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Short-term microfiltration (MF) fouling is commonly abated by periodically reversing the flow to remove foulants that weakly adhered to the membrane. Strong oxidants (i.e., chlorine) can be added to hydraulic backwash water to augment its efficacy—a process called chemically enhanced backwashing (CEB). Herein, we report a rigorous mathematical model for constant flux MF incorporating hydraulic backwashing and CEB, and validate it with laboratory data obtained using untreated and alum-coagulated water from the Foss Reservoir in Oklahoma, USA. We implemented an optimal control procedure and used it to predict MF behavior long past experimental timescales. We identified a frequency threshold beyond which the necessary transmembrane pressure (TMP) reached an asymptotic value, indicating a pseudo steady-state, periodic solution to the model when coupling hydraulic backwashing with CEB. We report differences in TMP saturation values and timescales by simulating transient MF of untreated and pretreated water. Numerical simulations revealed that the operating flux could be increased 10-fold after pretreatment (compared with raw water) before reaching the maximum manufacturer-recommended pressure for the hollow-fibers. The predicted higher flux and extended duration between cleaning-in-place demonstrated advantages of coagulation pretreatment under hydraulic backwashing and CEB. Model observations could guide decision making for CEB timing and frequency. 

Abstract Iron emissions from human activities, such as oil combustion and smelting, affect the Earth's climate and marine ecosystems. These emissions are difficult to quantify accurately due to a lack of observations, particularly in remote ocean regions. In this study, we used long‐term, near‐source observations in areas with a dominance of anthropogenic iron emissions in various parts of the world to better estimate the total amount of anthropogenic iron emissions. We also used a statistical source apportionment method to identify the anthropogenic components and their sub‐sources from bulk aerosol observations in the United States. We find that the estimates of anthropogenic iron emissions are within a factor of 3 in most regions compared to previous inventory estimates. Under‐ or overestimation varied by region and depended on the number of sites, interannual variability, and the statistical filter choice. Smelting‐related iron emissions are overestimated by a factor of 1.5 in East Asia compared to previous estimates. More long‐term iron observations and the consideration of the influence of dust and wildfires could help reduce the uncertainty in anthropogenic iron emissions estimates. 

Abstract. Aerosol particles are an important part of the Earth climate system, and their concentrations are spatially and temporally heterogeneous, as well as being variable in size and composition. Particles can interact with incoming solar radiation and outgoing longwave radiation, change cloud properties, affect photochemistry, impact surface air quality, change the albedo of snow and ice, and modulate carbon dioxide uptake by the land and ocean. High particulate matter concentrations at the surface represent an important public health hazard. There are substantial data sets describing aerosol particles in the literature or in public health databases, but they have not been compiled for easy use by the climate and air quality modeling community. Here, we present a new compilation of PM2.5 and PM10 surface observations, including measurements of aerosol composition, focusing on the spatial variability across different observational stations. Climate modelers are constantly looking for multiple independent lines of evidence to verify their models, and in situ surface concentration measurements, taken at the level of human settlement, present a valuable source of information about aerosols and their human impacts complementarily to the column averages or integrals often retrieved from satellites. We demonstrate a method for comparing the data sets to outputs from global climate models that are the basis for projections of future climate and large-scale aerosol transport patterns that influence local air quality. Annual trends and seasonal cycles are discussed briefly and are included in the compilation. Overall, most of the planet or even the land fraction does not have sufficient observations of surface concentrations – and, especially, particle composition – to characterize and understand the current distribution of particles. Climate models without ammonium nitrate aerosols omit ∼ 10 % of the globally averaged surface concentration of aerosol particles in both PM2.5 and PM10 size fractions, with up to 50 % of the surface concentrations not being included in some regions. In these regions, climate model aerosol forcing projections are likely to be incorrect as they do not include important trends in short-lived climate forcers. 

Microfiltration is a widely used engineering technology for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance and flux decline during membrane operations. The growth of bacteria constituting such a biological layer implicates the formation of a multispecies biofilm and the consequent increase of operational costs for reactor management and cleaning procedures. To predict the biofouling evolution, a mono-dimensional continuous free boundary model describing biofilm dynamics and EPS production in different operational phases of microfiltration systems has been well studied. The biofouling growth is governed by a system of hyperbolic PDEs. Substrate dynamics are modeled through parabolic equations accounting for diffusive and advective fluxes generated during the filtration process. The free boundary evolution depends on both microbial growth and detachment processes. What is not addressed is the interplay between biofilm dynamics, filtration, and water recovery. In this study, filtration and biofilm growth modeling principles have been coupled for the definition of an original mathematical model able to reproduce biofouling evolution in membrane systems. The model has been solved numerically to simulate biologically relevant conditions, and to investigate the hydraulic behavior of the membrane. It has been calibrated and validated using lab-scale data. Numerical results accurately predicted the pressure drop occurring in the microfiltration system. A calibrated model can give information for optimization protocols as well as fouling prevention strategies. 

Abstract We derive a class of exact solutions for Stokes flow in infinite and semi‐infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no‐slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi‐infinite channel domain, the ground‐state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane‐based water purification, heat and mass transfer, and fuel cells.