Convective Spreading Research Articles

Understanding Compartmentation Failure for High-Rise Timber Buildings

The traditional concept of compartmentation guaranteed by fire resistance is mainly concerned with the problem of destructive internal spread potential. External convective spread potential pertains to the loss of compartmentation associated with windows and facade systems. As such, it is assumed that internal fire spread occurs following mechanisms of excessive heat conduction and/or successive failure of the compartment boundaries, which can be, in most cases, conservatively characterised using traditional methods of performance assessment such as fire resistance. Nevertheless, external fire spread represents a potentially more effective route by which fire can spread through the convective advancement of flames and hot gases. This is particularly important in cases such as timber construction, where the presence of exposed timber can result in increased convective spread potential and where loss of compartmentation can result in disproportionate consequences. A simplified compartment fire model is proposed with the objective of quantifying the fuel contribution of exposed timber elements to the compartment fire and determining the impact of variable percentages of exposed timber on the convective spread potential. The overall results show that the convective fire spread potential increases with the increasing percentage of available timber.

Convective Plume Spreading in Model Transparent Porous Media

Convective Plume Spreading in Model Transparent Porous Media

Generalized multiscale finite element method for language competition modeling II: Online approach

In this paper, we consider language competition in a heterogeneous medium. The mathematical model considers bilingualism, population growth, and social pressure to use specific languages (diglossia). The transition from one language group to another is determined by probabilities that depend on status, group size, and spatial location. The model considers not only diffusive spread but also convective spread, which models seasonal migrations of speaker populations. We develop multiscale approaches for coarse grid modeling while maintaining reasonable accuracy. We present offline and online approaches based on the Generalized Multiscale Finite Element Method. We consider a model problem in a heterogeneous environment to test these approaches. The results show that both approaches can significantly reduce the discrete problem’s size. However, the online approach achieves better accuracy.

The Small-Amplitude Dynamics of Spontaneous Tropical Cyclogenesis. Part I: Experiments with Amplified Longwave Radiative Feedback

Abstract What determines the vortex size at the small-amplitude stage of spontaneous tropical cyclogenesis remains unclear. A doubly periodic domain is a standard setup for numerically studying this problem, but the convectively coupled standing waves inherent to the setup could directly trigger vortices, rendering an unrealistic path for tropical cyclogenesis. We increase the Coriolis parameter to suppress the wave and double the longwave radiative feedback to make the more realistic moisture–radiation instability dominant. Experiments show that the moisture–radiation instability has a short-wavelength cutoff due to the smoothing effect of convective dynamics, which includes the nonlocal convective triggering by cold pools and the nonlocal longwave radiative effect of anvil clouds. By approximating the spread of convective activity as a Gaussian filter on the column humidity, we derive a bulk convective spreading length lcp+av to parameterize the combined effect of cold pools and anvils. Using a novel diagnostic method, lcp+av is shown to be around 10 km. The contribution of cold pools and anvil clouds to convective spreading is comparable in the doubled radiative feedback experiments. An extrapolation to the normal radiative feedback state shows the anvil clouds play a smaller yet nonnegligible role.

Numerical simulation of language interactions using online coupled Generalized Multiscale Finite Element Method

In this paper, we present a new mathematical model of the interaction of two languages. In the model, we distinguish percentages of people who speak a non-target language, a target language with low and high proficiency, and both languages considering the low and high proficiency levels in the target language. Therefore, the solution consists of five fields. Furthermore, we assume the diffusive and convective spread of the languages, considering the overflow between them. Thus, the mathematical model is defined by a coupled system of partial differential equations for the five fields.Since the mathematical model is coupled and the medium is heterogeneous, we have implemented a multiscale method. The proposed multiscale method is based on the Generalized Multiscale Finite Element Method (GMsFEM). In addition to offline multiscale basis functions, we also construct online multiscale basis functions. The online basis functions can account for changes in the heterogeneity of the medium caused by migration flows. Numerical results have shown that such online enrichment can significantly improve the accuracy of multiscale modeling.

V14-03 TRANSURETHRAL WATER VAPOR ABLATION (STEAM) TO TREAT LOCALIZED PROSTATE CANCER (INVESTIGATIONAL USE ONLY)

You have accessJournal of UrologyProstate Oncology II & Testis Oncology & Misc. Oncology (V14)1 Sep 2021V14-03 TRANSURETHRAL WATER VAPOR ABLATION (STEAM) TO TREAT LOCALIZED PROSTATE CANCER (INVESTIGATIONAL USE ONLY) Christopher Dixon, and Christopher Warlick Christopher DixonChristopher Dixon More articles by this author , and Christopher WarlickChristopher Warlick More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000002111.03AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Convective water vapor is a unique technology that uses the thermal energy of water vapor (steam) to ablate tissue. The objective was in vivo validation of Transurethral Vapor Ablation (TUVA) in men with clinically significant localized prostate cancer by; Group 1 - TUVA/RRP assessed by immediate whole mount sectioning, Group 2 - TUVA assessed by pre/post treatment MRI in an early feasibility trial and Both Groups by intraoperative real-time ultrasound and AE assessment. METHODS: A tabletop generator and a transurethral endoscopic delivery device, along with real-time TRUS, were used to direct water vapor into any anatomic zone of the prostate to ablate malignant prostate tissue. The procedure technique currently used, including the endoscopic and real-time ultrasound monitoring of needle deployment, advancement and vapor delivery is demonstrated. To evaluate the convective principles of TUVA, real-time ultrasound patterns of vapor delivery and 7-day post treatment gadolinium MRI images were studied. Ablation effectiveness was assessed in two independent groups. In Group 1 by whole mount sectioning immediately following TUVA / radical prostatectomy. In Group 2 by assessing pre- and 7-day post TUVA MRI nonenhancement patterns as well as PIRADSv2 resolution. Immediate safety was assessed by intraoperative inspection, gross examination of the prostate (Group 1) and immediate post op adverse events along with 7-day MRI’s (Group 2). RESULTS: Real-time ultrasound vapor patterns confirmed convective spread within the zonal anatomy and boundaries of the prostate. Real-time ultrasound during treatment demonstrated the convective principles and the ability to “see” the treatment. Collectively, whole mount sectioning along with the non-enhancing areas seen on MRI’s at 7-days demonstrated ablation to ALL anatomic zones and boundaries consistent with the unique ablation capabilities of convection. In Group 2, after one treatment session, 14/17 PIRADSv2 lesions ≥3 were no longer visible within the ablation zone on 7-day MRI. There were no serious adverse events intraoperatively or within one week of the treatment. CONCLUSIONS: Transurethral delivery of water vapor thermal energy can effectively ablate any zone of the prostate from apex to base, anterior to posterior, and laterally to the prostatic “capsule”. Early feasibility data using this investigational device are favorable. Source of Funding: Francis Medical, Maple Grove, MN © 2021 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 206Issue Supplement 3September 2021Page: e1165-e1166 Advertisement Copyright & Permissions© 2021 by American Urological Association Education and Research, Inc.MetricsAuthor Information Christopher Dixon More articles by this author Christopher Warlick More articles by this author Expand All Advertisement Loading ...

Pore-scale modeling of coupled thermal and solutal dispersion in double diffusive-advective flows through porous media

In double diffusive-advective flows through porous media, the combined effects of fluid and solid properties, pore space geometry, and flow conditions on the transport rates and distribution of the thermal and solutal fronts can be characterized by dispersion coefficients. In this study, conjugate heat and solute transport in the process of miscible displacement through porous media is studied through pore-scale numerical simulations in 2D and 3D digital representations of the unconsolidated sandpacks. The temperature and solute concentration distributions during both viscously stable and unstable displacements are obtained by solving the point equations of flow and transport on the discretized computational domains. Next, the longitudinal components of the solute and thermal dispersion coefficients are determined by fitting the effluent profiles to the analytical solutions of the advection-diffusion equations for the transport of mass and heat, respectively. The length scales of the solutal and thermal transition zones are also measured along the principal direction of the flow and then correlated with the displacement time. In stable displacements, different dispersion regimes are identified based on the magnitude of the solutal and thermal Peclet numbers. It is observed that the onset of convective spreading is different in the 2D and 3D simulation runs. In unstable displacements, the results indicate that solutal dispersion is more affected by thermo-solutal viscous fingering compared to thermal dispersion. Moreover, as the viscosity contrast across the thermal and solutal fronts increases, the dynamics of the mixing length growth gradually changes from dispersion-dominated toward fingering-dominated. Finally, the results show that two-dimensional simulation runs may not completely characterize the dispersion-related phenomena that occurs during heat and solute transfer in a real porous medium. Therefore, it is essential to conduct three-dimensional runs to capture all the underlying mechanisms contributing to the mixing and dispersion in porous media. The outcomes of this study can pave the way for an optimal design and implementation of an efficient non-isothermal miscible displacement in porous media.

Similarity Search of Spatiotemporal Scenario Data for Strategic Air Traffic Management

Designing strategic air traffic management (ATM) solutions at a large spatiotemporal scale in real time is challenging, considering the range of uncertainties at the strategic time frame. Big data techniques have drawn increasing attentions to develop optimal ATM solutions to address these challenges. ATM data, such as convective weather spread and congestion propagation, represent a new data type called spatiotemporal scenario data, which has not been systematically studied. This new data type differs from the traditional spatiotemporal pointwise data in its unique spatiotemporally correlated spread patterns. As a step toward closing the loop of big data and real-time decision making for ATM, this paper introduces an effective similarity search algorithm for this new data type. This similarity search algorithm uses a multiresolution distance measure, which captures the difference between spatiotemporal scenarios. Unique properties of this distance measure are exploited to significantly reduce the computational cost associated with accessing and processing scenarios in a large database. Using real weather forecast datasets as the case study, this study investigates feasibility of the proposed similarity search algorithm. Systematic parameter impact analysis is conducted through simulation studies, which provide guidelines for parameter selection. Comparative simulation studies validate the effectiveness and efficiency of the proposed similarity search algorithm for spatiotemporal scenario data.

Spreading dynamics of a partially wetting water film atop a MHz substrate vibration

A MHz vibration, or an acoustic wave, propagating in a solid substrate may support the convective spreading of a liquid film. Previous studies uncovered this ability for fully wetting silicon oil films under the excitation of a MHz Rayleigh surface acoustic wave (SAW), propagating in a lithium niobate substrate. Partially wetting de-ionized water films, however, appeared immune to this spreading mechanism. Here, we use both theory and experiment to reconsider this situation and show partially wetting water films may spread under the influence of a propagating MHz vibration. We demonstrate distinct capillary and convective (vibrational/acoustic) spreading regimes that are governed by a balance between convective and capillary mechanisms, manifested in the non-dimensional number θ3/We, where θ is the three phase contact angle of the liquid with the solid substrate and We ≡ ρU2H/γ; ρ, γ, H, and U are the liquid density, liquid/vapour surface tension, characteristic film thickness, and the characteristic velocity amplitude of the propagating vibration on the solid surface, respectively. Our main finding is that the vibration will support a continuous spreading motion of the liquid film out of a large reservoir if the convective mechanism prevails (θ3/We < 1); otherwise (θ3/We > 1), the dynamics of the film is governed by the capillary mechanism.

Phosphor distribution optimization to decrease the junction temperature in white pc-LEDs by genetic algorithm

In this study, genetic algorithm (GA) was utilized to optimize the phosphor distribution to decrease the junction temperature of white phosphor-converted light-emitting diodes (pc-LEDs). The key steps of the GA were introduced, including selection, crossover, and mutation. Both the junction temperature and the entransy dissipation of each evolution were calculated. It was found that with evolutions, the phosphor particles tend to build a “thermal bridge” between the chip and the convective boundary and spread along the convective boundary. The junction temperature decreases from ∼157.5°C to ∼150°C and the entransy dissipation decreases from ∼18WK to ∼6WK. The least entransy dissipation principle was demonstrated to be the rule that governs the optimization processes.

Quasi-Immiscible Spreading of Aqueous Surfactant Solutions on Entangled Aqueous Polymer Solution Subphases

Motivated by the possibility of enhancing aerosol drug delivery to mucus-obstructed lungs, the spreading of a drop of aqueous surfactant solution on a physically entangled aqueous poly(acrylamide) solution subphase that mimics lung airway surface liquid was investigated. Sodium dodecyl sulfate was used as the surfactant. To visualize spreading of the drop and mimic the inclusion of a drug substance, fluorescein, a hydrophilic and non-surface-active dye, was added to the surfactant solution. The spreading progresses through a series of events. Marangoni stresses initiate the convective spreading of the drop. Simultaneously, surfactant escapes across the drop's contact line within a second of deposition and causes a change in subphase surface tension outside the drop on the order of 1 mN/m. Convective spreading of the drop ends within 2-3 s of drop deposition, when a new interfacial tension balance is achieved. Surfactant escape depletes the drop of surfactant, and the residual drop takes the form of a static lens of nonzero contact angle. On longer time scales, the surfactant dissolves into the subphase. The lens formed by the water in the deposited drop persists for as long as 3 min after the convective spreading process ends due to the long diffusional time scales associated with the underlying entangled polymer solution. The persistence of the lens suggests that the drop phase behaves as if it were immiscible with the subphase during this time period. Whereas surfactant escapes the spreading drop and advances on the subphase/vapor interface, hydrophilic dye molecules in the drop do not escape but remain with the drop throughout the convective spreading. The quasi-immiscible nature of the spreading event suggests that the chemical properties of the surfactant and subphase are much less important than their physical properties, consistent with prior qualitative studies of spreading of different types of surfactants on entangled polymer subphases: the selection of surfactant for pulmonary delivery applications may be limited only by physical and toxicological considerations. Further, the escape of surfactant from individual drops may provide an additional spreading mechanism in the lung, as hydrodynamic and/or surface pressure repulsions may drive individual droplets apart after deposition.

Surface tension gradient driven spreading on aqueous mucin solutions: a possible route to enhanced pulmonary drug delivery.

Surface tension gradient driven, or "Marangoni", flow can be used to move exogenous fluid, either surfactant dispersions or drug carrying formulations, through the lung. In this paper, we investigate the spreading of aqueous solutions of water-soluble surfactants over entangled, aqueous mucin solutions that mimic the airway surface liquid of the lung. We measure the movement of the formulation by incorporating dyes into the formulation while we measure surface flows of the mucin solution subphase using tracer particles. Surface tension forces and/or Marangoni stresses initiate a convective spreading flow over this rheologically complex subphase. As expected, when the concentration of surfactant is reduced until its surface tension is above that of the mucin solution, the convective spreading does not occur. The convective spreading front moves ahead of the drop containing the formulation. Convective spreading ends with the solution confined to a well-defined static area which must be governed by a surface tension balance. Further motion of the spread solution progresses by much slower diffusive processes. Spreading behaviors are qualitatively similar for formulations based on anionic, cationic, or nonionic surfactants, containing either hydrophilic or hydrophobic dyes, on mucin as well as on other entangled aqueous polymer solution subphases. This independence of qualitative spreading behaviors from the chemistry of the surfactant and subphase indicates that there is little chemical interaction between the formulation and the subphase during the spreading process. The spreading and final solution distributions are controlled by capillary and hydrodynamic phenomena and not by specific chemical interactions among the components of the system. It is suggested that capillary forces and Marangoni flows driven by soluble surfactants may thereby enhance the uniformity of drug delivery to diseased lungs.

Upscaling of Miscible Floods in Heterogeneous Reservoirs Considering Reservoir Mixing

Summary Inaccurate modeling of reservoir mixing by using large gridblocks in compositional simulation can affect recoveries significantly in miscible gasfloods and lead to inaccurate predictions of recovery performance. Reservoir mixing or dispersion is caused by diffusion of particles across streamlines; mixing can be enhanced significantly if the surface area of contact between the reservoir and injected fluid is increased as fluids propagate through the reservoir. A common way to convert geological models into simulation models is to upscale permeabilities on the basis of reservoir heterogeneity. Upscaling affects the degree of mixing that is modeled, but the importance of reservoir mixing in upscaling is largely ignored. This paper shows how to estimate the level of mixing in a reservoir and how to incorporate mixing into the upscaling procedure. We derive the key scaling groups for first-contact miscible (FCM) flow and show how they have an impact on reservoir mixing. Heterogeneities are assumed to dominate the flow regime so that gravity effects are negligible. We examine only local mixing, not apparent mixing caused by variations in streamline path lengths (convective spreading). Local mixing is important because it affects the strength of the injected fluid and can cause an otherwise multicontact miscible (MCM) flood to become immiscible. More than 1,000 2D numerical simulations are carried out using experimental design to estimate dispersivity as a function of the derived scaling groups. We show that reservoir mixing is enhanced owing to fluid propagation through heterogeneous media. Because mixing is dependent on heterogeneities, upscaling is an iterative process in which the level of mixing in both the longitudinal and transverse directions must be matched from the fine to the coarse scale. The most important groups that affect mixing are the mobility ratio, dispersion number, correlation lengths, and the Dykstra-Parson coefficient. Large dispersion numbers yield greater dispersivities away from the injection well. We show through simulations of both FCM and MCM floods that gridblock size can be increased significantly when reservoir mixing is large. Heterogeneous reservoirs with large longitudinal correlation lengths can be upscaled to larger gridblocks than reservoirs with random permeability fields. This paper shows how to determine a priori the maximum gridblock size allowed in both the x- and z-directions to predict the oil recovery from miscible gasfloods accurately.

Effect of Diffusion on Dispersion

Summary It is known that dispersion in porous media results from an interaction between convective spreading and diffusion. However, the nature and implications of these interactions are not well understood. Dispersion coefficients obtained from averaged cup-mixing concentration histories have contributions of convective spreading and diffusion lumped together. We decouple the contributions of convective spreading and diffusion in core-scale dispersion and systematically investigate interaction between the two in detail. We explain phenomena giving rise to important experimental observations such as Fickian behavior of core-scale dispersion and power-law dependence of dispersion coefficient on Péclet number. We track movement of a swarm of solute particles through a physically representative network model. A physically representative network model preserves the geometry and topology of the pore space and spatial correlation in flow properties. We developed deterministic rules to trace paths of solute particles through the network. These rules yield flow streamlines through the network comparable to those obtained from a full solution of Stokes’ equation. Paths of all solute particles are deterministically known in the absence of diffusion. Thus, we can explicitly investigate purely convective spreading by tracking the movement of solute particles on these streamlines. Then, we superimpose diffusion and study dispersion in terms of interaction between convective spreading and diffusion for a wide range of Péclet numbers. This approach invokes no arbitrary parameters, enabling a rigorous validation of the physical origin of core-scale dispersion. In this way, we obtain an unequivocal, quantitative assessment of the roles of convective spreading and diffusion in hydrodynamic dispersion in flow through porous media. Convective spreading has two components: stream splitting and velocity gradient in pore throats in the direction transverse to flow. We show that, if plug flow occurs in the pore throats (accounting only for stream splitting), all solute particles can encounter a wide range of independent velocities because of velocity differences between pore throats and randomness of pore structure. Consequently, plug flow leads to a purely convective spreading that is asymptotically Fickian. Diffusion superimposed on plug flow acts independently of convective spreading (in this case, only stream splitting), and, consequently, dispersion is simply the sum of convective spreading and diffusion. In plug flow, hydrodynamic dispersion varies linearly with the pore-scale Péclet number when diffusion is small in magnitude compared to convective spreading. For a more realistic parabolic velocity profile in pore throats, particles near the solid surface of the medium do not have independent velocities. Now, purely convective spreading (caused by a combination of stream splitting and variation in flow velocity in the transverse direction) is non-Fickian. When diffusion is nonzero, solute particles in the low-velocity region near the solid surface can move into the main flow stream. They subsequently undergo a wide range of independent velocities because of stream splitting, and, consequently, dispersion becomes asymptotically Fickian. In this case, dispersion is a result of an interaction between convection and diffusion. This interaction results in a weak nonlinear dependence of dispersion on Péclet number. The dispersion coefficients predicted by particle tracking through the network are in excellent agreement with the literature experimental data for a broad range of Péclet numbers. Thus, the essential phenomena giving rise to hydrodynamic dispersion observed in porous media are (1) stream splitting of the solute front at every pore, causing independence of particle velocities purely by convection; (2) velocity gradient in pore throats in the direction transverse to flow; and (3) diffusion. Taylor's dispersion in a capillary tube accounts only for the second and third of these phenomena, yielding a quadratic dependence of dispersion on Péclet number. Plug flow in the bonds of a physically representative network accounts only for the first and third phenomena, resulting in a linear dependence of dispersion on Péclet number. When all the three phenomena are accounted for, we can explain effectively the weak nonlinear dependence of dispersion on Péclet number.

Investigation of Mixing in Field-Scale Miscible Displacements Using Particle-Tracking Simulations of Tracer Floods With Flow Reversal

Summary Dispersivity data compiled over many lengths show that values at typical interwell distances are approximately two to four factors of 10 larger than those measured on cores. Such large dispersivities may represent significant mixing in the reservoir, or they may be a result of convective spreading driven by permeability heterogeneity. The work in this paper uses the idea of flow reversal to resolve the ambiguity between convective spreading and mixing. We simulate flow-reversal tests for tracer transport in several permeability realizations using particle-tracking simulations (free from numerical dispersion) on 3D, high-resolution models at the field scale. We show that convective spreading, even without local mixing, can result in dispersion-like mixing-zone growth with large disper- sivities because of permeability heterogeneity. But, for such cases, the dispersivity estimated on flow reversal is zero. With local mixing (diffusion or core-scale dispersion), the dispersivity value on flow reversal is nonzero and much larger than typical core values. Layering in permeability, while increasing the convective contribution to transport, also enhances mixing by providing larger area in the transverse direction for diffusion to act. This suggests that in-situ mixing is an important phenomenon affecting the transport of solutes in permeable media even at large scales. Dispersivity values increase with scale mainly because of the increase in the correlation in the permeability field, but they could also apparently appear to do so because the Fickian model fails to capture the mixing-zone growth correctly at early times. The results and approach shown here could be used to differentiate between displacement and sweep efficiency in field-scale displacements, to ensure accurate representation of dispersive mixing in reservoir simulation, and to guide upscaling workflows. The flow-reversal concept motivates a new line of inquiry for laboratory- and field-scale experiments.

Flow Reversal and Mixing

Summary Flow-reversal studies provide insights into mixing mechanisms in flow through porous media. In these studies, the direction of flow is reversed after the solute slug has penetrated into the medium (but not exited) to a predetermined distance. We simulated the effect of flow reversal on mixing in 2D porous media using two different approaches. In the first approach, we perform direct numerical simulation of a solute-slug transport (by solving Navier-Stokes and convection/diffusion equations) in a surrogate pore space. This approach allows a direct visualization of mixing in simple flow geometries. The effect of flow reversal on mixing is investigated for several diffusion coefficients, penetration depths, and flow geometries. The second approach uses particle tracking to simulate the effect of flow reversal at larger length scales. This approach is free of numerical dispersion, can be used in the absence of diffusion, and has no limits on the size of the simulation. It is, however, limited to layered-media flow. The simulation studies presented in this paper explain the mechanism of mixing and the origin of the irreversibility of dispersion in flow through porous media. We also explain several experimental observations on flow-reversal tests found in the literature. Mixing in porous media takes place because of interaction between convective spreading and molecular diffusion. The con-verging/diverging paths and flow around impervious sand grains cause the solute front to stretch and split. In this process, the area of contact between the solute slug and the resident fluid increases by an order of magnitude and diffusion becomes an effective mixing mechanism. This local mixing, caused by diffusion, is irreversible. For purely convective transport, solute particles retrace their path back to the inlet upon flow reversal. Convective spreading gets canceled, and echo dispersion is 0. Diffusion, even though small in magnitude, is responsible for local mixing and making dispersion in porous media irreversible. Thus, it is important to include the effect of diffusion when analyzing miscible displacements in porous media.

Pore-Scale Simulation of Dispersion in Porous Media

Summary Mixing of miscible gas with oil in a reservoir decreases the effective strength of the gas, which can adversely affect miscibility and recovery efficiency. The level of true mixing that occurs in a reservoir, however, is widely debated and often ignored in reservoir simulation in which very large grid blocks are used. Large grid blocks create artificially large mixing that can cause errors in predicted oil recovery. This paper examines mixing that occurs in porous media by solving for single-phase flow in a connected network of pores. We differentiate between true mixing that can reduce the effective strength of a miscible gas or surfactant from apparent mixing caused by convective spreading. This work differs from network models in that we directly solve the Navier-Stokes equation and the convection-diffusion equation to determine the velocities and concentrations at any location within the pores. Flow in series and layered heterogeneous porous media are modeled through use of many grains in different arrangements. We consider slug, continuous, and partial injection as well as echo tests (single-well tracer tests) and transmission tests (interwell tracer tests). We match the concentrations from the pore-scale simulations to the analytical convection-dispersion solution that includes both transverse- and longitudinal-dispersion coefficients. The results show that for flow in series and in layers, echo- and transmission-longitudinal dispersivities become equal and reach an asymptotic value if complete mixing over a cross section perpendicular to flow has occurred. In practice, the asymptotic value of dispersivity may never be reached, depending on pattern-scale heterogeneity and well spacing. Transverse-dispersion coefficients also are scale dependent, but they decrease with traveled distance. We further demonstrate that the classical Perkins-Johnston relationship between longitudinal-dispersion coefficient and fluid velocity is obtained. We conclude that echo dispersivities are reliable indicators of true mixing in porous media.

Implications of Alternative Macroscopic Descriptions Illustrated by General Balance and Continuity Equations

This article demonstrates the outstanding challenges of the application of well-established averaging procedures and rules, and shows that the results are not universal and alternative forms differ by inherent realization, difficulties, and conveniences for implementation in practical analyses of processes in porous media. Two alternative forms of the general macroscopic balance equation are derived by means of the representative elementary volume and mass-weighted-volume averaging rules and illustrated for the equation of continuity. Differences in the resulting mathematical expressions and their implications for practical problems are delineated. The macroscopic equation of continuity derived by combining the volume and mass-weighted-volume averaging rules may be convenient for conforming to the mathematical form of the microscopic equation of continuity. Using only the volume averaging rules yields an additional term compared to the conventional microscopic equation of continuity, which is referred to as transport by hydraulic dispersion due to convective mixing and spreading in porous media and contains a hydraulic dispersion parameter. An equation for empirical determination of the hydraulic dispersion parameter is also derived. Both averaging approaches are shown to be equally applicable when used with proper designations of various quantities as being the volume or mass-weighted-volume averaged. The macroscopic equation of continuity using only the volume-averaged quantities and conforming to the mathematical form of the microscopic equation of continuity is proven to involve an inherent error.

Local upper tropospheric/lower stratospheric clear‐sky water vapor and tropospheric deep convection

Local upper tropospheric and stratospheric water vapor profile retrievals by Stratospheric Aerosol and Gas Experiment II for July 1986–1990 are compared with concurrent International Satellite Cloud Climatology Project deep convective clouds to investigate the possible impact of deep convection on upper level moisture distributions. Results show that at low latitudes, clear‐sky water vapor values in the upper troposphere (above 300 mbar level) decrease following the onset of convection, perhaps because of compensatory subsidence. The drying lasts for a few hours and then is interrupted by a moistening trend centered at 6 hours after the convection breaks out, perhaps because of the detrainment of cloud liquid water from the convective tower and spreading anvil clouds. From about 9 hours later the tropical lower stratosphere shows moistening occurring. Largely because of these effects, the tropical lower stratosphere has 20–30% more moisture at sunrise compared to sunset. The later stratospheric moistening has the largest correlation significance with convection as well as the largest sampling number, though the absolute variation is much less than the variation in the troposphere. At northern hemisphere summer middle latitudes, upper tropospheric drying follows moist convection events, without an obvious moistening trend in the upper troposphere and impact in the stratosphere. The results indicate that the relationship between local upper tropospheric moisture and convective events is timescale and latitude dependent. They illustrate the utility of high vertical and temporal resolution data for proper averaging and interpretation of convection and water vapor studies.

Continuous-flow electrophoresis in the Taylor regime: a new possibility for preparative electrophoresis

A theoretical and numerical analysis shows that by performing continuous-flow electrophoresis in a chamber with a thickness of about 0.2 mm, most of the effects that cause spreading of protein filaments can be suppressed and the convective spreading is replaced by less extensive Taylor dispersion. An expression is derived that gives the resolution of the system as a function of the various design parameters. The optimum values for these parameters have been identified. Proteins with a mobility differing by only 10% can be completely separated and the sample treatment rate is of the order of 1 ml/h.