Understanding the salt−water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solutiondiffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane.In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst−Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.
Time-resolved dynamic light scattering is used to measure absolute heteroaggregation rate coefficients and the corresponding stability ratios for heteroaggregation between amidine and sulfate latex particles. These measurements are complemented by the respective quantities for the homoaggregation of the two systems and electrophoresis. Based on the latter measurements, the stability ratios are calculated using Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. In monovalent salt solutions, the two types of particles investigated are oppositely charged. In the presence of multivalent ions, however, one particle type reverses its charge, while the charge of the other particle type is hardly affected. In this region, the heteroaggregation stability ratio goes through a pronounced maximum when plotted versus concentration. This region of slow aggregation is wider than the one observed in the corresponding homoaggregation process. One also finds that the onset of this region sensitively depends on the boundary conditions used to calculate the double layer force. The present results are more in line with constant potential boundary conditions.
Shifts of the critical coagulation concentration (CCC) in particle suspensions in salt solutions containing multivalent co-ions and monovalent counterions are rationalized. One observes that the CCC is inversely proportional to the valence, and this behavior is referred to as the inverse Schulze-Hardy rule. This dependence is established by means of measurements of the stability ratio for positively and negatively charged latex particles with time-resolved light scattering. The same dependence is equally suggested by calculations of the CCC with the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby the full Poisson-Boltzmann equation for the asymmetric electrolytes has to be used. The latter aspect is essential, since in the case of multivalent co-ions the surface charge is principally neutralized by monovalent counterions. This rule complements the classical Schulze-Hardy rule, which applies in the case of multivalent counterions, and states that the CCC is inversely proportional to the sixth power of the valence.
Inorganic scaling caused by precipitation of sparingly soluble salts at supersaturation is a common but critical issue, limiting the efficiency of membrane-based desalination and brine management technologies as well as other engineered systems. A wide range of minerals including calcium carbonate, calcium sulfate, and silica precipitate during membrane-based desalination, limiting water recovery and reducing process efficiency. The economic impact of scaling on desalination processes requires understanding of its sources, causes, effects, and control methods. In this Critical Review, we first describe nucleation mechanisms and crystal growth theories, which are fundamental to understanding inorganic scale formation during membrane desalination. We, then, discuss the key mechanisms and factors that govern membrane scaling, including membrane properties, such as surface roughness, charge, and functionality, as well as feedwater characteristics, such as pH, temperature, and ionic strength. We follow with a critical review of current characterization techniques for both homogeneous and heterogeneous nucleation, focusing on the strengths and limitations of each technique to elucidate scale-inducing mechanisms, observe actual crystal growth, and analyze the outcome of scaling behaviors of desalination membranes. We conclude with an outlook on research needs and future research directions to provide guidelines for scale mitigation in water treatment and desalination.
It has recently been reported that polystyrene microbeads may be modified to realize plasticizer-free ion-selective optical sensors (optodes) on the basis of solvatochromic dye transducers. We show here that the functionalized microbeads, individually isolated by flow cytometry, exhibit unexpectedly poor fluorescent properties and that the sensor response is instead attributed to the supernatant. A more thorough study reveals that such optical microemulsion sensors can be made operationally functional and chemically selective, seemingly in the absence of any solvent matrix or added surfactant. Instead, it is shown that residual THF used in the fabrication of the emulsified sensors may solubilize the sensing components and give a functional optode response. To evaluate this further, the number of sensing components was stepwise simplified to assess their need. Variation of residual THF levels has no effect on the ion optode response when plasticizer is present, in support of established results. Lipophilic solvatochromic dye transducers are also shown not to require an added surfactant as their nature already endows the emulsified sensors with a stabilizing ionic surface charge. The ionophores are shown to exhibit much larger stability constants in the surfactant-free formulations than surfactant-based ones (Valionomycin: log!>9.2 compared to 6.1; Na +-ionophore X: 6.7 vs. 4.7), which is attributed to a less polar solvent environment for the ionophore. Potassium, sodium and calcium-selective sensors were used as model systems in this study.
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