The Lagrangian Picture, Part I : Fundamentals of the Lagrangian Approach to Solute Transport

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Velocity Field ◽  
Solute Transport ◽  
Complex Geometry ◽  
Concentration Field ◽  
Breakthrough Curves ◽  
Lagrangian Approach ◽  
Travel Times ◽  
Solute Fluxes ◽  
Reactive Solutes ◽  
Solute Particle

This chapter explores the principles of the Lagrangian approach to solute transport, with an emphasis on the dispersive action of the spatial variability of the velocity field. We start by developing the tools for characterizing the displacement of a single, small solute particle that will subsequently be used for characterization of the concentration’s variability and uncertainty, and we continue with a discussion of the stochastic description of solute travel times and fluxes. The principles presented in this chapter will be employed in chapter 10 to derive tools for applications such as macrodispersion coefficients, solute travel time moments, the moments of the solute fluxes and breakthrough curves, and transport of reactive solutes. As has been observed in many field studies and numerical simulations, the motion of solute bodies in geological media is complex, making the geometry of the solute bodies hard to predict. Furthermore, the concentration varies erratically, sometimes by orders of magnitude, over very short distances. The variability of the velocity field plays a significant role in shaping this complex geometry, and makes it impossible to characterize the concentration field deterministically. The alternatives we will pursue include characterizing the concentration through its moments such as the expected value and variance, and other descriptors of transport such as solute fluxes and travel times. This line was pursued in chapter 8 using the Eulerian framework. In this chapter we pursue this line from the Lagrangian perspective. Applications of these concepts are presented in chapter 10. Let us consider the displacement of a marked solute particle over time.

scholarly journals Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography

2020 ◽  
Vol 117 (38) ◽  
pp. 23443-23449 ◽  
Author(s):  
Sharul Hasan ◽  
Vahid Niasar ◽  
Nikolaos K. Karadimitriou ◽  
Jose R. A. Godinho ◽  
Nghia T. Vo ◽  
...  
Keyword(s):  
Solute Transport ◽  
High Speed ◽  
Three Dimensional ◽  
Concentration Field ◽  
Solute Concentration ◽  
Breakthrough Curves ◽  
Pore Scale ◽  
X Ray ◽  
Long Tails ◽  
Computed Microtomography

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids’ topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

scholarly journals An effective parameterization to quantify multiple solute flux breakthrough curves

2014 ◽  
Vol 11 (6) ◽  
pp. 6993-7017
Author(s):  
E. Bloem ◽  
M. de Gee ◽  
G. H. de Rooij
Keyword(s):  
Solute Transport ◽  
Flux Density ◽  
Breakthrough Curves ◽  
Solute Flux ◽  
Spatial Effects ◽  
Solute Fluxes ◽  
Spatial Aspect ◽  
Temporal Aspect ◽  
Temporal And Spatial ◽  
The Individual

Abstract. To understand soil and groundwater contamination we study the temporal and spatial aspects of solute transport in the unsaturated zone. One monitoring instrument that captures both aspects is the multi-compartment sampler (MCS). With the MCS developed by Bloem et al. (2010) we are able to measure the downward solute fluxes in 100 compartments at the depth of installation of the MCS, with a minimal disturbance of the flow field. Over time this dataset results in 100 individual solute flux breakthrough curves (BTCs) (temporal aspect). Sorting the BTCs in descending order of solute mass gives the spatial solute distribution curve (spatial aspect). We present a method to quantitatively characterize datasets gathered with MCS (or single samplers installed at multiple locations in a field at the same depth). The method approximates the full set of breakthrough curves using only a single function with four to eight parameters, which combines both temporal and spatial effects of solute transport in soils. This is achieved by modeling the scaled solute flux density breakthrough curves (BTCF) for each compartment as the solution of a conventional one-dimensional equilibrium convection disperion equation (CDE), without modifications. We detect and parameterize any relationships between the resulting transport velocities and dispersion coefficients of the individual BTCFs. Finally the spatial aspect is parameterized using the Beta distribution. This method is based on the flux density BTCs directly, which for transport phenomena is preferred over solute concentrations. In three experiments on undisturbed soils, the resulting approximation matched the data well.

Claudin Tight Junction Proteins: Novel Aspects in Paracellular Transport

2008 ◽  
Vol 28 (6) ◽  
pp. 577-584 ◽  
Author(s):  
Constanze Will ◽  
Michael Fromm ◽  
Dominik Müller
Keyword(s):  
Tight Junction ◽  
Solute Transport ◽  
Molecular Mechanisms ◽  
Family Members ◽  
Transport Processes ◽  
Paracellular Transport ◽  
Solute Flux ◽  
Solute Fluxes ◽  
Essential Components ◽  
Renal Tubular

Claudins are essential components of the intercellular tight junction and major determinants of paracellular solute fluxes across epithelia and endothelia. Many members of this family display a distinct charge or size specificity, whereas others render the epithelium impermeable to transport. Due to intercellular localization, claudin-mediated transport processes are passive and driven by an electrochemical gradient. In epithelial tissues, claudins exhibit a temporal–spatial expression pattern corresponding with regional and local solute transport profiles. Whereas paracellular transport mechanisms in organs such as intestine and kidney have been extensively investigated, little is known about the molecular mechanisms determining solute transport in the peritoneum, and thus the determinants of peritoneal dialysis. Given the ubiquitous expression of claudins in endothelia and epithelia, it is predictable that claudins also contribute to pore formation and determination in the peritoneum, and that they are involved in solute flux. Therefore, we review the basic characteristics of claudin family members and their function as exemplified in renal tubular transport and give an outlook to what extent claudin family members might be of importance for solute reabsorption across the peritoneal membrane.

scholarly journals An experimental evaluation of the solute transport volume in biodegraded municipal solid waste

1999 ◽  
Vol 3 (3) ◽  
pp. 429-438 ◽  
Author(s):  
H. Rosqvist ◽  
D. Bendz
Keyword(s):  
Solute Transport ◽  
Solid Waste ◽  
Volume Fraction ◽  
Tracer Tests ◽  
Travel Times ◽  
Volume Fractions ◽  
Rapid Flow ◽  
Set Up ◽  
Log Normal ◽  
Transport Volume

Abstract. A large undisturbed sample (3.5 m3) of 22-year-old, biodegraded solid waste set up to estimate the volume fraction participating in the transport of solutes through the waste material. Altogether, five tracer tests were performed under ponding and sprinkling conditions, and under steady-state and transient conditions. The experimental break through curves (BTCs), which indicated a non-equilibrium transport of the solute by early peaks and long right-hand tails, were used to parameterize log-normal solute travel time probability density functions. The expected solute travel times (i.e. the median solute travel times) were assessed and the corresponding fraction of the experimental volumes active in the transport of solutes was estimated. The solute transport volume fractions defined by the median solute travel times were estimated to vary between 5 and 10% of the total experimental volume. Further, the magnitudes of the solute transport volume fractions defined by the modal (peak) solute travel times were estimated to vary between 1 and 2% of the total experimental volume. In addition, possible boundary effects in terms of rapid flow along the wall of the experimental column were investigated.

scholarly journals Calculation of turbulent diffusion jets under effects of gravity and moving surrounding air

2001 ◽  
Vol 23 (2) ◽  
pp. 87-94
Author(s):  
Bui Van Ga ◽  
Nhan Hong Quang ◽  
Jean Marc Vignon
Keyword(s):  
Velocity Field ◽  
Turbulent Diffusion ◽  
Concentration Field ◽  
Integral Model ◽  
System Of Equations ◽  
Kutta Method ◽  
Air Velocity ◽  
Runge Kutta Method ◽  
Jet Axis ◽  
General Conditions

The basis theory for the turbulent diffusion of jet and flame has been presented previously [1, 2]. But that one applies only in quiet surrounding air with the effects of buoyancy neglected. In the present paper, the theory is developed further by establishing an integral model for a jet in more general conditions with variable inclined angles, under effects of gravity and surrounding air velocity in any direction compared to the jet axis. The system of equations is closed by turbulence k-E model and is solved by 4th order Runge-Kutta method. In the first stage, the model is applied to predict the velocity field, the concentration field and with development of a 0.3 m diameter jet.

scholarly journals Insight of thermally stratified Jeffrey fluid flow inside porous medium subject to chemical species and melting heat transfer

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987618
Author(s):  
Mubashar Javed ◽  
Muhammad Farooq ◽  
Aisha Anjum ◽  
Shakeel Ahmad
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Thermal Stratification ◽  
Heterogeneous Reaction ◽  
Concentration Field ◽  
Chemical Species ◽  
Internal Heat ◽  
Nonlinear Problems ◽  
Deborah Number ◽  
Jeffrey Fluid

This article concentrates on two-dimensional magnetohydrodynamic stagnation flow of Jeffrey liquid on a nonlinearly stretching sheet which possesses variable thickness. Simultaneous impact of melting as well as thermal stratification is specifically investigated in this study due to their tremendous involvement in plenty of natural and industrial processes. Internal heat generation and presence of chemical species are considered to ponder at heat transfer properties. Series solution has been obtained by solving the developed nonlinear problems. Physical behavior of various controlling parameters such as velocity, thermal, and concentration fields are investigated. It has been found that temperature field decays due to higher intensity of thermal stratification parameter, but thickness of thermal boundary layer boosts up. Larger Deborah number results in incremented velocity field. For uplifted wall thickness parameter, velocity field depreciates. Concentration field declines for enhanced parameters of homogeneous as well as heterogeneous reaction. Moreover, velocity is decreasing function of porosity parameter.

scholarly journals Physics-Based Simulation of Ocean Scenes in Marine Simulator Visual System

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 215 ◽  
Author(s):  
Haijiang Li ◽  
Hongxiang Ren ◽  
Shaoyang Qiu ◽  
Chang Wang
Keyword(s):  
Velocity Field ◽  
Complex Geometry ◽  
Single Layer ◽  
Strong Stability ◽  
Constant Density ◽  
Particle Hydrodynamics ◽  
Constant State ◽  
Divergence Free ◽  
Solution Efficiency ◽  
Physics Based Simulation

The realistic simulation of ocean scenes is of great significance in many scientific fields. We propose an improved Smoothed Particle Hydrodynamics (SPH) framework to simulate the ocean scenes. The improved SPH combines nonlinear constant density constraints and divergence-free velocity field constraint. Density constraints adjust the particle distribution on position layer, so that the density is constrained to a constant state. The addition of the divergence-free velocity field constraint significantly accelerates the convergence of constant density constraint and further reduces the density change. The simulation results show that the improved SPH has high solution efficiency, large time steps, and strong stability. Then, we introduce a unified boundary handling model to simulate coupling scenes. The model samples the boundary geometry as particles by means of single layer nonuniform sampling. The contribution of the boundary particles is taken into account when the physical quantities of fluid particles are computed. The unified model can handle various types of complex geometry adaptively. When rendering the ocean, we propose an improved anisotropic screen space fluid method, which alleviates the discontinuity problem near the boundary and maintains the anisotropy of particles. The research provides a theoretical reference for the highly believable maritime scene simulation in marine simulators.

scholarly journals Changes in discharge and solute dynamics between hillslope and valley-bottom intermittent streams

2012 ◽  
Vol 16 (6) ◽  
pp. 1595-1605 ◽  
Author(s):  
S. Bernal ◽  
F. Sabater
Keyword(s):  
Organic Carbon ◽  
Dissolved Organic Carbon ◽  
Stream Water ◽  
Valley Bottom ◽  
Solute Fluxes ◽  
Nitrate Export ◽  
Carbon And Nitrogen Dynamics ◽  
Reactive Solutes ◽  
Monthly Discharge ◽  
Solute Dynamics

Abstract. To gain understanding on how alluvial zones modify water and nutrient export from semiarid catchments, we compared monthly discharge as well as stream chloride, carbon, and nitrogen dynamics between a hillslope catchment and a valley-bottom catchment with a well-developed alluvium. Stream water and solute fluxes from the hillslope and valley-bottom catchments showed contrasting patterns between hydrological transitions and wet periods, especially for bio-reactive solutes. During transition periods, stream water export decreased >40% between the hillslope and the valley bottom coinciding with the prevalence of stream-to-aquifer fluxes at the alluvial zone. In contrast, stream water export increased by 20–70% between the hillslope and valley-bottom catchments during wet periods. During transition periods, stream solute export decreased by 34–97% between the hillslope and valley-bottom catchments for chloride, nitrate, and dissolved organic carbon. In annual terms, stream nitrate export from the valley-bottom catchment (0.32 ± 0.12 kg N ha−1 yr−1 [average ± standard deviation]) was 30–50% lower than from the hillslope catchment (0.56 ± 0.32 kg N ha−1 yr−1). The annual export of dissolved organic carbon was similar between the two catchments (1.8 ± 1 kg C ha−1 yr−1). Our results suggest that hydrological retention in the alluvial zone contributed to reduce stream water and solute export from the valley-bottom catchment during hydrological transition periods when hydrological connectivity between the hillslope and the valley bottom was low.

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