Particle Diffusion Model Research Articles

Preparation and kinetic study of organic amine‐loaded ion‐exchange resin as CO2 adsorbents

AbstractOrganic amine adsorbents prepared by template method using ion exchange resin (D001) as support and polyethyleneimine (PEI) as a modifier, and the preparation process was optimized by orthogonal experiment plan. The results showed that adsorbents prepared under conditions (the copper ion concentration was 0.2 mol/L, the ultrasonic time was 3 hr, and the PEI loadings were 30%) had an excellent CO2 adsorption properties. The effects of temperature and gas influent velocity on CO2 adsorption properties were investigated in a fixed bed reactor. When PEI loadings were 30%, the adsorption temperature was 65°C and the gas influent velocity was 40 ml/min, organic amine adsorbents performed a better PEI dispersion, stability, and CO2 adsorption capacity. Maximum CO2 adsorption capacity was 4.00 mmol/g. Besides, the CO2 adsorption capacity decreased by only 10% after 10 cycles of adsorption–desorption tests, attribute to a small amount of PEI was volatilize during the regeneration process. The external diffusion was eliminated by increasing the gas influent velocity, and the adsorption data were well fitted the Weber‐Morris particle diffusion model, indicating that CO2 adsorption was controlled by internal diffusion.

Influence of Ultrasound on the Adsorption, Diffusion and Kinetics of Leather Dyeing Process: Mechanistic Insight

Leather is a natural porous material, which is composed of a three-dimensional weave of tanned collagen fibre bundles. This paper studies the influence of power ultrasound on the adsorption and kinetics of leather dyeing process. Dyeing experiments have been carried out using ultrasound (150 W, 33 kHz) and compared with that of static control dyeing process. The data of dye uptake in leather have been analysed using Freundlich and Langmuir adsorption isotherms. Intra Particle diffusion model has been employed to calculate Intra particle diffusion rate constant and Boundary Layer effect. Diffusion coefficient (D) of dye through leather matrix has also been calculated. Kinetics of leather dyeing process has been studied through pseudo first and second order rate equation. The Freundlich constant (Kf), Langmuir parameter (Qm), Intra Particle diffusion rate constant (Kd) Apparent Diffusion coefficient (D) and Pseudo First order kinetic constant, K1 have been calculated to be 18.67 mg/g, 50 mg/g, 0.006 min-1, 1.89 * 10-6 cm2/s and 1.7 mg/g min0.5 respectively for ultrasound assisted leather dyeing as compared to that of 0.1 mg/g, 26.67 mg/g, 0.733 min-1, 0.19 * 10-6 cm2/s and 0.003 mg/g min0.5 respectively for control process. The results indicate that significant enhancement in adsorption capacity with more favorable dye adsorption as well as about 10- fold increase in Apparent Diffusion coefficient with significant reduction in boundary layer effect, improved kinetic parameters due to the use of ultrasound in leather dyeing as compared to control. Mechanisms for enhancement in Adsorption and Kinetic Parameters in leather dyeing due to the use of ultrasound have been presented and corroborate well with better dye penetration, color value and fastness properties. Therefore, the present study demonstrates that the use of ultrasound in leather dyeing helps both in adsorption of dyes as well as diffusion process through the leather matrix.

Dynamic prediction of PM2.5 diffusion in urban residential areas in severely cold regions based on an improved urban canopy model

Problems related to air pollution have become more serious over the past few years, and air particulates have attracted attention as one of the most significant air pollutants. The air quality in residential areas is closely related to human health, as urban residents spend most of their time here. Because of the unique climatic characteristics of cities in severely cold regions, their urban energy structure, underlying surface, and architectural form are different from other cities to a certain degree, which causes distinctive particulate pollution characteristics. This study establishes a urban local-scale particle diffusion model for cities in severely cold regions and investigates the particle diffusion process and vertical concentration distribution in a residential area through simulation. The simulation results show that the near-ground PM2.5 mass concentrations are significantly affected by traffic flow. The vertical distribution of PM2.5 mass concentrations in residential areas demonstrates a decreasing trend with an increase in height owing to the effect of vehicle emissions and fugitive road dust. This study systematically studies the vertical distribution of particulate matter in urban settlements in severely cold regions and provides a theoretical basis and technical support for further improving the air quality of such urban settlements.

Oxidized and Non-Oxidized Multiwalled Carbon Nanotubes as Materials for Adsorption of Lanthanum(III) Aqueous Solutions

The behavior of oxidized and non-oxidized multiwalled carbon nanotubes (MWCNTs) in the adsorption of lanthanum(III) from aqueous solutions is described. Metal uptake is studied as a function of several variables such as the stirring speed of the system, pH of the aqueous solution and metal and nanomaterial concentrations. The experimental results are fitted to various kinetic and isotherm models, the rate law being fitted to the film diffusion and particle diffusion models, when the non-oxidized and the oxidized nanomaterials are used to remove lanthanum from the solution, respectively. Sulfuric acid solutions seem to be appropriate to recover the metal from La-loaded nanomaterials.

Phosphorus removal from secondary wastewater effluent using copper smelter slag

This study investigated the use of copper smelter slag for the removal of phosphorus from secondary wastewater effluent through batch tests. The media was physically and chemically characterized and showed presence of Fe2O3 (45.22%), SiO2 (14.98%), Al2O3 (3.21%), CaO (1.99%), SO3 (1.77%) and MgO (1.33%). Scanning electron microscopy monographs revealed smooth and flat surface and no heterogeneity on the surface of the slag with visible micro pores before the experiment and less visible after the experiment. The point of zero charge of the media was 5.0. Equilibrium was reached after 4 h at 29.5 ± 0.71% phosphorus removal efficiency and media dosage of 0.4/100 mL. The kinetic data was best described by Pseudo second order equation. More than one mechanisms were involved in the adsorption of phosphorus onto copper smelter slag as suggested by multi-linearity of intra particle diffusion model. Ninety seven percent (97.5 ± 0.0%) removal efficiency was achieved at an equilibrium dosage of 160 gL-1. The equilibrium isotherm was described better by Langmuir equation with observed maximum adsorption capacity of 0.16 mg P g−1 media and the experimental maximum adsorption capacity was 0.26 mg P g−1 media. Regeneration studies showed low performance with maximum efficiency of 11.7% revealed during the first regeneration trial therefore low practical benefits. Copper smelter slag is a poor adsorbent for phosphorus and further studies on the media should be conducted.

Polymeric nanostructures for photocatalytic dye degradation: polyaniline for photocatalysis

The motivation for the work presented in this paper comes from the need to explore novel and efficient photocatalysts for the degradation of contaminants from waste water. In this regard and in addition to the existing class of semiconductor photocatalysts, polymeric structures such as polyaniline, have emerged with the potential to degrade common water contaminants through photocatalysis. This paper elucidates the preparation of polyaniline (PANI) nanofibers and its implementation as a photocatalyst for the degradation of organic dyes such as Methylene Blue (MB) and Methyl Orange (MO). PANI was obtained using oxidative polymerisation and was examined for morphological and structural properties using XRD, SEM, TEM and FTIR which confirmed the formation of fibrous PANI sample. The chemical composition and the bonding states were studied using XPS. Subsequently, photo induced degradation of MB was performed in the presence of PANI as photocatalyst which indicated 42% degradation while MO was degraded by 97% in less than 3 h. Kinetic analysis by pseudo first order, second order and intra particle diffusion model, showed well-fit results for first order kinetic model with a rate constant of 0.0505 (g mg−1 min−1). The photocatalytic efficiency of PANI was assigned to the π–π* transition wherein the excited state electrons were transferred from the π to the π* orbital. Therefore, polyaniline was observed to be a promising photocatalyst for the degradation of environmental pollutants.

Study on adsorption mechanism of silicate adsorbents with different morphologies and pore structures towards formaldehyde in water

Silicate with various pore structures and morphologies showed different adsorption effects on removing organic pollutants, but the corresponding adsorption mechanisms are ambiguous. In this work, the adsorption mechanisms of formaldehyde in water by silicate adsorbents with different morphologies and pore structures were investigated. Diatomite with disc-like morphology and calcium silicate with short rod-like morphology were selected for comparison. Results show that the adsorption capacity of calcium silicate with superior specific surface area and pore volume is higher than that of Diatomite. The pseudo-first-order and pseudo-second-order models were employed to fit the dynamics behaviors of adsorption process, and the pseudo-second-order model was more suitable one. Furthermore, the adsorption data was also modeled by the internal particle diffusion model and it was found that the adsorption process could be divided into surface fast adsorption and internal particle diffusion. The adsorption mechanism of diatomite on formaldehyde includes surface adsorption and internal particle diffusion, while surface adsorption is the main mechanism of removing formaldehyde by calcium silicate. Four adsorption isotherm models are used to describe the isotherm adsorption process, while Freundlich isotherm shows the best fit results, which indicates that both adsorbents are multilayer adsorption. It can be classified as physical adsorption.

Simultaneous removal of Cd(II), Co(II), Cu(II), Pb(II), and Zn(II) ions from aqueous solutions via adsorption on FAU-type zeolites prepared from coal fly ash

This study reports the potential for the simultaneous removal of Cd(II), Co(II), Cu(II), Pb(II), and Zn(II) ions from aqueous solutions by FAU-type zeolites prepared from coal fly ash. The zeolite synthesis route was via alkaline fusion followed by the addition of deionised water and hydrothermal treatment using fly ash to water mass ratios of 4, 10, 15, and 20. XRD, XRF, SEM and N2 adsorption measurements were used to characterize the prepared zeolites. Adsorption experiments were carried out for variations in concentration, time, and adsorbent loading. The adsorption process followed pseudo second-order kinetics and Langmuir adsorption isotherm; intra particle diffusion model fitting indicated that diffusion within the pores affected the rate controlling steps and mass transfer across boundary layers for the adsorbate – adsorbent system. The efficacy of FAU – type zeolite for the quinary-metal ions adsorption studied decreased in the order Pb(II) > Cu(II) > Cd(II) > Zn(II) > Co(II).

2,4-D adsorption from agricultural subsurface drainage by canola stalk-derived activated carbon: insight into the adsorption kinetics models under batch and column conditions

In this study, the experimental and kinetic modeling investigations were performed to evaluate the ability of mesoporous and microporous canola stalk-derived activated carbon (CSAC) on 2,4-dichlorophenoxyacetic acid (2,4-D) removal from synthetic and natural water in both batch and continuous systems. Three empirical models (pseudo-first-order equation (PFOE), pseudo-second-order equation (PSOE), and the Elovich equation (EE)) and three theoretical models (film diffusion model (FDM), particle diffusion model (PDM), and second-order chemical reaction rate model (SOCRRM)) were compared in terms of diffusion coefficients, maximum 2,4-D adsorption, and rate constants at various operating conditions. CSAC was prepared at 600°C and activated with water steam under a controlled flow and subsequently characterized by various analytical methods. The results showed that the maximum 2,4-D uptake by CSAC was achieved as 135.8mgg-1 under a pH of 2 and an initial 2,4-D concentration of 150mgL-1. The CSAC removed 38.3% of Na+, 43.49% of K+, 8.96% of Mg2+, 45.14% of Ca2+, 17.2% of Cl-1, 39.48% of HCO3-, 63.74% of SO42-, and 100% of the herbicide from agricultural subsurface drainage water and also retained its usability after regenerated by acetone for five cycles. It was concluded that the 2,4-D was adsorbed on the surface of the CSAC through its aromatic ring interaction with the reactive functional groups of the adsorbent. The model result indicated that the PDM is the best-fitting kinetic model for the adsorption of 2,4-D by CSAC, followed by FDM, SOCRRM, PSOE, PFOE, and EE. The mass balance equation based on PDM describes the dynamic behavior of the column satisfactorily. Graphical abstract.

Study of the mechanism of removing ultrafine particles using SBA-15

In 2017, China’s industrial dust emissions accounted for 7.96 million tons, of which the iron and steel industry contributed approximately 25%. Particulate matter discharged from the iron and steel industry is mostly of a small size, high in temperature, and complex in composition. The mass concentration of ultrafine particles(UFPs) with particle sizes that are less than0.1 μm is low;however, the proportion of quantity concentration can be as high as 90%. Currently, the commonly used bag filters and electrostatic precipitators are not sufficiently efficient at collecting fine particles. Additionally, owing to the larger specific surface area of fine dust particles, they easily become carriers of adsorbing harmful gases, which has a greater impact on the environment and human health;thus, it is imperative to determine a simple and efficient filtration method to remove ultrafine particles. In this paper, the removal efficiency and mechanism of UFPs(2.5–25 nm) were investigated by using a scanning electromobility particle size spectrometer(SMPS)test system for SBA-15 for different pore sizes. This was done to provide a theoretical basis for the application of mesoporous materials in the control of ultra-low emission of particulate matter in the iron and steel industry. Based on the experimental results and characterization analysis, it is found that a mesoporous filtration medium with a large pore size is more efficient at affecting UFPs entry.There are many affinity sites for UFPs on the inner and outer surfaces of mesoporous materials with a specific pore size. Increasing the complexity of the ends is beneficial for improve the filtration performance of the materials. The presence or absence of nitrogen has little effect on the removal of UFPs. The diffusion effect of UFPs is stronger owing to the existence of mesoporous particles, and the diffusion coefficient is increased when particles enter the pore. Therefore, there is a difference between the theoretical exponent(m=-2/3) in the traditional model for particle diffusion and the actual diffusion results of UFPs in mesoporous materials.

Equilibrium, kinetics and thermodynamics studies of Cd sorption onto a dithizone-impregnated Amberchrom CG-300m polymer resin

Amberchrom CG-300m, a styrene acrylic ester polymer resin, was studied for the first time as sorbent for metal ion sorption in a solid-phase extraction system. The polymer sorbent was modified via impregnation with dithizone to improve its efficiency. Efficiency of the modified sorbent improved by more than 47%. The loading capacity of the resin is 3.2 mg dithizone per gram of sorbent. The mechanisms of Cd(II) sorption from aqueous solutions are presented. Capacity of the modified resin for Cd(II) was investigated in batch experiments as a function of pH, initial metal ion concentration, temperature and time. Maximum capacity of 0.551 mg Cd(II) per gram of sorbent was achieved. The dimensionless separation factor, 0 < RL < 1, associated with the Langmuir isotherm (at T = 294 K) signifies sorption of Cd(II) was favorable, as do negative values of free energy of sorption (ΔG) at temperatures exceeding 293 K. Sorption was endothermic (ΔH > 0) while ΔS > 0 reflects the affinity of the sorbent towards Cd(II). The pseudo-second order model proved to be the best fit model for Cd(II) sorption kinetics data. Particle-diffusion models suggest sorption follows film as well as pore diffusion mechanisms.

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

Sodium itaconate grafted nanocellulose for facile elimination of lead ion from water

Nanocellulose from jute fiber was grafted with sodium itaconate through esterification with itaconic anhydride followed by replacement of surface protons with sodium ions. A tea-bag pouch containing sodium itaconate grafted nanocellulose (SINC) acted as a chemisorbant for lead ions through ion exchange when dipped in an aqueous solution. Surface morphology and surface modification of SINC were characterized by FTIR, SEM, EDX, TEM, AFM and BET N2 adsorption isotherm techniques. The effective diminution of lead ion concentration was ascertained by AAS and ICP-MS methods. The impact of operating parameters like residence time, temperature, ion concentration and pH on the chemisorption capability was evaluated. The kinetic data conformed to the intra particle diffusion model and pseudo second order reaction. The Freundlich model was found to be the best for describing isotherm equilibrium. The maximum chemisorption capacity (mg g−1) of SINC, nanocellulose itaconate and nanocellulose in aqueous solution for Pb2+ were found to be 85, 58 and 10 respectively at pH 5.5. The used SINC was easily regenerated via desorption of lead ion using NaCl. The regenerated SINC could be reused for four consecutive cycles with no loss of chemisorption efficiency. The SINC was also effective for removal of other metal ions such as chromium, cadmium and mercury. This is an easily synthesizable, adaptable and well-chemisorbing system with proven reusability. This could emerge as an economical alternative to the conventional cation exchange resins. Itaconic acid functionalization of nanocellulose resulted in a cation exchange resin with good chemisorption capability, regenerability and reusability in solution.

Novel synthesis of Ni/Fe layered double hydroxides using urea and glycerol and their enhanced adsorption behavior for Cr(VI) removal

Novel modified Ni/Fe layered double hydroxides with different morphology of spherical – like shape were fabricated via using urea as a ligand and glycerol (Ni/Fe LDH/GL) with Ni:Fe molar ratios of 2:1 by the simplest co -precipitation method. Also, for comparison purposes, Ni/Fe LDH was synthesized to be used as a control one. A suggested interpretation for the morphology change was also given. The materials were characterized by X-ray diffraction (XRD), The Fourier transform infrared (FT - IR) spectroscopy, field emission scanning electron microscopy (FESEM), EDX for elemental analysis, high resolution transmission electron microscopy (HRTEM), Brunauer, Emmett, and Teller (BET) equation, particle size distributions and Zeta potential measurements. In addition, the synthesized materials were used as adsorbents for removal of potassium dichromate from aqueous solutions under various experimental conditions. The adsorption of Cr (VI) was strongly pH dependant and the pHPZC was studied. Kinetic studies were evaluated through different models including, pseudo first and second orders, mixed 1, 2 orders, intra particle diffusion and Avrami models. For adsorption isotherms, two-parameter models (Langmuir, Freundlich and Temkin) and three parameter models (Sips, Langmuir-Freundlich and Tooth) were investigated showing maximum adsorption capacity of 50.43 mg/g and 136.05 mg/g for Ni/Fe LDH and Ni/Fe LDH/GL, respectively. Also, the effect of temperature was investigated at (23, 35, 45, 55 °C) and the thermodynamic parameters (∆H°, ∆S° and ∆G°) were calculated showing exothermic and spontaneous adsorption process. The effect of coexisting anions (Cl−, SO42− and HPO42−) and humic acid at different concentrations on the removal efficiency of dichromate ions was investigated. Chemical stability and recyclability of these adsorbents were also studied. The intermolecular hydrogen bonds formation between dichromate ion, urea, glycerol, LDH was explored by Monte Carlo simulation This study suggested that the modified Ni/Fe LDH/GL materials were promising nanoadsorbents for efficient potassium dichromate removal.

Rapid defluoridation of drinking water by calcium carbonate nanoadsorbent: characterization, adsorption studies and application to real samples’ treatment

Abstract Groundwater contamination of fluoride is a serious global issue leading to its excessive intake and subsequently numerous adverse health issues. This research was designed to assess the efficiency of nanoadsorbent for removal of fluoride levels from water. For this purpose, calcium carbonate nanoparticles (average particle size 14.6 nm) were prepared and later applied for effective removal of fluoride from simulated as well as real drinking water (DW) samples collected from different areas of Lahore, Pakistan. The particles were characterized by powder X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy/energy-dispersive X-ray spectroscopy, and atomic force microscopy. Physico-chemical parameters were studied in batch mode which revealed high adsorption capacity (i.e. 754.36 mg g−1) at room temperature and neutral pH within 10 min. The kinetic isotherms (general, pseudo-first, and pseudo-second order), diffusion studies (intra-particle diffusion and particle diffusion models), and adsorption models (Langmuir, Freundlich, Liu, and Redlich–Peterson) were also applied to evaluate the suitability of adsorption process. The applicability of nanoadsorbent to fluoride-contaminated real DW samples led to 98–100% efficacy of defluoridation.

Adsorptive performances and characterisations of biologically synthesised zinc oxide based nanosorbent (ZOBN)

In the present study, we have synthesised zinc oxide based nanosorbent (ZOBN) by using the leaves extract of Shorea robusta (Sal) and removed Pb2+ and Cd2+ ions from waste water. Biologically synthesised ZOBN has been characterised by using different analytical methods such as UV–Visible spectroscopy, FTIR, powder XRD, FESEM and EDX. Adsorption study of Pb2+ and Cd2+ ions onto ZOBN from waste water was performed under the batch adsorption experiments and maximum adsorption of Pb2+ and Cd2+ ions found at optimized conditions such as higher contact time, higher acidic pH and moderate temperature. The adsorption efficiencies of Pb2+ and Cd2+ ions have been recorded as 52.5% and 35.5% at contact time 60 min, 92.9% and 89.9% at pH 6 and 45.1% and 39.9% at temperature 60OC, respectively. Regression values indicated that the Pseudo first order kinetic model was best fitted to the adsorption of Pb2+ and intra particle diffusion model for Cd2+ ions onto ZOBN. The diffusion constant (kd) for Pb2+ and Cd2+ ions have been evaluated as 0.41 and 0.28 mg/g min1/2. Langmuir isotherm model was found highly suitable for the equilibrium data of adsorption as compared to Freundlich, Temkin and Dubbin-Radushkevich isotherm models. The values of Langmuir equilibrium constant (L/g) and theoretical monolayer saturation capacity have been evaluated for Pb2+ ions as 7.19 L/g and 0.092 and for Cd2+ ions as 12.01 L/g and 0.03, respectively.

On the Active Adsorption of Chromium(III) from Alkaline Solutions Using Multiwalled Carbon Nanotubes

The present investigation deals with the adsorption of chromium(III) from alkaline media, as representative of highly-caustic component solutions of nuclear tank wastes, using multiwalled carbon nanotubes. The adsorption of Cr(III) has been studied under various experimental conditions, i.e., stirring speed of the aqueous solution, initial metal and adsorbent concentrations, NaOH concentration in the aqueous solution, and temperature. The rate law indicated that chromium adsorption is well represented by the particle diffusion model, whereas the adsorption process fits with the pseudo-second order kinetic model within an exothermic setting. Equilibrium data fit to the Langmuir type-2 equilibrium isotherm in a spontaneous process. Chromium(III) can be eluted from metal-loaded nanotubes using acidic solutions, from which fine chromium(III) oxide pigment can ultimately be yielded.

Kinetics, equilibrium and isotherms of Pb2+ adsorption from aqueous solutions on carbon nanotubes functionalized with 3-amino-5a,10a-dihydroxybenzo[b] indeno [2,l-d]furan-10-one

Multi-wall carbon nanotubes functionalized with 3-Amino-5a, 10a-dihydroxybenzo [b] indeno [2,ld]furan-10-one (ADIF), (MWCNT-ADIF), were used as the adsorbent to remove lead ions (Pb2+) from aqueous solutions. The samples were characterized by FT-IR, SEM, TGA and DTG. Effects of pH, initial Pb2+ concentration, adsorbent dosage and contact time on adsorption kinetics and equilibrium were investigated in a batch mode. Adsorption isotherms of Pb2+ ions were investigated using four two-parameter models (Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich) and six three-parameter models (Redlich-Peterson, Khan, Sips, Radke-Prausnitz, Toth, Hill). Adsorption kinetics were investigated by the pseudo first-order kinetic model, the pseudo second-order kinetic model and the intra particle diffusion model. Three error analysis methods, correlation coefficient, chi-square test and average relative errors, were used to determine the best fitted isother. Results indicated that adsorption kinetics was best described by the pseudo second-order kinetic model. Error analysis indicated that three-parameter models described the Pb2+ sorption data better than the two-parameter models . The isotherm data were best fitted by the Langmuir, Hill and Sips models. Pb2+ ions could be desorbed from MWCNT-ADIF up to 92% at pH=3 and the recycled MWCNT-ADIF could be reused for 5 regeneration cycles.

Kinetics and Diffusion Analysis for the Removal of Cadmium Ion from Aqueous Solutions Using Chitosan-iso-Vanillin Sorbent

Kinetic and diffusion analysis of the process of cadmium ion removal from water via sorption has been explored. The experimental kinetics data were approximated with pseudo-first and pseudo-second-order equations, Elovich equation, and Ritchie modified second-order models. Diffusion analysis is performed using homogeneous particle diffusion model and Weber–Morris kinetics. Kinetic results reveal that chemisorption is the sole-controlling step representing high sorption rate during the first 2 h of agitation with 50‒90% removal. Activation energy is also calculated (26.57 kJ mol−1) disclosing chemical interaction among solute-adsorbent phase. Weber–Morris plots show the sorption process is controlled by two or more simultaneous mechanisms with higher Kid values at higher initial concentrations. The study demonstrates that rate values of pore and film diffusion are improved with increase of initial ion concentration and the effect of diffusion resistance is not efficiently removed or minimized by sufficient agitation time.

On diffusions with stochastic resettings: noisy restarts, optimal rates and interaction modelling

In this paper we address a model of particle diffusion, introduced by Evans and Majumdar (2011 J. Phys. A: Math. Theor. 44 435001) where, at random times, at rate , a particle resets to a position drawn from a probability distribution with density . We study an invariance law for the standard error of first-passage time observed by Reuveni (2016 Phys. Rev. Lett. 116 170601) and find that, when dealing with restarts, noise around the resetting position breaches such a law. We show that the mean first-passage time is finite and can be minimized with respect to , for a rather general class of functions . Moreover, we propose a model of a particle system evolution where the particles independently diffuse and reset but also at random times interact. We exhibit the non-equilibrium stationary distribution for the case of two interacting particles.