Development of a footwear sizing system for diabetic feet.

The number of diabetic patients is increasing rapidly who have vulnerable feet and might be easily affected by different adversities. Since there is no available footwear sizing system for diabetic patients, manufacturers produce diabetic footwear of different sizes and fittings based on other available footwear sizing systems, which may result in inappropriate fitting. To get footwear with proper fittings, diabetic patients may go for customized or bespoke footwear based on their foot conditions, which is very costly. This study attempts to explore the foot complications of diabetic patients and categorize their feet to create a new sizing system using foot measurements from 102 male diabetic patients based on three dimensions of human feet, namely foot length, ball girth, and instep circumference. K-means data clustering is followed to categorize the data into three broad groups, namely small, medium, and large groups for footwear sizing. The developed footwear sizing system uses a sizing interval of 8 mm and a fitting interval of 6 mm. This study suggests a total of 11 sizes along with 24 different fittings for the footwear manufacturers for producing diabetic footwear. This newly developed footwear sizing system has a total of 79.41 % coverage where there are 10, 10, and 4 fittings in the small, medium, and large groups, respectively. The proposed footwear sizing system can help footwear manufacturers understand the proper size and fit of diabetic patients' feet so that they can make appropriate footwear for diabetic patients economically.

CharActeristics, sizing anD outcomes of stenotic, tapered, rapHe-type bicuspid aOrtic valves treated with trans-catheter device implantation: Insights the AD HOC registry.

BACKGROUND: Raphe-type bicuspid aortic valve (BAV) is a potential hostile scenario in trans-catheter aortic valve replacement (TAVR) due to pronounced calcium burden, possibly associated with tapered valve configuration. Trans-Catheter heart valve (THV) sizing strategy (annular vs. supra-annular) is controversial in this valve subtype. OBJECTIVES: To describe the phenotypical characteristics of severe, tapered, raphe-type, BAV stenosis undergoing TAVR and to explore safety and efficacy of modern-generation THVs, analysing the impact of annular and supra-annular sizing strategies on short- and mid-terms outcomes. METHODS: This is a retrospective, multicenter registry enrolling consecutive stenotic Sievers type 1 BAV treated with TAVR. Study population was divided into tapered and non-tapered configuration according to MSCT analysis. Matched comparison between annular and supra-annular sizing groups was performed in tapered population. RESULTS: From January 2016 to June 2023, 897 patients were enrolled. Of them, 696 patients displayed a tapered configuration. Of those, 510 received a THV according to annular sizing. After propensity score matching 186 matched pairs were selected. Technical success (96.2 % vs 94.1 %, OR 1.61 [0.61-4.24], p = 0.34), 30-day device success (83.6 % in both groups, OR 1.42 [0.78-2.57], p = 0.25) and 30-day early safety (71.8 % vs 70.5 %, OR 1.07 [0.68-1.68], p = 0.78) were similar between the annular and supra-annular sizing groups; a higher post-TAVR gradient was observed in supra-annular group, although it was only 2 mmHg mean. At mid-term follow-up, the rate of clinical efficacy was 84.7 %. CONCLUSIONS: TAVR with modern-generation devices is safe and effective for tapered raphe-type BAV, showing comparable results for annular and supra-annular sizing strategies.

Optimal size of Frozenix for true thoracic aneurysms: is downsizing an option?

OBJECTIVE: During total arch replacement (TAR) using frozen elephant trunk (FET) technique with Frozenix for true thoracic aortic aneurysm (tTAA), oversized FET tends to be chosen similar to the endovascular devise selection. However, the oversized FET is considered a risk factor for intimal injury. The appropriate size selection of FET remains insufficiently understood. METHODS: Between October 2014 and March 2022, a total of 49 patients underwent TAR using Frozenix for tTAA. Out of 49 patients, four patients planned to staged surgery were excluded, 19 patients were operated on with an undersized Frozenix compared with the descending aorta (undersized FET group) and in 26 patients an equal or oversized Frozenix was used (oversized FET group). Clinical outcomes and postoperative diameter changes were investigated. RESULTS: In-hospital mortality was 0%. The mean diameter of Frozenix and the descending aorta was 30.7 mm and 28.8 mm, respectively, in the oversized FET group, and 26.7 mm and 30.1 mm in the undersized FET group. Postoperative computed tomography (CT) demonstrated no endoleaks not only in the oversized FET group but also in the undersized FET group. CT also revealed that undersized FET had expanded more than the original diameter in all cases except for two, with an average of 2.47 ± 1.53 mm. Additionally, the descending aorta covered with Frozenix shrank in 10 patients (53%). Postoperative adverse aortic events were not observed. CONCLUSIONS: Undersized Frozenix tightly fit the descending aorta and resulted in complete sealing without endoleaks. Oversized FET is not strictly necessary considering the size-related adverse complications.

Analysis of hybrid solutions with Li-ion battery system for DP-2 vessels.

An economical approach for incorporating Battery Energy Storage Systems (BESS) onto DP-2 vessels is presented in this research. The paper deals with developing a Battery Optimization for Optimal Sizing and Throughput Energy Regulation (BOOSTER) framework for putting research findings into practice by optimizing battery size, technology choice and power generation scheduling while considering battery degradation. Twelve battery sizes are analyzed based on three key performance metrics: return on investment, payback period, and years of profitability. A Mixed Integer Linear Programming (MILP) is developed to operate the energy and power management system of the vessel in a fuel and economically efficient manner. The study considers two load profiles of a DP-2 vessel operating near Taiwan and the North Sea. Our findings emphasize the significance of taking battery ownership costs in the form of energy throughput cost and fuel price into account, resulting in a longer battery lifetime and higher return on investment. The research also proposes a BESS operation matrix that provides vessel operators with valuable information on BESS usage for economic benefits. This matrix translates analytics and decision-making into tangible actions that can be implemented in real-time operations. Based on the findings, energy systems may be optimized for a sustainable future, which benefits vessel operators and industry stakeholders.

Fabrication of an Amino Functionalized Paper-Based Material for Highly Efficient Detection and Adsorption of Formaldehyde.

An amino functionalized paper-based material that utilized amino functionalized polymer particles as sensing probes and adsorption sites was fabricated via internal sizing technology for application in formaldehyde detection and adsorption. A large specific surface area and the porous structure of the paper fibers enable the application of the composite paper-based material as a sensor at low concentrations of primary amine groups. The material reacts with low levels of formaldehyde, resulting in a concentration-based change in the pH, which is rapidly expressed as a color change. After exposure to formaldehyde (0.02 mg/m3) for 10 min, the color of the composite paper-based material changed from pink to brown, demonstrating the high sensitivity of the material, and this transition could be clearly observed using the naked eye. Additionally, the composite paper-based material acts as an adsorbent at a high content of amino groups, owing to a rapid addition reaction with formaldehyde, exhibiting a high adsorption capacity. Considering the high sensitivity, adsorption capacity, and adsorption speed for formaldehyde, the as-developed composite paper-based material exhibits promising application potential in the field of formaldehyde detection and adsorption.

Elastomeric Fire and Heat-Protective Materials Containing Functionally Active Microheterogeneous Systems.

This research aims to explore how functionally active structures affect the physical, mechanical, thermal, and fire-resistant properties of elastomeric compositions using ethylene-propylene-diene rubber as a base. The inclusion of aluminosilicate microspheres, microfibers, and a phosphorus-boron-nitrogen-organic modifier in these structures creates a synergistic effect, enhancing the material's heat-insulating properties by strengthening coke and carbonization processes. This results in a 12-19% increase in heating time for unheated sample surfaces and a 6-17% increase in residual coke compared to existing analogs. Microspheres help counteract the negative impact of microfibers on composition density and thermal conductivity, while the phosphorus-boron-containing modifier allows for controlling the formation of the coke layer.

Modelling and optimization of an existing onshore gas gathering network using PIPESIM.

Pakistan has limited natural gas reserves, and most are found onshore. This article reports on the problems of an onshore gas gathering network (GGN) analysed through steady-state simulation modelling using PIPESIM software. The research methodology incorporates a comprehensive steady-state hydraulic analysis considering fluid flowing velocity limitations, liquid holdup and slugging along with other issues faced by gas gathering networks. The steady-state hydraulic analysis has led us to pinpoint specific GGN pipelines facing critically low gas velocities and consequent liquid holdup. Addressing these issues involved application of PIPESIM software for modelling, considering various operating schemes of gas-producing wells and their associated pipelines. To select an optimal operating scheme, the study utilized the Analytic Hierarchy Process (AHP) for operational optimization, to identify the most effective solution for reduced liquid holdup, improving production, and ensuring the safe operation among available alternatives. Findings from our hydraulic analysis highlight the importance of reducing GGN outlet pressure to mitigate challenges associated with liquid holdup which causes slugging and back pressure effect at source leading to low production and poor performance of the GGN. Study of three alternative cases reveals that decreasing outlet pressure lowers the liquid holdup, improve gas flowing velocities, and enhanced overall production. These findings validate our hypothesis that reducing GGN outlet pressure is a viable strategy to lower the liquid holdup in pipelines. This research offers significant value by providing a comprehensive solution to GGN liquid holdup, low flowing velocities, back pressure and low production challenges. The integration of steady-state hydraulic analysis, simulation modelling with PIPESIM, and the application of AHP for optimization contributes novel insights into the optimization of operation of gas gathering networks. Emphasizing the reduction of liquid holdup and enhancing production through outlet pressure adjustments offers a practical framework for optimizing the functionality of gas gathering networks.

Modified Harris Hawks optimization for the 3E feasibility assessment of a hybrid renewable energy system.

The off-grid Hybrid Renewable Energy Systems (HRES) demonstrate great potential to be sustainable and economically feasible options to meet the growing energy needs and counter the depletion of conventional energy sources. Therefore, it is crucial to optimize the size of HRES components to assess system cost and dependability. This paper presents the optimal sizing of HRES to provide a very cost-effective and efficient solution for supplying power to a rural region. This study develops a PV-Wind-Battery-DG system with an objective of 3E analysis which includes Energy, Economic, and Environmental CO2 emissions. Indispensable parameters like technical parameters (Loss of Power Supply Probability, Renewable factor, PV fraction, and Wind fraction) and social factor (Human Developing Index) are evaluated to show the proposed modified Harris Hawks Optimization (mHHO) algorithm's merits over the existing algorithms. To achieve the objectives, the proposed mHHO algorithm uses nine distinct operators to obtain simultaneous optimization. Furthermore, the performance of mHHO is evaluated by using the CEC 2019 test suite and the most optimal mHHO is chosen for sizing and 3E analysis of HRES. The findings demonstrate that the mHHO has achieved optimized values for Cost of Energy (COE), Net Present Cost (NPC), and Annualized System Cost (ASC) with the lowest values being 0.14130 $/kWh, 1,649,900$, and 1,16,090$/year respectively. The reduction in COE value using the proposed mHHO approach is 0.49% in comparison with most of the other MH-algorithms. Additionally, the system primarily relies on renewable sources, with diesel usage accounting for only 0.03% of power generation. Overall, this study effectively addresses the challenge of performing a 3E analysis with mHHO algorithm which exhibits excellent convergence and is capable of producing high-quality outcomes in the design of HRES. The mHHO algorithm attains optimal economic efficiency while simultaneously minimizing the impact on the environment and maintaining a high human development index.

Lignin-Based Carbon Fiber/Epoxy Resin Biocomposites with Excellent Fire Resistance and Mechanical Properties.

Carbon fiber (CF)-reinforced epoxy resin (EP) composites are lightweight materials with excellent comprehensive performance. However, the flammability of EP and the poor interfacial bonding between CF and EP are two key disadvantages that limit their further applications. Here, a kind of water-soluble lignin-based CF sizing agent (ELBEDK) is prepared through hydrophilic modification of enzymatic lignin, which can significantly enhance the interfacial interaction between CF and EP. Additionally, a highly efficient intumescent flame retardant (LMA) is prepared. The EP, enzymatic lignin, LMA and CF sized ELBEDK are compounded to obtain the fire-safety CF reinforced composites (SCF/FEP/L). The flame retardancy of SCF/FEP/L with 7% LMA (SCF/FEP7) reached V-0 rating. Moreover, SCF/FEP/L with 7% LMA and 15% lignin (SCF/FEP7/L15) present an limiting oxygen index (LOI)of 30.2% and V-0 of UL-94. Specifically, the total smoke production and the heat release rate are 47.8% and 46.81% lower than that of SCF/EP, respectively, indicating the improved smoke suppression and flame retardancy. The IFSS and flexural strength of SCF/FEP7/L15 are improved to be 59.4 MPa and 511.1 MPa, respectively. This study presents a simple approach to fabricate low-cost high performance lignin-based flame retardant CF/EP biocomposites with wide application potential.

Self-Healable Interfaces with Improved Mechanical Properties Induced by Dynamic Network Reconfiguration in Carbon Fiber-Reinforced Epoxy Laminates.

Interfacial failure in carbon fiber-reinforced epoxy (CFRE) laminates is a prominent mode of failure, attracting significant research attention. The large surface-energy mismatch between carbon fiber (CF) and epoxy results in a weaker interface. This study presents a facile yet effective method for enhancing the interfacial adhesion between CF and epoxy with self-healable interfaces. Two variants of a designer sizing agent, poly(ether imide) (PEI), were synthesized, one without a self-healing property termed BO, and the second one by incorporating disulfide metathesis in one of its monomers that renders self-healing properties at the interface-mediated by network reconfiguration, termed BA. 0.25 wt % of CF was found to be the optimum amount of BO and BA sizing agents. The surface free energy of CF drastically increased and became quite close to the surface energy of epoxy after the deposition of both sizing agents and the higher surface roughness. The improved surface wettability, presence of functional groups, and mechanical interlocking worked in tandem to strengthen the interface. The interlaminar shear strength (ILSS) and flexural strength (FS) of CFRE laminate sized with BO consequently increased by 35% and 22% and of CFRE laminate sized with BA increased by 26% and 19%, respectively. Fractography analysis revealed outstanding bonding between epoxy and PEI-CF, indicating that matrix fracture is the predominant mode of failure. The self-healable interfaces due to the preinstalled disulfide metathesis in the sizing agent resulted in 51% self-healing efficiency in ILSS for BA-sized CFRE laminate. Interestingly, the functional properties, deicing, and EMI shielding effectiveness were not compromised by modification of the interface with this designer sizing agent. This study opens new avenues for interfacial modification to improve the mechanical properties while retaining the key functional properties of the laminates.

Multi-objective placement and sizing of energy hubs in energy networks considering generation and consumption uncertainties.

This paper presents the placement and sizing of energy hubs (EHs) in electricity, gas, and heating networks. EH is a coordinator framework for various power sources, storage devices, and responsive loads. For simultaneous modeling of economic, operation, reliability, and flexibility indices, the proposed scheme is expressed as a three-objective optimization in the form of Pareto optimization based on the sum of weighted functions. The objective functions of this problem respectively minimize the planning cost of EHs (equal to the total cost of construction of hubs and their expected operating cost), the expected energy loss of the mentioned networks, and the expected energy not-supplied (EENS) of these networks in the case of an N - 1 event. The problem is constrained by power flow equations and operation and reliability constraints of these network together with the EH planning and operation model, and flexibility constraints of the EHs. Then, to achieve unique optimal solution in the shortest possible time, a linear approximation model is extracted for the proposed scheme. Moreover, scenario-based stochastic programming (SBSP) is employed to model uncertainties of load, energy cost, renewable power, and accessibility of the mentioned network equipment. Finally, the obtained numerical results indicate the capability of the proposed scheme in enhancing the economic and flexibility situation of EHs and improving the reliability and operation status of energy networks along with achieving optimal planning and operation for EHs.

Gas engine CCHP system optimization: An energy, exergy, economic, and environment analysis and optimization based on developed northern goshawk optimization algorithm.

This paper aims to enhance the design and operation of a Combined Cooling, Heating, and Power (CCHP) system utilizing a gas engine as the primary energy source for a residential building in China. An Energy, Exergy, Economic, and Environment (4E) analysis is employed to assess the system's performance and impact based on energy, exergy, economic, and environmental criteria. The effectiveness of the DNGO algorithm is evaluated on a case study site and compared with Northern Goshawk Optimization (NGO) and Genetic Algorithm (GA). The findings demonstrate that the DNGO algorithm identifies the optimal gas engine size of 130 kW. The algorithm's search capabilities are greatly enhanced by this unique blend, surpassing what traditional methods can offer. The DNGO algorithm brings several advantages, including unparalleled energy efficiency, reduced exergy destruction, and a substantial decrease in C O 2 emissions. This not only supports environmental sustainability but also aligns with global standards. Economically, the algorithm enhances the performance of the CCHP system, evident through a reduced payback period and increased annual profit. Additionally, the algorithm's rapid convergence rate allows it to reach the optimal solution faster than its counterparts, making it advantageous for time-sensitive applications. Incorporating innovative methods like chaos theory, the DNGO algorithm effectively avoids local optima, enabling a broader search for the best solution. The utilization of Lévy flight further enhances the algorithm's ability to escape local optima and navigate the search space more efficiently. Additionally, swarm intelligence is employed to simulate the collective behavior of decentralized systems, aiding in problem-solving. This research represents a significant advancement in optimization techniques for CCHP systems and offers a fresh perspective to the field of swarm-based optimization algorithms.

Acceleration for Efficient Automated Generation of Operational Amplifiers.

Operational amplifiers (Op-Amps) are critical to sensor systems because they enable precise, reliable, and flexible signal processing. Current automated Op-Amp generation methods suffer from extremely low efficiency because the time-consuming SPICE-in-the-loop sizing is normally involved as its inner loop. In this paper, we propose an efficiently automated Op-Amp generation tool using a hybrid sizing method, which combines the merits together from a deterministic optimization algorithm and differential evolution algorithm. Thus, it can not only quickly find a decent local optimum, but also eventually converge to a global optimum. This feature is well fit to be serving as an acute filter in the circuit structure evaluation flow to efficiently eliminate any undesirable circuit structures in advance of detailed sizing. Our experimental results demonstrate its superiority over traditional sizing approaches and show its efficacy in highly boosting the efficiency of automated Op-Amp structure generation.

Dissecting PM sensor capabilities: A combined experimental and theoretical study on particle sizing and physicochemical properties.

Recent advancements in particulate matter (PM) optical measurement technology have enhanced the characterization of particle size distributions (PSDs) across various temporal and spatial scales, offering a more detailed analysis than traditional PM mass concentration monitoring. This study employs field experiments, laboratory tests, and model simulations to evaluate the influence of physicochemical characteristics of particulate matter (PM) on the performance of a compact, multi-channel PM sizing sensor. The sensor is integrated within a mini air station (MAS) designed to detect particles across 52 channels. The field experiments highlighted the sensor's ability to track hygroscopicity parameter κ-values across particle sizes, noting an increasing trend with particle size. The sensor's capability in identifying the size and mass concentration of different PM types, including ammonium nitrate, sodium chloride, smoke, incense, and silica dust particles, was assessed through laboratory tests. Laboratory comparisons with the Aerodynamic Particle Sizer (APS) showed high consistency (R2 > 0.96) for various PM sources, supported by Kolmogorov-Smirnov tests confirming the sensor's capability to match APSsize distributions. Model simulations further elucidated the influence of particle refractive index and size distributions on sensor performance, leading to optimized calibrant selection and application-specific recommendations. These comprehensive evaluations underscore the critical interplay between the chemical composition and physical properties of PM, significantly advancing the application and reliability of optical PM sensors in environmental monitoring.

High-Speed Fluorescence Imaging Corroborates Biological Data on the Influence of Different Nozzle Types on Cell Spray Viability and Formation.

Treating severe dermal disruptions often presents significant challenges. Recent advancements have explored biological cell sprays as a promising treatment, but their success hinges on efficient cell delivery and complete wound coverage. This requires a good spray distribution with a small droplet size, high particle number, and ample surface coverage. The type of nozzle used with the spray device can impact these parameters. To evaluate the influence of different nozzles on spray characteristics, we compared air-assisted and unassisted nozzles. The unassisted nozzle displayed small particle size, high particle number, good overall coverage, high cell viability, preserved cell metabolic activity, and low cytotoxicity. Air-assisted nozzles did not perform well regarding cell viability and metabolic activity. Flow visualization analysis comparing two different unassisted nozzles using high-speed imaging (100 kHz frame rate) revealed a tulip-shaped spray pattern, indicating optimal spray distribution. High-speed imaging showed differences between the unassisted nozzles. One unassisted nozzle displayed a bi-modal distribution of the droplet diameter while the other unassisted nozzle displayed a mono-modal distribution. These findings demonstrate the critical role of nozzle selection in successful cell delivery. A high-quality, certified nozzle manufactured for human application omits the need for an air-assisted nozzle and provides a simple system to use with similar or better performance characteristics than those of an air-assisted system.

DNA Sizing with pg/µL Sensitivity for Cell-Free DNA Analysis with the µLAS Technology.

The µLAS technology enables in-line DNA concentration and separation in a microchannel. Here, we describe its operation to analyze the size profile of cell-free DNA (cfDNA) extracted from blood plasma. Operated on commercial systems for capillary electrophoresis, we provide the size distribution of healthy individuals or patients using an input of 10 µL.

Effect of three-dimensional to one-dimensional orientation of cellulose nanofiber sizing agents on carbon fibers under magnetic and electric fields on composite material properties.

Nanoparticle-containing sizing agents are essential for the overall performance of high-quality carbon fiber (CF) composites. However, the uneven dispersion of nanoparticles often leads to agglomeration on the surface of CF after sizing, consequently diminishing the material properties. In this study, the properties of cellulose nanofibers (CNFs) that can respond to magnetic and electric fields were utilized to achieve three-dimensional to one-dimensional orientations in CFs containing sizing agents. Cobalt ferrite (CoFe2O4) was utilized to enhance the response of CNFs to a magnetic field, and subsequently, it was combined with an electric field to attain a higher degree of orientation. The occurrence of nanoparticle agglomeration is diminished on CF surface, while establishing a structured network. The flexural strength and thermal conductivity of CF composites treated with CoFe2O4 self-assembled CNF sizing agent exhibit an increase of 54.23 % and 57.5 %, respectively, compared to those of desized CF composites, when subjected to magnetic and electric fields. Consequently, the approach can depolymerize the nano-fillers within the sizing agent and orient it into the carbon fiber under the influence of magnetic and electric fields, effectively improving the mechanical properties and thermal conductivity of the composite material.

Reliability of an extended version of the 3m™ Eargage tool to assess earcanal size and assist earplug selection.

OBJECTIVE: Evaluate the ability of an extended version of the 3 MTM Eargage to estimate the earcanal size and assess the likelihood that a particular earplug can fit an individual's earcanal, ultimately serving as a tool for selecting earplugs in the field. DESIGN: Earcanal morphology, assessed through earcanal earmolds scans, is compared to earcanal size assessed with the extended eargage (EE) via box plots and Pearson linear correlations coefficients. Relations between attenuation measured on participants (for 6 different earplugs) and their earcanal size assessed with the EE are established via comparison tests. STUDY SAMPLE: 121 participants exposed to occupational noise (103 men, 18 women, mean age 47 years). RESULTS: The earcanal size assessed with the EE allows for estimating the area of the earcanal's first bend cross-section (correlation coefficient  r = 0.533, p < 0.001). Extremely large earcanals (12.7% of earcanals in our sample) lead to significantly lower earplug attenuation (potentially inadequate) than smaller earcanals. CONCLUSIONS: The EE is a simple and inexpensive tool easily deployable in the field to assist earplugs selection. When extended with sizes larger than the maximum size of the commercial tool, it allows for detecting individuals with extremely large earcanals who are most likely to be under-protected.

Comparative electron microscopy particle sizing of TiO2 pigments: sample preparation and measurement.

Titanium dioxide (TiO2) pigment is a non-toxic, particulate material in widespread use and found in everyone's daily life. The particle size of the anatase or rutile crystals are optimised to produce a pigment that provides the best possible whiteness and opacity. The average particle size is intentionally much larger than the 100 nm boundary of the EU nanomaterial definition, but the TiO2 pigment manufacturing processes results in a finite nanoscale content fraction. This optically inefficient nanoscale fraction needs to be quantified in line with EU regulations. In this paper, we describe the measurement procedures used for product quality assurance by three TiO2 manufacturing companies and present number-based primary particle size distributions (PSDs) obtained in a round-robin study performed on five anatase pigments fabricated by means of sulfate processes in different plants and commonly used worldwide in food, feed, pharmaceutical and cosmetic applications. The PSDs measured by the three titanium dioxide manufacturers based on electron micrographs are in excellent agreement with one another but differ significantly from those published elsewhere. Importantly, in some cases, the PSDs result in a different regulatory classification for some of the samples tested. The electron microscopy results published here are supported by results from other complementary methods including surface area measurements. It is the intention of this publication to contribute to an ongoing discussion on size measurements of TiO2 pigments and other particulate materials and advance the development of widely acceptable, precise, and reproducible measurement protocols for measuring the number-based PSDs of particulate products in the size range of TiO2 pigments.