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For an effectively one-dimensional, semi-infinite disordered system connected to a reservoir of tracer particles kept at constant concentration, we provide the dynamics of the concentration profile. Technically, we start with the Montroll–Weiss equation of a continuous time random walk with a scale-free waiting time density. From this we pass to a formulation in terms of the fractional diffusion equation for the concentration profile C ( x , t ) in a semi-infinite space for the boundary condition C ( 0 , t ) = C 0 , using a subordination approach. From this we deduce the tracer flux and the so-called breakthrough curve (BTC) at a given distance from the tracer source. In particular, BTCs are routinely measured in geophysical contexts but are also of interest in single-particle tracking experiments. For the ‘residual’ BTCs, given by 1 − P ( x , t ) , we demonstrate a long-time power-law behaviour that can be compared conveniently to experimental measurements. For completeness we also derive expressions for the moments in this constant-concentration boundary condition.

Kidney stone formation remains enigmatic, largely because of its multifactorial nature, and because assessment is by necessity based mostly on a posteriori analysis and/or on specific analyses (e.g., prescribed components found in urine) that focus on particular conditions. Here, we offer a different perspective to assess overall aspects of stone formation, delineating a method to calculate minimum times of stone formation as a function of stone type (calcium oxalate, calcium phosphate, and uric acid) and size (up to 10 mm), in the form of the pure mass of the stone, without consideration of actual formation or aggregation causes or processes. The calculations thus represent characteristic measures that delineate limits on times required to form specific stone volumes as a function of chemical content and mass. The times to form each stone type and specific size vary considerably, ranging from days to years. A key factor is the amount of the “building block” material in urine that actually contributes to stone formation, i.e., the % yield from solution to solid phase. In some cases, unrealistically high yields (e.g., 5–10%) are required to form a stone with a specified size, type, and time; this indicates that other factors – at least some of which can be deduced from the analysis – play key roles in stone formation. This information thus provides estimates that constrain assessments of stone formation mechanisms and interpretation of clinical findings.

Increased availability of nanoparticle-based products will, inevitably, expose the environment to these materials. Engineered nanoparticles (ENPs) may thus find their way into the soil environment via wastewater, dumpsters and other anthropogenic sources; metallic oxide nanoparticles comprise one group of ENPs that could potentially be hazardous for the environment. Because the soil bacterial community is a major service provider for the ecosystem and humankind, it is critical to study the effects of ENP exposure on soil bacteria. These effects were evaluated by measuring bacterial community activity, composition and size following exposure to copper oxide (CuO) and magnetite (Fe3O4) nanosized (<50 nm) particles. Two different soil types were examined: a sandy loam (Bet-Dagan) and a sandy clay loam (Yatir), under two ENP concentrations (1%, 0.1%). Results indicate that the bacterial community in Bet-Dagan soil was more susceptible to change due to exposure to these ENPs, relative to Yatir soil. More specifically, CuO had a strong effect on bacterial hydrolytic activity, oxidative potential, community composition and size in Bet-Dagan soil. Few effects were noted in the Yatir soil, although 1% CuO exposure did cause a significant decreased oxidative potential and changes to community composition. Fe3O4 changed the hydrolytic activity and bacterial community composition in Bet-Dagan soil but did not affect the Yatir soil bacterial community. Furthermore, in Bet-Dagan soil, abundance of bacteria annotated to OTUs from the Bacilli class decreased after addition of 0.1% CuO but increased with 1% CuO, while in Yatir soil their abundance was reduced with 1% CuO. Other important soil bacterial groups, including Rhizobiales and Sphingobacteriaceae, were negatively affected by CuO addition to soil. These results indicate that both ENPs are potentially harmful to soil environments. Furthermore, it is suggested that the clay fraction and organic matter in different soils interact with the ENPs and reduce their toxicity.

There is a notable scarcity of information concerning particulate matter in urine. This study presents an initial investigation that uses flow cytometry to determine the particulate content in the urine of healthy individuals, focusing on particles within a diameter range of 0.33–70 µm. Imaging flow cytometry was combined with fluorescent tagging and a birefringence technique to characterize particulate matter in terms of concentration, type, and size. This method enabled the identification and quantification of total particles within a sample, as well as the characterization of specific subtypes, including lipid-associated particles, protein aggregates, lipid-protein complexes, particles containing calcium (such as calcium oxalate crystals), DNA-containing particles (including cells and bacteria), and crystalline structures. Benchmark ranges for particulate matter present in urine were categorized according to subgroups that account for the influence of age, gender, and time of sampling, yielding valuable insights into the total number of particles traversing the human urinary tract daily. Significantly, the analysis here suggests that approximately 320 × 10 6 particles may pass through the urinary tract each day. Examination of a range of potential correlations among samples indicated that the total particle concentrations remained statistically similar. More specifically, there were no significant concentration differences in urine samples relative to sampling time, gender, or age. These findings provide valuable insights into the variability of urinary particulate matter and lay the groundwork for future, larger-scale studies. Ultimately, this research contributes to understanding urinary tract function and may potentially lead to identifying novel markers for various health conditions.

We investigate the occurrence of anomalous (non‐Fickian) transport in an hydrological catchment system at kilometer scales and over a 36‐year period. Using spectral analysis, we examine the fluctuation scaling of long‐term time series measurements of a natural passive tracer (chloride), for rainfall and runoff. The scaling behavior can be described by a continuous time random walk (CTRW) based on a power‐law distribution of transition times, which indicates two distinct power‐law regimes in the distribution of overall travel times in the catchment. The CTRW provides a framework for assessing anomalous transport in catchments and its implications for water quality fluctuations. Plain Language Summary Rain falling on an hydrological catchment, and chemicals dissolved in the rain, can follow circuitous pathways below the ground surface until they reach a stream outlet that drains the catchment. Dissolved chemicals can diffuse into lower conductivity regions within the subsurface, and chemicals can also be transported in relatively fast pathways. We investigate a unique data set that monitors chemical transport over kilometer scales, and over a long, 36‐year duration. We develop a mathematical framework to describe the transport and retention of chemical tracers in a catchment, and their arrival times to a draining outlet. Solutions of the equations exhibit characteristic features of tracer concentration variations, and offer a means to characterize and quantity catchment response to chemical inputs. Key Points An hydrological catchment system at kilometer scales is shown to exhibit anomalous (non‐Fickian) transport over a 36‐year period A continuous time random walk suggests two distinct power‐law regimes in the distribution of overall catchment travel times In the catchments considered here, preferential flow appears to occur at all length and time scales

We present the synthesis of new composite materials based on copper nanoparticles (Cu NPs) deposited onto montmorillonite (MK10) and quartz sand, for degradation of atrazine, in the context of an advanced oxidation process (AOP). The synthesis involves a first step in which polyethylenimine (PEI) capped Cu NPs (PEI_Cu NPs) are prepared, and then deposited onto, separately, MK10 and sand, through a solvent impregnation method. The resulting products are characterized in detail; the copper is found to exist as a mixture of copper (I, II) oxide. The degradation of atrazine follows a second-order kinetic model with constant values of K 2  = 1.7957 g mg −1 min −1 for MK10_PEI_Cu NPs and K 2  = 0.8133 g mg −1 min −1 for sand_PEI_Cu NPs. The reaction rate is linked to Cu 2 O and CuO redox-active species within the layers, pores and surface of the host materials. A degradation mechanism is found with application of these composite materials in the presence of H 2 O 2 ; adsorption occurs in the absence of H 2 O 2 . In contrast, the unmodified MK10 and sand exhibit adsorption in both of the above reaction conditions. Finally, the stability of the Cu NPs following degradation is evaluated, and no significant amount of copper leaching is found.

We use neutron radiography to provide high‐resolution images of water distribution patterns inside the pore space of a uniformly packed sand in a flow cell, during drainage, induced by a sequence of suction tensions. The experiments reveal the emergence of heterogeneous water distribution patterns within the pore space of the sand, although its corresponding retention function suggests homogeneity. This demonstrates that truly homogeneous water movement does not occur even under controlled laboratory conditions in an, as much as possible, homogeneous porous medium, and over dimensions of only a few millimeters. Furthermore, we conduct simulations with a Darcy‐Richards model aimed at (a) capturing the overall 1D drainage process of the flow cell, to obtain a macroscopic perspective on the system using spatially averaged saturation levels, and (b) gaining a more detailed microscopic understanding of the internal 2D pore space processes and spatial distribution patterns during water drainage. Simulation results show that the model can reproduce the macroscopic 1D drainage process of the flow cell with high accuracy. However, the microscopic, heterogeneous 2D distribution of water observed inside the flow cell can be reproduced only qualitatively, after manually introducing local heterogeneities into the pore space. This highlights that the successful reproduction of macroscopic dynamics with a Darcy‐Richards model does not imply that the model can accordingly capture truly heterogeneous process patterns on the microscale.

We re‐examine—in light of recent theoretical developments—classical experiments on dispersion of a passive tracer in fully and partially saturated porous columns. We find that the dispersion breakthrough curves (BTCs) exhibit anomalous (non‐Fickian) early arrival times and late time tailing, which can be explained by the Continuous Time Random Walk (CTRW) theory. The CTRW framework includes as a special case the classical advection‐dispersion equation (ADE) for Fickian transport. We argue that existing measurements and interpretations of dispersion should be carefully reconsidered in the framework of these advances in conceptual understanding and quantification.

We use a particle tracking approach to analyze the dynamics that control bimolecular reactive transport (A + B → C) in porous media. Particle transitions are governed by spatial and temporal distributions to account for the transport within a continuous time random walk framework. Particle tracking simulations are compared to measurements from a laboratory experiment of bimolecular reactive transport in a constant flow field. The simulations capture the experimental sequence of evolving C particle profiles using a marginally Fickian temporal distribution to quantify the particle transitions. The first profile is a fit with the model parameters, and subsequent ones are predictions. The rate of production of reaction product C over time is found to follow a power law. At early times after the injection of A particles into a uniform distribution of B particles, the strong contact and reaction between A and B particles induces the formation of a spatial void between the reactants. At longer times, the production of C is nearly constant and depends on the fluctuations of velocities of reactant particles that can surmount the void. We probe the behavioral dependence of the A, B, and C spatial profiles on the spectra of velocity fluctuations of the reactants. The latter are generated by different temporal distributions, namely, a decaying exponential distribution, which is equivalent to advective‐dispersive (Fickian) transport, and the truncated power law with degrees of non‐Fickian behavior, which is characteristic of transport in heterogeneous media. We demonstrate that the C profile exhibits subtle dynamics because of competition between the dispersion (spreading of the plumes) of A and B and the (power law) production rate.

Background To compare the efficacy of different ureteral stents subject to extrinsic ureteral obstruction (EUO), in a controlled in vitro stented ureter experiment. Methods We employ an in vitro ureter-stent experimental set-up, with latex tubing simulating flexible ureters attached to vessels simulating renal units and bladders. The flow behavior of five ureteral stents—polymeric 8F, tandem 6F, tandem 7F, endopyelotomy and metal—was tested under a ureteral deformation configuration of 40°, with 2000 g external force over a 3.5 cm length of the ureter. A constant fluid flow was applied through the ureter-stent configurations, and pressure fluctuations in the renal unit were monitored. We considered a renal unit pressure of 10 cmH 2 O or flow discontinuation in the bladder as stent failure. Urine containing debris was mimicked by use of a colloidal solution. Results Of all assessed ureteral stents, under EUO conditions, only the single 8F stents remained patent throughout the length of the experiment. All other stents—tandem 6F and 7F, single 7F, metal and endopyelotomy—displayed limitations. Conclusions Tandem and metal stents show no superiority over large luminal polymeric stents for EUO treatment in this in vitro model. Larger luminal stents offer excellent resistance to external pressure and allow adequate colloidal flow. The need for frequent exchange and bladder irritation should also be considered in the choice of stent configuration for treatment of kidney drainage under EUO.