake resistance. The velocity profiles of particles near the membrane surface during filtration were observed during the formation of stagnant and fluidised fouling layers. During backwashing, the fouling layer was removed with a combination of cake expansion and gradual erosion mechanisms at low crossflow velocities and direct erosion of cake height at higher crossflow velocities. These results provide further insights into fouling dynamics in systems such as submerged hollow fiber modules.

Simulation of Soil Moisture Profiles Using K(h) from Coupling Experimental Retention Curves and One-Step Outflow Data

In the present work, the effect on the soil moisture profiles development and the cumulative infiltration when three different equations for calculating the diffusivity versus volumetric water content, D(θ) function, from one-step outflow experimental data are used, is investigated. These D(θ) functions are coupled with moisture retention curves θ(h) (h being the soil matric potential) obtained independently for the determination of the hydraulic conductivity function K(θ) or K(h). The so obtained hydraulic conductivity function, together with θ(h), were employed in solving Richards equation numerically under constant flux conditions in one dimensional vertical infiltration process. Two different porous materials were used for this investigation. It is shown that the three different equations used for the prediction of K(h) have no significant effect on the shape of the moisture profiles for the sand mixture and that a Green–Ampt advancement of the wetting front is observed. For the case of sandy clay soil there are some noticeable differences in the moisture profiles and their shape is comparatively more effusive. Also, one could mention that for both porous media the time of incipient ponding (T) differentiates among the three equations used.

Impact of Sea‐Level Rise on Sea Water Intrusion in Coastal Aquifers

Despite its purported importance, previous studies of the influence of sea-level rise on coastal aquifers have focused on specific sites, and a generalized systematic analysis of the general case of the sea water intrusion response to sea-level rise has not been reported. In this study, a simple conceptual framework is used to provide a first-order assessment of sea water intrusion changes in coastal unconfined aquifers in response to sea-level rise. Two conceptual models are tested: (1) flux-controlled systems, in which ground water discharge to the sea is persistent despite changes in sea level, and (2) head-controlled systems, whereby ground water abstractions or surface features maintain the head condition in the aquifer despite sea-level changes. The conceptualization assumes steady-state conditions, a sharp interface sea water-fresh water transition zone, homogeneous and isotropic aquifer properties, and constant recharge. In the case of constant flux conditions, the upper limit for sea water intrusion due to sea-level rise (up to 1.5 m is tested) is no greater than 50 m for typical values of recharge, hydraulic conductivity, and aquifer depth. This is in striking contrast to the constant head cases, in which the magnitude of salt water toe migration is on the order of hundreds of meters to several kilometers for the same sea-level rise. This study has highlighted the importance of inland boundary conditions on the sea-level rise impact. It identifies combinations of hydrogeologic parameters that control whether large or small salt water toe migration will occur for any given change in a hydrogeologic variable.

Comparison of Turbulent Thermal Convection between Conditions of Constant Temperature and Constant Flux

We report the results of high-resolution direct numerical simulations of two-dimensional Rayleigh-Bénard convection for Rayleigh numbers up to Ra=10;{10} in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law Nu approximately 0.138xRa;{0.285} with a scaling exponent indistinguishable from 2/7=0.2857... above Ra=10;{7}. The overall flow dynamics for both scenarios, in particular, the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers.

The effect of breast compression on mass conspicuity in digital mammography

This study analyzed how the inherent quality of diagnostic information in digital mammography could be affected by breast compression. A digital mammography system was modeled using a Monte Carlo algorithm based on the Penelope program, which has been successfully used to model several medical imaging systems. First, the Monte Carlo program was validated against previous measurements and simulations. Once validated, the Monte Carlo software modeled a digital mammography system by tracking photons through a voxelized software breast phantom, containing anatomical structures and breast masses, and following photons until they were absorbed by a selenium-based flat-panel detector. Simulations were performed for two compression conditions (standard compression and 12.5% reduced compression) and three photon flux conditions (constant flux, constant detector signal, and constant glandular dose). The results showed that reduced compression led to higher scatter fractions, as expected. For the constant photon flux condition, decreased compression also reduced glandular dose. For constant glandular dose, the SdNR for a 4 cm breast was 0.60 +/- 0.11 and 0.62 +/- 0.11 under standard and reduced compressions, respectively. For the 6 cm case with constant glandular dose, the SdNR was 0.50 +/- 0.11 and 0.49 +/- 0.10 under standard and reduced compressions, respectively. The results suggest that if a particular imaging system can handle an approximately 10% increase in total tube output and 10% decrease in detector signal, breast compression can be reduced by about 12% in terms of breast thickness with little impact on image quality or dose.

Permeability of 3D discontinuity networks: New tensors from boundary-conditioned homogenisation

Two equivalent permeability tensors are defined for 3D heterogeneous media, K p and K q , valid respectively for linear pressure and constant flux conditions at the block boundary. Both tensors are symmetric and positive-definite and the second one produces lower magnitude of directional permeability than the first one. These tensors only depends upon the internal block structure and 3D distribution of the local permeability values. On this basis, we develop first a straightforward method for evaluating the coefficients of the 2D tensor for the problem of flow through fracture traces in a cross-section, subject to linear pressure conditions. A quartzite rock mass is used as an example to illustrate this method. Then, an approximated method is proposed to build up the 3D permeability tensor of the fractured block from the ellipses within cross-sections in varied orientations.

Application of local material properties to prediction of constant flux filtration behaviour of compressible matter

Difficulties with existing approaches to the modelling of filtration of compressible materials under constant flux conditions are addressed in this paper and a new approach to modelling simultaneous consolidation and cake build-up based on dewatering theory is presented. Flocculated yeast is used as the test system with the predicted trans-membrane pressure rise as a function of time under constant flux conditions compared with experimental data. Good agreement is observed between model and experimental trends. The close correspondence between experimental and predicted results also suggests that it may be possible to predict trans-membrane pressure rise during constant flux filtration on the basis of material properties determined through simple constant pressure steady-state experiments.

Blocking of capillaries as fouling mechanism for dead-end ultrafiltration

In this paper plugging of capillaries in the potting is investigated. A lot of research has been done on fouling of the membrane surface (pore blocking, cake filtration) but research on other types of membrane fouling like plugging of capillaries is not so common. Experiments were performed with a lab-scale test installation under constant flux conditions with synthetic feed water containing ferric hydroxide flocks as a fouling component. The experiments showed that during operation capillaries became blocked by fouling plugs. The presence of blockages, especially in the potting at the concentrate side of the capillaries, could not be detected by measuring the clean water resistance. However such blockages did result in an increased forward flush pressure. A combination of the clean water resistance and the forward flush pressure is suitable for determining the fouling of a membrane and the effectiveness of a cleaning procedure. The part of the capillaries in the potting is not backwashed and therefore the hydraulic as well as the chemical cleaning is not efficient at this place.

Shock-induced Near-wall Two-phase Flow Structure Over a Micron-sized Particles Bed

The present paper studies numerical modelling of near-wall two-phase flows induced by a normal shock wave moving at a constant speed, over a micron-sized particles bed. In this two-fluid model, the possibility of particle trajectory intersection is considered and a full Lagrangian formulation of the dispersed phase is introduced. The finiteness of the Reynolds and Mach numbers of the flow around a particle as well as the fineness of the particle sizes are taken into account in describing the interactions between the carrier- and dispersed-phases. For the small mass-loading ratio case, the numerical simulation of flow structure of the two phases is implemented and the profiles of the particle number density are obtained under the constant-flux condition on the wall. The effects of the shock Mach number and the particle size and material density on particle entrainment motion are discussed in detail. The obtained results indicate that interphase non-equilibrium in the velocity and temperature is a common feature for this type of flows and a local particle accumulation zone may form near the envelope of the particle trajectory family.

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.

Point defect dynamics in bcc metals

We present an analysis of the time evolution of self-interstitial atom and vacancy (point defect) populations in pure bcc metals under constant irradiation flux conditions. Mean-field rate equations are developed in parallel to a kinetic Monte Carlo (kMC) model. When only considering the elementary processes of defect production, defect migration, recombination and absorption at sinks, the kMC model and rate equations are shown to be equivalent and the time evolution of the point defect populations is analyzed using simple scaling arguments. We show that the typically large mismatch of the rates of interstitial and vacancy migration in bcc metals can lead to a vacancy population that grows as the square root of time. The vacancy cluster size distribution under both irreversible and reversible attachment can be described by a simple exponential function. We also consider the effect of highly mobile interstitial clusters and apply the model with parameters appropriate for vanadium and $\alpha-$iron.

Dense gas extraction using a hollow fiber membrane contactor: experimental results versus model predictions

Hollow fiber membrane contactors offer a number of advantages over dispersed phase contactors for mass transfer operations such as extraction of aqueous feeds. In addition, dense gases provide benefits that traditional extraction solvents do not. A mathematical model of a membrane contactor was developed that predicts the steady state fluid velocities and solute concentrations by solving the applicable conservation equations. The gravitational force term was included because the low kinematic viscosity of dense gases can render buoyancy-induced flow significant. A method of calculating the individual and overall mass transfer coefficients from the model results is also presented. The model was validated by comparing predicted Sherwood versus Graetz numbers for tube flow to those obtained from the classical equations that have been repeatedly confirmed by experiment. The three boundary conditions examined were constant wall concentration, constant flux, and linear variation of wall concentration with length. For all three cases the model predictions were in close agreement with those of the classical equations over a wide range of Graetz numbers, except for the constant flux condition at Graetz numbers greater than about 1000. This exception reflects a limit on the mass transfer rate imposed by the constant flux boundary condition. Graetz numbers greater than 1000 (found with short tubes or very high velocities) are not usually encountered in practical applications. Model results are compared to experimental data for the extraction of isopropanol or acetone from water into dense CO 2, obtained over a range of flow rates using modules of different packing densities. Overall the model predicted the data reasonably well, proving the model to be a useful tool for evaluating potential new applications of the technology. For the isopropanol extractions the average absolute errors in the predicted mass transfer coefficients and yields were 29% and 31%, respectively, while for the acetone work the average absolute errors were 39% and 11%. In both cases the predicted mass transfer coefficients were lower than the observed values at the highest aqueous flow rates studied; usually the error became less negative (then increasingly positive in some instances) with decreasing flow rate. This trend is partly attributable to flow maldistribution (leading to reduced efficiency) caused by unavoidable non-uniform fiber spacing and variation in fiber diameter. Other possible sources of modeling error are discussed as well. With acetone, most of the resistance to mass transfer was in the aqueous phase boundary layer, as expected for a solute with a relatively high partition coefficient ( m A). On the other hand, for isopropanol (a lower m A compound) a greater portion of the resistance was attributable to the solvent-filled pore and the solvent phase boundary layer, although the aqueous resistance was still significant. Mass transfer coefficients and yields were higher for acetone than for isopropanol, and aqueous boundary layer penetration was more rapid; both results were a consequence of the higher m A of acetone. For both solutes, usually the mass transfer coefficient increased with increasing aqueous phase Graetz number, as expected when the aqueous phase mass transfer resistance is important. Moreover, yield generally increased with increasing solvent/feed ratio as anticipated.

ATTENUATION WITH SOIL DEPTH OF DYNAMIC FLUCTUATIONS IN THE RATIO OF CHEMICALS TO IRRIGATION WATER IN CHEMIGATION

Use of chemigation for the application of fertilizers and chemicals through the irrigation system has increasedworldwide. The concentration is usually controlled and maintained constant over the irrigation duration. Dynamicfluctuation in the concentration may, however, result in inaccurate application of the fertilizers and chemicals. This may, inturn, cause a reduction in crop yield when the application amounts are lower than the planned amounts, or present anenvironmental hazard when they are higher. These dynamic fluctuations in the chemical concentration of the irrigation waterdecay with soil depth due to the convection-dispersion nature of the transport process of infiltrating water during irrigation.An analytical solution, which employs the Fourier Transform method, is used here to estimate the decay of these dynamicfluctuations as water infiltrates from the soil surface to the root zone. This solution assumed constant irrigation flux and soilmoisture conditions, typical to high frequency irrigation. It assumes periodic fluctuations in the chemical concentration ofthe irrigation water. A general analytical solution was derived for these asymmetric dynamic periodic fluctuations. The effectsof fluctuation period, asymmetric time factor, and high and low concentration values within the irrigation period on the decayprocess were evaluated and results are presented for clay loam and sandy loam soils. Damping depth was chosen tocharacterize this decay process. It is the depth at which the amplitude of the chemical concentration decays by a factor exp(-1). 37% of its value at the soil surface Two (high and low) damping depths characterize the decay process of asymmetric timefluctuations. Damping depths for symmetric fluidations in clay loam were 21, 58, 138 mm for periods of 2, 10, 30 days, and78, 239, 682 mm in sandy loam for the same periods, showing the significance of soil texture and fluctuation periods. Theeffect of asymmetry was assessed for constant average concentration. High damping depths values of 92, 156, 235, and308 mm were computed for asymmetric factors 0.1, 0.25, 0.50, and 0.80, while the low damping depths were 322, 296, 239,and 145 mm, respectively, in sandy loam and 10 days period, showing a significant effect of asymmetry. This analysis is usefulfor assessing the level of accuracy required for controlling chemical concentration during chemigation, considering the soilbuffer effect.

Application of gas/liquid two-phase flows during crossflow microfiltration of skimmed milk under constant flux conditions

This work constitutes a first approach to determine the critical zone of stability during gas-sparged crossflow microfiltration ( 0.1 μm ) of skimmed ultra-high temperature (UHT) and reconstituted milks for the separation of casein micelles from soluble proteins. Conditions for stable operation were investigated with and without air sparging by imposing, at a constant wall shear stress, different levels of permeate flux while monitoring the variation in the transmembrane pressure (TMP). The determination of the critical fluxes allowed to assume a common domain of stability for single- and two-phase flows conditions, thus confirming the relevance of the wall shear stress value during 0.1 μm microfiltration of skimmed milk whichever way it is generated (standard crossflow filtration or unsteady gas/liquid flow). Whatever the filtration conditions (single-phase flows/two-phase flows), during the phase of increasing flux, a significant decrease in soluble protein transmission was observed: for reconstituted milk, under two-phase flow conditions, the transmission decreased from 80% to 60% for α -lactalbumin ( α -LA) and from 50% to 30% for β -lactoglobulin ( β -LG). This was due to the sharp increase in TMP when the flux was close to the limiting flux. During the phase of decreasing J , separation performance was strongly altered: for the same J , the TMP was significantly higher and lower soluble protein transmissions were observed, especially for the β -LG. These results showed the transition to an irreversible fouling, which led to a more tightly packed, thus less porous, cake structure. Unsteady filtration conditions, as well as standard ones, failed to disrupt it.

Application of gas/liquid two-phase flows during crossflow microfiltration of skimmed milk under constant flux conditions

This work constitutes a first approach to determine the critical zone of stability during gas-sparged crossflow microfiltration ( 0.1 μm ) of skimmed ultra-high temperature (UHT) and reconstituted milks for the separation of casein micelles from soluble proteins. Conditions for stable operation were investigated with and without air sparging by imposing, at a constant wall shear stress, different levels of permeate flux while monitoring the variation in the transmembrane pressure (TMP). The determination of the critical fluxes allowed to assume a common domain of stability for single- and two-phase flows conditions, thus confirming the relevance of the wall shear stress value during 0.1 μm microfiltration of skimmed milk whichever way it is generated (standard crossflow filtration or unsteady gas/liquid flow). Whatever the filtration conditions (single-phase flows/two-phase flows), during the phase of increasing flux, a significant decrease in soluble protein transmission was observed: for reconstituted milk, under two-phase flow conditions, the transmission decreased from 80% to 60% for α-lactalbumin ( α-LA) and from 50% to 30% for β-lactoglobulin ( β-LG). This was due to the sharp increase in TMP when the flux was close to the limiting flux. During the phase of decreasing J, separation performance was strongly altered: for the same J, the TMP was significantly higher and lower soluble protein transmissions were observed, especially for the β-LG. These results showed the transition to an irreversible fouling, which led to a more tightly packed, thus less porous, cake structure. Unsteady filtration conditions, as well as standard ones, failed to disrupt it.

Threshold flux in fouling of OF membranes by colloidal iron

Fouling of 50 kDa MWCO OF membranes by iron colloid solutions was studied under constant pressure conditions and constant flux conditions at pH 5 and 7 and at various iron concentrations. By using measurements of both deposit density and changes in the transmembrane zeta potential, threshold fluxes were found that were significantly lower than the critical flux based on the increase in membrane resistance. Results are consistent with the initial phase of fouling involving pore blockage followed by cake filtration-like behavior. The dependence of fouling rate on iron colloid concentration can best be understood by realizing that only a small fraction of the iron colloid is of a size that contributes to fouling.

Two-Phase Flow Visualization of R134A in a Multiport Microchannel Tube

Results are presented from a flow visualization investigation of a multiport microchannel tube using R134a, a medium pressure refrigerant. The study covers mass fluxes from 50-300 kg/s.m 2 and qualities ranging from 10-90%, with a 6-port microchannel tube with a hydraulic diameter of 1.5 mm under adiabatic conditions. The results from the flow visualization studies indicate that several flow configurations may exist in multiport microchannel tubes at the same time while constant mass flux and quality flow conditions are maintained. Based on these observations, development of a typical flow regime map does not appear to be an appropriate manner for describing the flow field if the flow conditions for each port are not known. Flow mapping of the fluid regimes in this multiport microchannel is accomplished by developing functions that describe the fraction of time or the probability that the fluid exists in an observed flow configuration. An application of the alternative method of flow description for pressure drop predictions in multiport channels is included.

Validation of classical density-dependent solute transport theory for stable, high-concentration-gradient brine displacements in coarse and medium sands

A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcy's and Fick's laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcy's law was not necessary. On the other hand, an extension to Fick's Law was needed to model the experimental data accurately.

Human epidermal membrane constant conductance iontophoresis: alternating current to obtain reproducible enhanced permeation and reduced lag times of a nonionic polar permeant

An experimental protocol, using an initial 1 min direct current (DC) applied potential of 4 V followed by alternating current (AC), was established to: (a) increase conductance and permeability and decrease lag time for human epidermal membrane (HEM) relative to unaltered HEM and; (b) maintain constant conductance and permeability during flux studies. The protocol allowed specific permeation parameters of the membrane to be characterized under electrically enhanced, constant flux conditions. The permeability, lag time, and effective membrane thickness were determined using a nonionic polar permeant, urea, while the enhanced conductance was maintained at a constant level with AC. A tortuous pore pathway model was employed to analyze the data. The AC protocol increased membrane permeability, and decreased lag time and effective membrane thickness relative to similar parameters obtained in previous studies from unaltered HEM. Lag times ranged from 32.0 to 105.5 min, and permeability coefficients calculated from steady state fluxes ranged from 1.68 to 6.03×10 −7 cm/s for HEM samples with electrical resistance values during transport of 2.3–8.0 kΩ cm 2. Effective membrane thicknesses were calculated to range from 0.34 to 0.61 cm during AC iontophoresis. Significant additional results were obtained when the protocol was applied for two consecutive runs using the same HEM sample, with time for the HEM sample to recover between runs. During the second run, the applied potential was adjusted to reproduce the conductance obtained on the first run. Under these conditions, the consecutive runs yielded essentially the same lag time, permeability and effective membrane thickness values. These results suggest that constant fluxes can be achieved by keeping HEM electrical conductance constant during AC iontophoresis.