Diffusion Boundary Layer Research Articles

Biosorption of hexavalent chromium from aqueous solution by pristine and CaCl2-modified erythromycin production residues.

In this study, the adsorptive removal of hexavalent chromium [Cr(VI)] from aqueous solutions by the pristine and salt-treated (CaCl2) erythromycin production residue (EPRs and SEPRs) were investigated. Batch experiments were carried out to determine the effect of contact time, sorbent dosage, pH, initial Cr concentration, and temperature on Cr(VI) sorption by EPRs and SEPRs. The highest adsorptive removal capacities were achieved at the pH equal to 1.0, and the maximum adsorption capacities for EPRs and SEPRs at optimized conditions were 21.74 and 35.24mgg-1, respectively. The FTIR spectra and SEM studies were examined for the pristine adsorbent and after the adsorption of Cr(VI). Moreover, thermodynamic results indicated that Cr sorption by EPR/SERPs was feasible, spontaneous, and endothermic under the optimum conditions. Langmuir model fitted well with the experimental data. Kinetic modeling revealed that the biosorption of Cr(VI) by EPRs and SEPRs obeyed the second-order model than the first-order model. The process involving rate-controlling step is much complex involving both boundary layer and intra-particle diffusion processes. Furthermore, the adsorption-coupled-reduction process was believed as the main mechanism of Cr(VI) removal by EPRs and SEPRs. In summary, both adsorbents could be considered as promising low-cost biosorbent for the removal of Cr(VI) from aqueous systems.

Partitioning of Ti, Al, P, and Cr between olivine and a tholeiitic basaltic melt: Insights on olivine zoning patterns and cation substitution reactions under variable cooling rate conditions

The mechanism governing the kinetic growth of olivine in dynamic volcanic settings has been the subject of considerable attention in recent years. Under variable cooling rate (CR) and undercooling (−ΔT) regimes, the textual maturation of olivine proceeds from skeletal/dendritic crystals to polyhedral morphologies by infilling of the crystal framework. Owing to the establishment of a diffusion-controlled growth regime, a sharp diffusive boundary layer develops in the melt next to the advancing olivine surface. In this context, we have quantified the apparent partitioning of Ti, Al, P, and Cr between olivine and a Hawaiian tholeiitic basaltic melt at P = 1 atm, fO2 = QFM-2 buffer, and CR = 4, 20, and 60 °C/h over a constant -ΔT = 85 °C. Differences in charge and/or size between the substituent minor cations and the major species in the olivine crystallographic site dominate the energetics of homovalent and heterovalent cation substitutions. While the entry of Ti in the olivine lattice site accounts for the simple exchange [TSi4+] ↔ [TTi4+], more complex charge-balancing coupled-substitution mechanisms have been determined for the incorporation of Al, P, and Cr, i.e., [MMg2+, TSi4+] ↔ [MAl3+, TAl3+], [2 TSi4+] ↔ [TP5+, TAl3+], and [MMg2+, TSi4+] ↔ [MCr3+, TAl3+], respectively. In order to maintain charge balance, the disequilibrium uptake of minor cations in rapidly growing crystals is controlled by the same substitution mechanisms observed under equilibrium crystallization. This finding is consistent with the achievement of a local interface equilibrium at the olivine-melt interface independently of the diffusive boundary in the melt. A statistical approach based on multivariate analysis of olivine/melt compositional parameters confirms that the control of melt structure on the partitioning of Ti, Al, P, and Cr is almost entirely embodied in the olivine structure and chemistry via charge compensation reactions. Therefore, the magnitude of minor element partition coefficients is weakly dependent on diffusion kinetics in the melt but rather strongly governed by olivine zoning patterns resulting from fast crystal growth rates.

Modeling the effect of mineral armoring on the rates of coupled dissolution-precipitation reactions: Implications for chemical weathering

One of the mechanisms influencing weathering rates is mineral armoring, which is the build-up of insoluble coatings on primary mineral phases. Such armoring is often the result of coupled dissolution-precipitation reactions that occur during weathering. While the role of armoring in reducing dissolution rates is widely recognized, a quantitative mechanistic description of the way it impacts mineral weathering rates has not yet been developed. This paper demonstrates how a diffusion boundary layer model can simulate the effect of a porous secondary mineral layer on the rate of primary mineral dissolution under acidic conditions. In the model, the rates are affected by 3 parameters: layer thickness, the ratio of porosity to tortuosity, and the Biot number, which defines the ratio of dissolution to diffusion. Numerical solutions to the equations show that when the porosity/tortuosity ratio is low (~0.01), dissolution rates can be reduced by several orders of magnitude relative to armor-free minerals. Biot numbers greater than 1 were also found to lead to a significant reduction in the dissolution rate. Moreover, comparison with reported experimental data shows that the model can accurately simulate the change in thickness of the secondary mineral coating with time. The dissolution rates of pristine coating-free minerals in laboratory experiments can be orders of magnitude higher than those observed under field conditions, and the results suggest that mineral armoring can account for much of this discrepancy.

Evidence for chromium, cobalt and molybdenum volatilisations during high temperature oxidation of Co-27Cr-6Mo Alloy

A Co-27Cr-6Mo alloy was oxidised in pure O2 between 800 and 1000 °C for durations up to 96 h. The flow rate was varied between 2 and 5 cm.s–1. In these conditions, volatilisations of chromium, cobalt and molybdenum were observed. The chromium volatilisation values were in good agreement with calculations assuming (CrO3)g volatilisation limited by diffusion in the gas boundary layer. On the contrary, the measured flux of evaporated Co was higher than the calculated Co volatilisation flux from the metallic Co. The theoretical relation between the solid Co particle size and its vapour pressure was suggested to help explaining such difference.

Tutorial review of reverse osmosis and electrodialysis

Reverse osmosis (RO) and electrodialysis (ED) are the two most important membrane technologies for water desalination and treatment. Their desalination and transport mechanisms are very different, but on a closer look also have many similarities. In this tutorial review, we describe state-of-the-art theory for both processes, focusing on simple examples that are helpful for the non-specialist and for classroom teaching. We describe relevant theory for ion and water transport and the coupling with theory for chemical and mechanical equilibrium on membrane/solution interfaces. For RO of neutral solutes, we explain the solution-friction (SF) model which is closely related to the classical sieving or pore flow model. The SF model includes advection, diffusion, and solute partitioning, and leads to simple relationships for the coupled fluxes of water and solutes (and thus for solute retention as well), also when a diffusion boundary (or concentration polarization) layer is included in the model. Subsequently this theory is extended to describe RO for symmetric salt solutions with charged membranes. For the desalination of salt solutions, both for RO and ED we present two-dimensional module-scale calculations which lead to a characteristic curve that determines optimum operational conditions based on a simple cost calculation that offsets energy and material costs. We discuss the two-fluid model (TFM) that comprehensively describes ion and water flow both in RO and ED, and we explain how this theory also accurately describes osmosis experiments where water and ions are transported in opposite directions through a membrane. Finally, we present results of optimization studies of the combination of multiple modules for RO and ED, and we evaluate the relevance of concentration polarization by using a 3D model for cross-current flow in an ED module.

Application of Diffusive Gradients in Thin Films for Monitoring Groundwater Quality

Diffusive gradients in thin films (DGTs) provide time-weighted solute concentrations in well-mixed fluvial environments. However, the DGT method has rarely been applied to relatively slowly moving groundwater systems, where the increased length of the diffusive boundary layer (DBL) must be accounted for, to give accurate concentration measurements. Because the DGT method pre-concentrates trace-level solutes (e.g., Cd2+) and averages out fluctuations in more dynamic contaminants (e.g., NO3–), it has potential advantages over conventional methods. This study evaluated the application of DGT methods for monitoring trace contaminants in groundwater, which are often present at levels below standard instrumental detection limits. We tested three different DGT deployment approaches using NO3– to estimate the DBL thickness: a static DGT suspension, a DGT shaker, and a pumped flow-cell unit coined the “universal DGT monitoring system” (UDMS). Unlike static and DGT shaker approaches, the UDMS reduced the DBL thickness (∼0.02 cm) to values within the range of well-mixed waters (DBL ≤ 0.03 cm). Comparable DBL thicknesses for NO3– and Cd2+ and correlations with grab sample measurements (R2 = 0.99 and 0.98, respectively) demonstrate the suitability of DGTs combined with the UDMS for groundwater monitoring. This approach is particularly suitable for analysis of trace-level solutes including organic contaminants.

RADIv1: a non-steady-state early diagenetic model for ocean sediments in Julia and MATLAB/GNU Octave

Abstract. We introduce a time-dependent, one-dimensional model of early diagenesis that we term RADI, an acronym accounting for the main processes included in the model: chemical reactions, advection, molecular and bio-diffusion, and bio-irrigation. RADI is targeted for study of deep-sea sediments, in particular those containing calcium carbonates (CaCO3). RADI combines CaCO3 dissolution driven by organic matter degradation with a diffusive boundary layer and integrates state-of-the-art parameterizations of CaCO3 dissolution kinetics in seawater, thus serving as a link between mechanistic surface reaction modeling and global-scale biogeochemical models. RADI also includes CaCO3 precipitation, providing a continuum between CaCO3 dissolution and precipitation. RADI integrates components rather than individual chemical species for accessibility and is straightforward to compare against measurements. RADI is the first diagenetic model implemented in Julia, a high-performance programming language that is free and open source, and it is also available in MATLAB/GNU Octave. Here, we first describe the scientific background behind RADI and its implementations. Following this, we evaluate its performance in three selected locations and explore other potential applications, such as the influence of tides and seasonality on early diagenesis in the deep ocean. RADI is a powerful tool to study the time-transient and steady-state response of the sedimentary system to environmental perturbation, such as deep-sea mining, deoxygenation, or acidification events.

Lightweight and anisotropic cellulose nanofibril/rectorite composite sponges for efficient dye adsorption and selective separation

Constructing lightweight and porous adsorbents which can effectively remove dye contaminants is of great significance in the field of the sewage treatment. In this work, anisotropic cellulose nanofibril (CNF) composite sponges assisted by rectorites are fabricated through directional freeze-drying. The resulted composite sponge exhibits the superior saturated adsorption capacity and removal efficiency of 120.0 mg/g and 96.1% for methylene blue (MB), respectively, which is better than the pure CNF sponge and rectorite powders. This is attributed to the strong electrostatic interaction between CNFs and MB, and good cation exchange property of rectorites inside the three-dimensional (3D) highly porous composite sponge. The MB adsorption process of the composite sponge fits to the pseudo-second-order kinetic model and the Langmuir isotherm model well, which is affected by both boundary layer and intraparticle diffusion, resulting in a theoretical maximum adsorption capacity of 214.6 mg/g. Moreover, it also possesses a selective adsorption capacity for anionic and cationic dyes, which is expected to realize the separation treatment of different dyes according to actual application requirements.

Exploring the link between ozone pollution and stratospheric intrusion under the influence of tropical cyclone Ampil

Tropical cyclones (TCs) are synoptic-scale systems with a diameter of up to 2000 km, and may persist for several days to weeks. They can significantly affect the atmospheric conditions and ozone (O3) concentrations in coastal areas. They also induce stratospheric intrusion (SI, the injection of stratospheric O3 into the troposphere) by changing the height of the tropopause. Focusing on the Yangtze River Delta (YRD) region, a highly urbanized coastal area with severe O3 pollution, we systematically analyze the characteristics of O3 pollution and SIs as well as their connections under the influence of tropical cyclone Ampil. Based on surface observations, 120-h backward trajectories and ERA5 reanalysis meteorological data, the urban O3 pollution affected by tropical cyclone Ampil mainly resulted from active photochemical reactions inside the boundary layer and poor diffusion conditions characterized by weak winds. SIs induced by tropical cyclone Ampil were important for the upper and middle troposphere, where O3 concentration could increase up to 180 ppbv. But they hardly reached the ground over the YRD. Therefore, there was no direct connection between O3 pollution and SIs. However, the location of SIs can predict urban O3 pollution. SIs moved with tropical cyclone Ampil but appeared on the northwest side of Ampil, usually 500–1000 km away from tropical cyclone Ampil center. At 200 hPa, they corresponded to a high-PV (>2 PVU) air mass rich in O3 (>200 ppbv). Below this stratospheric PV signature, urban O3 concentration was usually high.

A perspective on multi-component resistance analogy analysis for process intensification: Taking supercritical water gasification of coal as an example

Resistance analysis widely focuses on many aspects of scientific research such as flow, heat transfer, and electrical conductivity. However, resistance analysis is often limited to a specific field, and engineering applications (such as supercritical water gasification process) often require the coupling of multiple resistances. Supercritical water gasification (SCWG) provides a clean and low-carbon way of coal utilization for hydrogen production. Realizing the complete gasification of coal under mild temperature conditions is the prerequisite for the industrialization of this technology. Therefore, measures must be taken to reduce the process resistance and accomplish the process intensification. In this paper, a novel idea of multi-component resistance analogy analysis was applied to solve this problem from the perspective of intensification of interface reaction, boundary layer, and vertex diffusion, respectively. Based on the current research progress and outstanding issues, the further research will focus on the application of resistance analogy analysis to general multiphase flow and reactor optimization design and scale-up.

Mathematical Modeling of the Effect of Pulsed Electric Field Mode and Solution Flow Rate on Protein Fouling during Bipolar Membrane Electroacidificaiton of Caseinate Solution.

A one-dimensional non-stationary model was developed for a better understanding of the protein fouling formation mechanism during electroacidification of caseinate solution using electrodialysis with bipolar membranes (EDBM) in pulsed electric field (PEF) mode. Four different PEF modes were investigated with pulse–pause durations of 10–10 s, 10–20 s, 10–33 s, 10–50 s. For each current mode 3 different flow rates were considered, corresponding to Reynolds numbers, Re, equal to 187, 374 and 560. The processes are considered in the diffusion boundary layer between the surface of the cation-exchange layer of bipolar membrane and bulk solution of the desalination compartment. The Nernst–Planck and material balance equation systems describe the ion transport. The electroneutrality condition and equilibrium chemical reactions are taken into account. The calculation results using the developed model are in qualitative agreement with the experimental data obtained during the previous experimental part of the study. It is confirmed that both the electrical PEF mode and the flow rate have a significant effect on the thickness (and mass) of the protein fouling during EDBM. Moreover, the choice of the electric current mode has the main impact on the fouling formation rate; an increase in the PEF pause duration leads to a decrease in the amount of fouling. It was shown that an increase in the PEF pause duration from 10 s to 50 s, in combination with an increase in Reynolds number (the flow rate) from 187 to 560, makes it possible to reduce synergistically the mass of protein deposits from 6 to 1.3 mg/cm2, which corresponds to a 78% decrease.

Математическое моделирование тепломассопереноса при аэродинамическом нагреве носовых частей гиперзвуковых летательных аппаратов

The study focuses on heat and mass transfer on the side surfaces of blunt nose cones of hypersonic aircraft under aerodynamic heating conditions and formulates the problem of viscous flow and heat and mass transfer in dynamic, thermal, and diffusion boundary layers. After minor simplifications, we found approximate analytical solutions related to the gas-dynamic, thermal, and diffusion characteristics of the dissociating flow and obtained closed analytical expressions for the distribution of enthalpy and concentrations of the gas mixture components over the thickness of the boundary layers. Furthermore, by the derivatives of the enthalpies and concentrations distributions with respect to the vertical variable on the wall, we determined convective and diffusion heat fluxes to the aircraft surface. Using the balance between the supplied convective-diffusion heat fluxes and the fluxes removed due to radiation and heat elimination into the body, we obtained a nonlinear equation for the wall temperature, which is solved numerically. Numerical results are obtained and analyzed on convective-diffusion heat fluxes and wall temperatures of hypersonic aircraft, depending on the Mach number and flight altitude in a wide range of values, which make it possible to determine the boundaries of speeds and altitudes at which the mass of the heat-shielding coating is not removed. Finally, we investigated the influence of the catalytic properties of the aircraft surface on heat transfer in the same ranges of the Mach number and flight altitude

CO2 Hydrate dissolution rates in unsaturated water quantified with laboratory experiments

Measuring the dissolution rates of CO2 hydrates in marine environments is urgently needed because CO2 hydrate is a powerful means in CO2 ocean sequestration as well as a product of CO2-CH4 gas replacement in hydrate exploitation. The stability of CO2 hydrates is a significant index to evaluate the feasibility of gas hydrate technologies. It is generally agreed that the dissolution of hydrates is diffusion-controlled rather than reaction-controlled. In this work, the dissolution rates of CO2 hydrates in sediments under a variety of experimental conditions were calculated by the CO2 fluxes and mass balance. The in situ CO2 concentrations in static and flowing water layers were measured by Raman spectroscopy. Firstly, the dissolution rates of CO2 hydrate in sediments in different diffusion stages were 314 to 3.5 cm/year and 194 to 1.2 cm/year in static deionized water and brine layer, respectively. The CO2 hydrate underwent a rapid dissolution stage in the beginning of the experiment. Then the dissolution rate slowed down because of the decreasing concentration gradients. The difference of dissolution rates between deionized water and brine is related to the CO2 solubility in different solutions. CO2 hydrates covered with sediments dissolved much slower than hydrates dissolved in direct contact with water layers due to the increased diffusion boundary layers and the decreased diffusion coefficients. Additionally, the dissolution rates of CO2 hydrate that exposed to a variety of flow rates showed a strong velocity dependency. In this work, the dissolution rates of CO2 hydrate under flowing water layers ranged from 5.6 to 365 cm/year with volume flow rates ranged from 1.01 to 8.57 ml/min.

3D simulation of microfluidic biosensor for SARS-CoV-2 S protein binding kinetics using new reaction surface design.

In this study, we performed 3D finite element simulations on the binding reaction kinetics of SARS-CoV-2 S protein (target analyte) and its corresponding immobilized antibody (ligand) in a heterogeneous microfluidic immunoassay. Two types of biosensors with two different shapes and geometries of the reaction surface and electrodes were studied. Alternating current electrothermal (ACET) force was applied to improve the binding efficiency of the biomolecular pairs by accelerating the transport of analytes to the binding surface. The ACET force stirs the flow field, thereby reducing the thickness of the diffusion boundary layer, often developed on the reaction surface due to the slow flow velocity, low analyte diffusion coefficient, and surface reaction high rate. The results showed that the detection time of one of the biosensors can be improved by 69% under an applied voltage of 10 Vrms and an operating frequency of 100 kHz. Certain control factors such as the thermal boundary conditions as well as the electrical conductivity of the buffer solution were analyzed in order to find the appropriate values to improve the efficiency of the biosensor.

Hydrodynamically driven facet kinetics in crystal growth

In this paper we show that the presence of liquid flow around a crystal growing from melt can induce dissymmetry in growth similar to that described by anisotropic interfacial kinetic coefficients. A front tracking interface model based on a cellular automaton approach was applied to the growth of a Fe2Al5 crystal (also known as top dross particle) in a saturated Zn melt at constant temperature. The growth rate was found to be influenced by the intensity of the melt flow and by the direction of the flow with respect to the crystal orientation. The magnitude and the direction of flow modify the diffusion boundary layer, changing the conditions (temperature and concentration) at the facet interface, therefore the mass transfer. We have shown that despite the isotropy of interfacial kinetics, hydrodynamics was able to introduce an anisotropy in the crystal growth similar to the natural anisotropy in interfacial kinetics of the facets. The facets grow rate was found to be strongly dependant on the Reynolds number as well as on the orientation of the crystalline orientation with respect to the flow direction.

First order approximation for coupled film and intraparticle pore diffusion to model sorption/desorption batch experiments

A simple first order approximation was derived to model sorption/desorption kinetics of hazardous compounds in batch experiments based on a coupled film and intraparticle diffusion model. The solution is accurate enough to replace infinite series expansions needed in analytical solution for intraparticle diffusion and it accounts for the mass transfer shift from diffusion in the external aqueous boundary layer to the intraparticle pore space. With increasing distribution coefficient (Kd) and intraparticle particle porosity (ε) or decreasing Sherwood number (Sh) this mass transfer shift from film diffusion to intraparticle pore diffusion is delayed. The simple first order approximation equation allows analyses of mass transfer resistances and calculation of characteristic times which is relevant for the planning of batch experiments. The proposed solution is verified by a semi-analytical solution in Laplace space for fractional mass uptakes in the solid phase at equilibrium ranging from 50% to 91%, representing scenarios typically encountered in batch experiments.

In situ high-resolution two-dimensional profiles of redox sensitive metal mobility in sediment-water interface and porewater from estuarine sediments

Metals in contaminated sediments may present high environmental risks and ecological threats to benthic organisms. Redox sensitive elements with different oxidation states show variations in solubility as a function of redox status of the sediment water environment. The novel high-resolution ZrO-Chelex-AgI diffusive gradients in thin film (HR-ZCA DGT) technique provided sensitive in situ mapping of metals in the estuarine sediments. The present study investigated the sub-millimeter two-dimensional distributions of DGT-labile S(-II), P(V), and six redox sensitive metals (Fe, Mn, V, Cu, Ni, and Zn) across sediment-water interface (SWI) severely influenced by anthropogenic activity. We for the first time used the V-turning value (the V/Fe ratios at ~0.03) to accurately identify the actual SWI. The diffusion boundary layer (DBL) thickness of Ni, Cu and Zn was consistent with those identified by the dissolved oxygen microelectrode method, and was 3–6 mm above the SWI. No significant release of dissolved Fe and P from sediments into the overlying water was found by diffusion process. The estimated fluxes (Fdif) of Ni, Cu, and Zn at DBL were 4.0–176, −1.1–235, and 5.0–108 μg m−2 d−1, respectively, and were significantly higher in sediments near the industrial effluent dumping sites than those in sediments impacted by domestic wastewater releases. Metal diffusion flux was mainly controlled by the particulate matter on the surface sediment and organic degradation. Traditional diffusion flux may have underestimated the flux of metals from the surface sediments. The discharge of hypoxic tributary was an important source of metal pollution in the contaminated estuarine sediments.

Transient Effects Caused by Gas Depletion during Carbon Dioxide Electroreduction.

The novel use of carbon dioxide (CO2) electroreduction to generate carbon-based products which do not contribute to the greenhouse effect has promoted the vision of carbon dioxide as a renewable feedstock for future clean fuel production. Depending on the material choice for the electrocatalysis, a certain variety of products is expected from the carbon dioxide reduction reaction (CO2RR). However, as the CO2 concentration in areas close to the working electrode (relative to the diffusive boundary layer) decreases as it is being consumed and transformed into other products, the generation of H2 is favored to the detriment of CO2 electroreduction. Therefore, the extent to which H2 is produced can be used as a metric to evaluate the efficiency of CO2RR. This article proposes a model that accounts for the modes in which aqueous gas depletion evolves over time and affects the long-term CO2 electroreduction and the corresponding pH evolution near the electrode's surface. For the latter, two main contributions are distinguished: gas depletion due to CO2 consumption and ion generation in areas close to the electrocatalyst surface. pH is then suggested as an accurate and indirect means to measure CO2 concentration in a liquid electrolyte. We conclude that CO2 depletion causes a strong decay in the electrochemical reaction efficiency. In the end, we discuss several methods which may delay the onset of the adverse effects caused by gas depletion, such as the utilization of pulsed electroreduction, cycling the applied current to electrodes on and off periodically.

Feasibility of Adsorption Kinetic Models to Study Carrier-Mediated Transport of Heavy Metal Ions in Emulsion Liquid Membranes.

Emulsion liquid membranes have been successfully used for the removal of different types of organic and inorganic pollutants by means of carrier-mediated transport mechanisms. However, the models that describe the kinetics and transport of such mechanisms are very complex due to the high number of model parameters. Starting from an analysis of the similarity between the elemental mechanisms of carrier-mediated transport in liquid membranes and of transport in adsorption processes, this paper presents an experimental analysis of the possibility of applying kinetic and mechanistic models developed for adsorption to carrier-mediated transport in emulsion liquid membranes. We study the removal of a target species, in this case, Cu(II), by emulsion liquid membranes containing membrane phase solutions of benzoylacetone (carrier agent), Span 80 (emulsifying agent) and kerosene (diluent), and hydrochloric acid as a stripping agent in the product phase. The experimental results fit the pseudo-second-order adsorption kinetic model, showing good relationships between the experimental and model parameters. Although both Cu(II) diffusion through the feed/membrane interface boundary layer and complex Cu-benzoylacetone diffusion through the membrane phase controls Cu(II) transport, it is the former step that mainly controls the transport process.

Experimental and theoretical study of vapor/air mixture condensation inside an inclined blind-end pipe in natural convection with considering fog formation

This study investigated the vapor condensation characteristics in an inclined pipe under natural convection conditions experimentally and numerically. The inclined blind-end concentric pipe had an inner diameter of 134 mm and a length of 680 mm, which is cooled by cooling water. The experimental pressure range was 0.2–0.6 MPa, and the dimensionless mass number range was 0.44 to 202. The fog formation phenomenon was observed in the experiment. An empirical correlation with a broad range of dimensionless mass numbers was developed based on the experimental results to predict the heat transfer coefficient (HTC). When the air mass fraction was large and the HTC was low, the effect of fog formation on the HTC had to be considered. In the numerical simulation, this study aimed to develop an HTC prediction model with broader applicability. Based on the diffusion boundary layer theory, this study improved Peterson's model by adding fog effect and wave effect. The model showed high adaptability to this experiment and other experiments in the natural convection condensation database. The improved model performed significantly better, with 96% of the data falling within an error zone of 30%. The wide range of dimensionless mass number test data might complement the natural convection condensation experimental database.