Diffusion Coefficient Of Water Research Articles

Assessment of calcium alginate gels as wall materials for encapsulation systems.

Calcium alginate gels are widely used to encapsulate active compounds. Some characteristic parameters of these gels are necessary to describe the release of active compounds through mechanistic mathematical models. In this work, transport and kinetics properties of calcium alginate gels were determined through simple experimental techniques. The weight-average molecular weight ( = 192 × 103 Da) and the fraction of residues of α-l-guluronic acid ( = 0.356) of sodium alginate were determined by capillary viscometry and 1 H-nuclear magnetic resonance at 25 °C, respectively. Considering the half egg-box model, both values were used to estimate the molecular weight of calcium alginate as = 2.02 × 105 Da. An effective diffusion coefficient of water ( = 2.256 × 10-9 m2 s-1 ) in calcium alginate was determined using a diffusion cell at 37 °C. Finally, a kinetics constant of depolymerization ( = 9.72 × 10-9 m3 mol-1 s-1 ) of calcium alginate was obtained considering dissolution of calcium to a medium under intestinal conditions. The experimental techniques used are simple and easily reproducible. The obtained values may be useful in the design, production, and optimization of the alginate-based delivery systems that require specific release kinetics of the encapsulated active compounds. © 2023 Society of Chemical Industry.

Water Effective Diffusion Coefficient in Dairy Powder Calculated by Digital Image Processing and through Machine Learning Algorithms of CLSM Micrographs.

Rehydration of dairy powders is a complex and essential process. A relatively new quantitative mechanism for monitoring powders' rehydration process uses the effective diffusion coefficient. This research focused on modifying a previously used labor-intensive method that will be able to automatically measure the real-time water diffusion coefficient in dairy powders based on confocal microscopy techniques. Furthermore, morphological characteristics and local hydration of individual particles were identified using an imaging analysis procedure written in Matlab©-R2023b and image analysis through machine learning algorithms written in Python™-3.11. The first model includes segmentation into binary images and labeling particles during water diffusion. The second model includes the expansion of data set selection, neural network training and particle markup. For both models, the effective diffusion follows Fick's second law for spherical geometry. The effective diffusion coefficient on each particle was computed from the dye intensity during the rehydration process. The results showed that effective diffusion coefficients for water increased linearly with increasing powder particle size and are in agreement with previously used methods. In summary, the models provide two independent machine measurements of effective diffusion coefficient based on the same set of micrographs and may be useful in a wide variety of high-protein powders.

Simulation study on the coupled heat and mass transfer of CO2 in a heavy oil-water liquid system based on an improved lattice Boltzmann (LB) method

This study investigates the heat and mass transfer when low-temperature CO2 diffuses in a heavy oil–water liquid system based on an improved Lattice Boltzmann (LB) method. First, we determine the CO2 diffusion coefficients in heavy oil and water and the heat transfer coefficients of heavy oil and water using the pressure drop (DP) method and the laser flash (LF) method, respectively. Then, a numerical model that couples the heat and mass transfer in the system is established based on the improved LB method. The effect of low-temperature CO2 on the temperature field of the system and the effect of changes in the temperature field on CO2 diffusion are investigated. Finally, we develop a micro-model reproducing the heat and mass transfer of CO2 in water and heavy oil-saturated porous media to validate the accuracy of the numerical model. The results demonstrate that the CO2 diffusion coefficients in heavy oil and water linearly increase with the temperature increases. The heat transfer coefficients of heavy oil and water are insensitive to the changes in temperature. The heat transfer process has a great impact on the mass transfer of CO2 in the liquid system. The CO2 diffusion velocity slows down as the system temperature decreases because of the heat transfer (from 400 K to 300 K), leading to a reduction percentage of 300 % in the CO2 front movement velocity. Compared to the scenarios neglecting heat transfer, CO2 diffusion distance and amount decrease by 38 % and 50 %, respectively because of the changes in the temperature field of the system.

Hydrothermal aging of glass fiber epoxy‐carbon nanocomposites and its service life predictions based on tensile strength

AbstractThis paper investigates the hydrothermal aging of pultruded glass‐fiber reinforced epoxy nanocomposite rods with carbon nanofillers. The nanocomposites developed in this study are proposed for the core of high‐tension low‐sag conductors in power transmission. Nanocomposites were fabricated with a nanomodified matrix containing 0.2 wt.% of multi‐walled carbon nanotubes and 0.6 wt.% of graphene nanoplatelets. The epoxy nanocomposites tensile strength and life predictions were determined under different water aging conditions. Objective of the study is to evaluate the water absorption kinetics and its impact on tensile strength, microstructure and to compute the service life under hydrothermal aging by predictive techniques. Nanocomposites were aged in water at 30, 50, and 80°C for a duration of 3000 h, and the microstructure and chemical composition were investigated. Based on Arrhenius's theory, a service life prediction model based on the tensile‐strength of the nanocomposite is established for hydrothermal aging. The results have shown that the addition of carbon nanofillers to the epoxy matrix improves the hydrophobicity and reduces the water diffusion coefficient. Water absorptions of the nanocomposites are observed to follow Fick's law, and its influence on the mechanical properties of the nanocomposite is evident and is more significant in epoxy composites without carbon nanofillers. After 3000 h of immersion at 50 and 80°C, the tensile strength retention is above 85%. The hydrothermal environment accelerates the development of micro‐voids and cracks, which are initially formed and observed to be the primary reason for the degradation in mechanical strength under service conditions, in addition to debonding of the fibers.Highlights Carbon nanocomposites were aged at different temperatures and durations. Service life prediction model established based on Arrhenius's theory. Addition of carbon nanofillers enhances hydrophobicity and reduces water diffusion. Tensile strength retention above 85% after 3000 h of aging. Hydrothermal aging accelerates aging contributing to strength degradation.

Evaluation of water diffusion, water vapor permeability coefficients, physicochemical and antimicrobial properties of thin films of nopal mucilage, orange essential oil, and orange pectin

There is a growing interest in the development of biodegradable, safe materials to extend the shelf life of food and replace non-biodegradable plastics. Several materials have been investigated that can be used as edible coatings to extend the shelf life of fruit and vegetable products. In the present work, the design and characterization of different films of nopal mucilage, orange pectin, and orange essential oil were investigated for their potential use as edible coatings. It was found that the pectin concentration had a significant effect (p<0.05) on the thickness, color, and transparency of the edible films. According to the results, the formulation 0.5% mucilage-0.25 % pectin-0.25 % essential orange oil was chosen. Infrared spectroscopy showed no changes in the chemical compounds of the film formulation. The XRD pattern showed that this thin film is amorphous and contains calcium oxalate of nopal mucilage and oleic acid. In the water vapor permeability tests, the films containing orange essential oil in their formulation showed a higher effective water diffusion and water permeability coefficients as compared to the other formulations. In addition, the concentration of orange essential oil has an antimicrobial effect (p<0.05) on some bacteria of interest for food safety. This work demonstrates a new methodology and measurement technique to determine the effective water diffusion and water permeability coefficients for edible thin films based on the photoacoustic effect.

Effect of Sonication and Edible Coating on Total Phenolic Content, Antioxidant Capacity, and Physical Characteristics of Infrared-Dried Sweet Cherries

This research studied the influence of combined ultrasonic (40 kHz, 150 W, for 3 min) and 0.2% xanthan gum (XG), guar gum (GG), and wild sage seed gum (WG) coating pretreatments on total phenolic content, antioxidant activity, drying time, effective water diffusivity coefficient ( D eff ), rehydration ratio (RR), total color difference ( Δ E ), and surface shrinkage (SS) of infrared-dried sweet cherries. The ultrasonic pretreatment increased the water transfer rate and water diffusivity during infrared drying and decreased the drying time of fresh sweet cherries. The edible coating enhanced the total phenolic content, antioxidant activity, dehydration time, and RR and decreased the D eff , Δ E , and SS values of infrared-dried sweet cherries. The highest value of total phenolic content (3469.7 μg galic acid/g dry) was recorded for pretreated sweet cherry samples by GG. The mean antioxidant activities for uncoated, XG-coated, GG-coated, and WG-coated sweet cherries were 35.64, 59.88, 54.38, and 61.19%, respectively. In this study, the sweet cherry D eff varied from 2.23 × 10 − 9 m2/s (for untreated cherries) to 5.00 × 10 − 9 m2/s (for sonicated and uncoated cherries). The experimental data for the drying curves were fitted to various single-layer equations, and the Page equation using the experimental constants best described the drying rate of sweet cherries. The mean Δ E values for uncoated, XG-coated, GG-coated, and WG-coated sweet cherries were 15.11, 9.91, 8.74, and 10.69, respectively.

Impact of water diffusion on electrical properties of epoxy nanocomposites

This study investigates the effects of water ageing at 80 °C on glass fibre hybrid epoxy nanocomposites with multi-walled carbon nanotubes and graphene nanoplatelets. Effect of water uptake in the epoxy matrix is mitigated by the inclusion of carbon nanofillers, leading to improved hydrophobic nature. A comparative study is performed on the water uptake of the epoxy-amine matrix cured with aliphatic amine, with 0.4 weight percent of MWCNT and 0.6 weight percent of graphene nanoplatelets (GNPs). Gravimetric assessment and electrical impedance measurements are carried out over a period of 3000 h to assess water diffusion coefficients and water saturation. Water absorption is measured until saturation, and results show that the water diffusion coefficient of the hybrid nanocomposites is increased from 2.51 × 10−8 (m2 s−1) at 27 °C to 3.32 × 10−8 (m2 s−1) at 80 °C and it is higher than that of the base epoxy composites. Cole–Cole diagrams have revealed heterogeneity of the composites studied. Water diffusion results in the plasticization of the matrix, and it manifests in the broadening of the tanδ peak observed in water-aged epoxy composites. With the inclusion of hybrid MWCNT and GNP nanofillers.,the water diffusion coefficient is reduced to half, and saturation is increased by four times.

Water Sorption in Hybrid Polyester/Glass/Jute Composites Processed via Compression Molding and Vacuum-Assisted Resin Transfer Molding.

The aim of this work is to analyze water sorption in hybrid polyester/glass fabric/jute fabric composites molded via compression and VARTM (Vacuum-Assisted Resin Transfer Molding). The laminates were produced with five different stacking sequences and subjected to water sorption testing at room temperature, 50 °C and 70 °C. This study consisted of two stages: experimental and theoretical stages. The composites had a fiber volume content ranging from 30% to 40%. Water absorption and diffusion coefficient in the hybrid composites were intermediate to those reinforced with a single type of fiber. There were no significant differences in these properties based on fiber arrangement once the composites reached saturation. Diffusion coefficient values were higher for specimens with jute fiber on at least one of the outer surfaces. Water sorption rates increased with higher immersion temperatures. The water sorption at saturation point was not affected by the manufacturing process. Among the hybrid composites, those with jute on the surfaces showed the highest diffusion coefficient, while those with glass on the surface had the lowest values. Higher diffusion coefficient values were observed at temperatures of 50 °C and 70 °C. The main influencing factors on the absorbed moisture content for composites are the presence and content of jute fibers in the system and the immersion temperature. The manufacturing process does not affect the water sorption at saturation point.

The role of gellan gum in the selective flotation separation of fluorite from calcite: An experimental and molecular dynamics simulation study

Fluorite as the main source of fluorine generally coexists with calcite. The highly similar floatabilities and physicochemical properties make it tough to separate these two minerals. Herein, gellan gum (GG) was used as depressant to separate fluorite from calcite for the first time. Several experiments and tests were utilized to explain the inhibiting performance and mechanism of GG. Flotation experiments illustrated that GG displayed an outstanding depression performance for the calcite flotation, whereas it hardly depressed fluorite. Zeta potential analyses, surfaces wettability measurements and Fourier transform infrared (FTIR) indicated that GG strongly adhered onto calcite and prevented the NaOL from adhering on it. Adsorption amount measurements indicated that the GG adhered onto calcite with a higher amount compared to fluorite. X-ray photoelectron spectroscopy (XPS) tests pointed out that GG adsorbed onto calcite and fluorite surfaces by strong chemisorption and weak physisorption, respectively. Atomic force microscopy (AFM) measurements implied visually that GG adsorbed denser and stronger on the calcite than fluorite. Molecular dynamics (MD) simulations demonstrated that compared with fluorite, more GG adsorbed on the calcite surface due to the reaction between hydroxyl groups and the mineral surface, as evidenced by higher diffusion coefficient for water (Dwater) value, smaller interaction distance, and higher relative concentration of GG on the calcite surface. Therefore, GG could be employed as a promising flotation depressant in separating fluorite from calcite.

Effect of Hydrothermal Aging Behavior on Surface Treated Kevlar Fiber Laminated Composites

The water sorption characteristics of Kevlar fiber–reinforced epoxy composites were studied by immersion in water at 80 degrees Celsius. The hydrothermal aging process was conducted on treated and untreated Kevlar/epoxy composites; also, the composite was evaluated by the three-point bending test. The phosphoric acid (PA) pretreated with epichlorohydrin (ECH) was used for the surface modification of Kevlar. In the case of chemically modified fiber composites, water uptake was found to be dependent on the chemical treatment done on the fiber surface. The lowest water uptake was observed for composites treated with PA with ECH. The effect of thermal aging on the flexural strength of the treated Kevlar composite was 20.42% higher than the untreated composite. Consequently, the flexural modulus was 13.9% higher than the untreated Kevlar composite. Moreover, the water diffusion coefficient of treated composite 23.19% higher with untreated composite. It was concluded that fiber/matrix degradation time at the interface region was increased in the case of treated composite

Diffusion of LiCl electrolytes in 3D-nanoporous graphene structures

In this work, we investigate the diffusion of LiCl electrolytes in 3D-nanoporous graphene structures (3D-NGSs) through molecular dynamics simulations. The diffusion coefficients, D, of water, Li+, and Cl− are calculated in 3D-NGSs with different LiCl concentrations, porosities, and surface charge densities under various temperatures. It is found that the diffusion coefficients follow the Arrhenius Equation and power laws for the dependence on the temperature and porosity, respectively. They decrease with increasing salt concentration. At high surface charge densities, the diffusion coefficients decrease with increasing charge density, which, however, plays a minor role in affecting the diffusion coefficients in the range of 0–0.2 C m−2. The mechanisms are investigated through the potential energy distribution in the 3D-NGSs. General scaling laws for the diffusion coefficients of water, Li+, and Cl− are proposed. The results in this work provide useful information for the design of electrodes and various energy systems.

The Effect of Drying Variables on the Microwave–Vacuum-Drying Characteristics of Mulberries (Morus alba L.): Experiments and Multivariate Models

It is easy to cause increases in temperature and the gasification of water in materials, facilitated via supercharging and the generation of instantaneous strong pressure under the collaborative action of a microwave and a vacuum, thus facilitating the internal cell swelling of materials, changes in fibre structures, and the formation of loose and uniform microstructures. In this experiment, mulberries were dehydrated using microwave–vacuum drying technology. The drying characteristics were disclosed by using crispness as the evaluation index and multiple drying parameters (e.g., products’ surface temperature, microwave power, chamber vacuum level and drying height) as the control variables. The optimised Two-term model can predict the dehydration process of mulberries under multiple drying variables, as determined through the experimental data. The optimal drying variables were determined according to the crispness of the dried mulberries. The optimal puffing quality of mulberries could be gained under a product surface temperature = 50 °C, microwave power = 5.45 W/g, a chamber vacuum level = 0.08 MPa and a drying height = 0 cm. The diffusion coefficient of the available water of the mulberries during the microwave–vacuum drying process ranges from 4.98 × 10−8 to 3.81 × 10−7, and the activation energy for drying is 183.923 KJ/mol.

Effect of nanographene oxide and ionizing radiation on mechanical, physical, and thermal properties of composites based on high‐density polyethylene and waste bagasse fibers

AbstractThe impact of graphene oxide (GO) nanoparticle content and exposure to electron beam (EB) on the tensile, dynamic mechanical, water uptake, and thermal properties of high‐density polyethylene/bagasse fibers composite was investigated. The GO was added at different loading levels: 0.25, 0.5, 0.75, and 1 parts per hundred parts of plastic (php), while 2 doses of EB were used (100 and 200 kGy). The influence of adding 10 php of carbon black (CB) to the HDPE/BF was also investigated. The addition of GO and irradiation up to 100 kGy, along with the inclusion of 10 php of CB, led to improvements in tensile strength, elastic modulus, storage modulus, and hardness. The composite containing 1 php of GO and exposed to 100 kGy, demonstrated the highest tensile strength value, with a 47.3% improvement compared with the unirradiated one. This composite also, exhibited the lowest values of water absorption percent (3.7%) and diffusion coefficient (0.007 mm2/h) compared with the unirradiated HDPE/BF composite. These results suggest that the resulting composite has potential for use in advanced industrial applications due to its improved physicomechanical properties.Highlights Composites based on high‐density polyethylene (HDPE) and bagasse fibers (BF) were fabricated The incorporation of graphene oxide (GO) improved the mechanical properties. GO and electron beam (EB) irradiation enhanced the water resistance of HDPE/BF composite. Both GO and EB increased the thermal stability of HDPE/BF composite.

Anisotropy in particle orientation controls water diffusion in clay materials

Clay minerals are used in a wide number of natural or artificial materials for municipal or nuclear waste management in which water diffusion is the principal transfer process. However, a quantitative assessment of the impact of the preferred orientation of lamellar clay particles on water diffusion is still lacking. Using 3D Brownian dynamics simulation on representative virtual clay porous media, a systematic study of water diffusion for single-porosity (illite or kaolinite) and dual-porosity (vermiculite) systems was conducted. The simulated water diffusion coefficients were validated through comparison with experiments and were used to build an Archie model including the degree of anisotropy in particle orientation. The results showed that water diffusion can be predicted based on a correct description of the solid phase organization and that clay particle orientation, such as interparticle porosity, is a primary parameter governing water mobility. Moreover, the anisotropy of water diffusion can be linked to the degree of particle preferred orientation, irrespective of the porosity value. The modified version of the Archie model for water diffusion in clay systems proposed here has many potential applications where decoupling of porosity and preferred orientation is needed, including better prediction of water transfers or improved designs of clay liners with sustainable use of natural mineral resources.

Impact of clod (aggregate) size on evaporation rate and soil moisture profile during the drying process

AbstractLarge clods (centimetres in size) can be formed by tillage in clayey paddy fields where upland crops are planted. These clods cause early water depletion near the soil surface, which decreases crop germination and emergence rates. Because of the difficulty in reducing clod size, desiccation damage to seeds can be avoided by adjusting the seeding depth based on the clod size‐dependent soil moisture profile. This study aimed to clarify the effect of clod size on (1) the evaporation rate (E) and soil moisture profile and (2) the mobility of soil water during the drying process. Evaporation experiments were conducted in an air‐conditioned greenhouse with natural light using cylindrical columns filled with artificially made clods 3 (L columns) and 1 cm (S columns) in diameter. We measured E, potential evaporation rate (PE), and total soil moisture content (wtot) throughout the experiment and the soil moisture profiles at the end of the experiment. The water diffusivity (Dw) and apparent vapour diffusion coefficient (dvap) were calculated as the mobility of soil water and water vapour, respectively. We found that wtot was lower in the L column than in the S column, although not at the onset of the experiment. At the end of the experiment, the soil moisture content was lower in the L column than in the S column throughout the soil layer. In contrast, E/PE was higher in the L column than in the S column throughout the experiment and even at the same wtot. Regarding mobility, Dw was slightly greater in the L column than in the S column in the soil moisture content range, where vapour movement could be greater than liquid water movement. In addition, the ratio of dvap to the diffusion coefficient of water vapour in soil was higher than unity in both columns and was 2.4–3.2 times higher in the L column than in the S column. In summary, larger clods caused a higher evaporation rate and lower soil moisture content, owing to the increased enhancement of water vapour movement probably induced by wind.

Fluorination as a powerful tool for improving water/salt selectivity of hydrophilic polyethersulfone

Fluorination is an important tool for tuning polymer free volume properties, but the effect of fluorination on the water/salt transport properties of desalting polymers remains uncertain. In this work, a series of novel cysteine-based polyethersulfones (PES-Cys and PES-Cys-2F, PES-Cys-6H and PES-Cys-6F, PES-Cys-8H, and PES-Cys-8F) were designed in pair (4,4'-difluorodiphenyl sulfone versus 3,3',4,4'-tetrafluorodiphenyl sulfone, bisphenol A versus hexafluorobisphenol A, and 4,4'-dihydroxybiphenyl versus decafluorobiphenyl). Upon casting into membranes via the solvent evaporation method, the membranes/polymers were characterized by 1H NMR, FTIR, XRD, DSC, Zeta potential, and the water/salt transport properties of the membranes was investigated systematically. It has been demonstrated that fluorination brings out greater spatial site resistance, stronger hydrophobicity, and higher electronegativity to polyethersulfone chains, leading to decreased water sorption but increased salt sorption. Fluorinated polyethersulfone displayed higher water diffusion coefficient because the C–F group can shatter water clusters into water molecules, which can diffuse more rapidly. Fluorinated polyethersulfone exhibit superior water/salt selectivity, with the most rigid PES-Cys-8F of the highest fluorine content showing water/salt selectivity over the empirical upper bound line. The enhanced water/salt selectivity is mostly because that fluorination improves water permeability by significantly increasing the water diffusion coefficient, while the electrostatic barrier provided by the electronegative fluorine atoms inhibits salt diffusion. This study provides valuable theoretical guidance for future molecular design of antioxidant desalting polymers.

Water diffusion behavior and transient internal stress analysis of steel/rubber composites

This paper focuses on modeling the water absorption and the resulting internal stress behavior of steel/rubber composites. A three-dimensional finite element model, which includes the internal microstructure of bundled long steel wire reinforced composite, is established to accurately simulate water diffusion behavior. The water diffusion coefficient and rubber matrix's hygroscopic expansion parameter are estimated by experiments. The outcomes demonstrated that the earliest stages of water diffusion of steel/rubber composites conformed to the Fickian model. Then the weight gain continued to increase and followed the Langmuir model instead of Fickian model owing to the presence of bound water. Both the free water and bound water in steel/rubber composites were modeled by FE software. The internal stress caused by the differential swelling between steel and rubber was revealed and quantitatively analyzed through finite element simulation. The internal stress is the main cause of damage initiation in the steel/rubber composites, which was in good agreement with experimental measurements.

Molecular dynamics simulations on the water diffusion in modified silica membrane with TiO2

Today, the use of modified silica membranes for the osmosis process has received attention. Titanium dioxide (TiO2) has a significant application in increasing the efficiency of osmotic membranes due to its hydrophilic, antibacterial, and nontoxic properties. A molecular dynamics (MD) simulations approach is applied to theoretical insights into the effect of concentration of TiO2 in silica membrane on the water molecules diffusion. The diffusion coefficient of water in modified forward osmosis silica membranes with 10−6, 10−4, 10−2, 0, 1, and 100-mole ratios of TiO2 has been calculated from the mean square displacement (MSD) of H2O molecules and obtained (0.015,1.952,2.570,2.810,0.078and0.086)×10−9m2s, respectively. The results of our simulations are in excellent agreement with the experimental results and also can be compared to the diffusion coefficient of water in Polyamide (PA) membrane as one of the most important membranes at reverse osmosis for water desalination about 0.600×10−9m2s.

State and role of water confined in cement and composites modified with metakaolin and additives

Cement as a porous material contains pores and cracks on the whole nanoscale forming an interconnected pore structure. Its interaction with water during the rehydration of cement plays a key role in every application, such as in nuclear waste treatment, where cement binders are commonly used for conditioning liquid radioactive waste. In the prediction of the long-term disposal the knowledge of water mobility and distribution in the formed porous cement matrix is essential.In this study we systematically investigate the effects of metakaolin and several components of the liquid phase (complexing agents, model ions, boric acid, etc.) on the hydrated solid structure by various nuclear magnetic resonance (NMR) methods. The novelty lies in the complex use of such non-conventional techniques that separately provide only partial information of the cement structure; however, the gained results complete each other to offer a new approach in the structural study under several conditions. Water mobility is deduced from NMR T2 relaxation distributions and D2O-H2O exchange diffusion measurements, and the conclusion on structural properties is supported by the macropore structure revealed from NMR cryoporometry and SEM (scanning electron microscopy) images, as well as by following the formation of pores and water domains in the curing process with NMR relaxometry. The results confirm that metakaolin was built into the CSH (calcium silicate hydrate) gel region without altering its mesoporous structure, however, it significantly decreased the capillary pore size and the diffusion coefficient of water. Complexing agent concentration between 2 and 20 g/l and the presence of model ions did not cause significant structural changes, while the rehydration decreased the size of capillary pores due to swelling.

Modeling the swelling kinetics of preformed particle gels coated with a silicate layer

This study presented an organic–inorganic hybrid preformed particle gels (PPG) by coating a tetramethyl orthosilicate layer on acrylamide-based PPG to control the swelling rate of PPG in simulated aqueous media. The coated silicate layer on the PPG delayed the equilibrium swelling time by several hours. Furthermore, jump boundary conditions at interfaces were applied to develop a mathematical model for the swelling kinetics of hybrid PPG with three distinct regions and three moving boundaries. The proposed model results showed that the diffusion coefficient of distilled water and saltwater in the coated layer and its thickness control the swelling process of these hybrid gel particles. Furthermore, the error percentages of predictive results by the proposed mathematical model for experimental swelling kinetic measurements of coated PPG were less than 5.25%. The experimental results also showed that the silicate layer controlled PPG swelling kinetics and improved hybrid PPG's strength and thermal stability.