Particle Size Polydispersity Research Articles

Size-polydispersity-induced effects on the structure of active Brownian pseudo-hard disks

Studies of the effects of particle-size polydispersity or of particle interactions on active matter have been limited to determine and analyze the system short-time dynamics in the high-density regime. On the other hand, the effects of polydispersity on the structural behavior of active systems are of relevance and have received much less attention. In this paper, we comprehensively analyze the effects of size dispersion of pseudo hard-disk active Brownian particles, on its structural behavior at different system densities and different self-propelling velocities, thus elucidating the interplay of these features with the polydispersity. This is introduced into our analysis by well-known particle size distributions in such a manner that the average size is fixed, but with a variance that accounts for different dispersion of the particle size according to: Gaussian, Weibull, uniform and “two point” distribution. Local and global structural properties of the system are determined under these considerations. We observe that activity and size polydisperse effects become relevantly conspicuous at densities above the motility induced phase separation critical point of the monodispersal fluid. We notice that, while the activity promotes a more defined local and global structural arrangement, the polydispersity decreases such structure, observing the greatest effect when the particle size is defined by a uniform distribution.

The effect of particle size distribution on the collapse of wet polydisperse granular materials

Low-saturation liquid-containing granular materials are commonly encountered in both natural and industrial settings, where interstitial liquids significantly affect the motion of particles, while particle size polydispersity plays a crucial role in determining the level of system cohesion. In this study, the collapse of wet polydisperse granular columns is numerically investigated based on the developed discrete element model, with corresponding dam-break experiments performed to validate our numerical model and methodology. The dependence of the dynamics and flow mobility on particle size distribution is primarily examined, and the underlying mechanisms are also explored by analyzing particle path lengths and average fidelity. Building upon the effective Bond number proposed using the mixing theory, a macroscopic cohesion parameter at the material scale is defined by considering the dependence of the collapse on the system size effect. The relevance of this cohesion parameter in describing different wet polydisperse granular collapses is further validated based on our designed experimental tests and DEM simulations. The approach of constructing the cohesion parameters at different scales can be extended to characterize cohesion effects in more complex wet polydisperse granular flows and describe their associated rheological behaviors.

Numerical simulations on non-reactive multiphase flow during the transition from vent activation to venting with vent cap fragments in 18650 lithium-ion batteries

Mandatory safety devices, prevalent in lithium-ion batteries (LIBs), enable current interrupt device (CID)-and vent-activated power-off protection by sensing the electrochemical gas production boost triggered by thermal runaway (TR). For an in-depth understanding of the early warning of safety devices, the thermodynamic and multiphase flow behaviour of gases-vent particles interaction under the non-combustion venting phase is numerically investigated. From the gas phase simulation results, the flow field structure of the counter-rotating vortex pairs (CVPs) bounded by vent cap fragments enhances the heat transfer between ambient air and the venting gas, and the local venting gas temperature can reach a drop of >100 K. The transient three-dimensional spatial evolution characteristics of vent particles interacting with vent cap fragments at the early stage of the venting process after 18650 thermal runaway-induced vent-activation is originally demonstrated, including gas temperature and velocity as well as particle size and temperature. The spatial distributions of polydisperse particle size and temperature under the process of non-combustion venting are used to characterize the ejected particles' behaviour, which reveals the particle trajectories in particle-laden streams and their heat-transfer characteristics. The results show that ejected particles with relatively high temperatures and large sizes are mainly clustered within the cell diameters, and possible thermal runaway propagation inside the module can be triggered by the smaller-size particles of higher temperature sprayed in the periphery when the blocking effect of the vent cap fragment is weakened.

Strong Impact of Particle Size Polydispersity on the Thermal Conductivity of Yukawa Crystals

Control of thermal transport in colloidal crystals plays an important role in modern technologies. A deeper understanding of the governing heat transport processes in various systems, such as polydisperse colloidal crystals, is required. This study shows how strongly the particle size polydispersity of a model colloidal crystal influences the thermal conductivity. The thermal conductivity of model colloidal crystals has been calculated using molecular dynamics simulations. The model crystals created by particles interacting through Yukawa (screened-Coulomb) interaction are assumed to have a face-centered cubic structure. The influence of the Debye screening length, contact potential, and particle size polydispersity on the thermal conductivity of Yukawa crystals was investigated. It was found that an increase in particle size polydispersity causes a strong—almost fivefold—decrease in the thermal conductivity of Yukawa crystals. In addition, the obtained results showed that the effect of the particle size polydispersity on reducing the thermal conductivity of Yukawa crystals is stronger than changes in values of the Debye screening length or the contact potential.

Exploratory study on physicochemical properties of nitazoxanide nanocrystalline suspension obtained by evaporative solvent-antisolvent technique

Nitazoxanide (NTZ) is a broad-spectrum antiparasitic drug with low bioavailability due to its poor aqueous solubility, classified as a Biopharmaceutical Classification System (BCS) class II drug. This study aimed to improve the understanding of NTZ nanocrystalline suspensions produced via the solvent-antisolvent technique. NTZ was extracted from commercially available coated tablets and characterized using DSC, TG, UV-Vis, and FTIR, revealing the presence of impurities likely from excipients. Nanocrystalline suspensions were prepared using three different stabilizers (Lecithin, Poloxamer 188, and Tween® 80) and evaluated for particle size distribution (PSD) and polydispersity index (PDI) over a one-week stability study. Poloxamer 188 was the most effective in reducing particle size (934.7 nm), though Lecithin achieved a more favorable PDI (0.289), indicating better particle uniformity. These findings suggest the solvent-antisolvent technique is a promising approach for producing NTZ nanocrystalline suspensions, but further reduction in particle size and exploration of alternative stabilizers are needed to optimize stability and performance.

Two-step emulsification for the fabrication of homogeneous PCL microspheres encapsulating geniposidic acid with antioxidant properties

The mortality rate of neurological disorders is increasing globally, and natural antioxidant geniposidic acid (GPA) holds great potential in the treatment of neuronal oxidative damage. Nevertheless, its inherent instability constrains its pragmatic utilization. Herein, we introduced a drug delivery system capable of protecting unstable natural active compounds from degradation. Among the various methods for preparing drug-loaded microspheres, the emulsification-solvent evaporation technique is one of the most commonly employed due to its efficiency and simplicity. Nevertheless, this method results in microspheres with heterogeneous particle sizes. To address this limitation, we developed a two-step emulsification method involving stirring and homogenization. Using the biocompatible, synthetic, biodegradable polymer polycaprolactone (PCL) as the drug delivery carrier, we prepared GPA-loaded PCL microspheres via the two-step emulsification method. The results demonstrated that the microspheres possessed uniform particle size (polydispersity index = 0.12), excellent drug loading capacity (∼4.86%), sustained drug release profiles (∼68.55% in 264 h), and biocompatibility (cell viability >85%). The in vitro tests showed that the microspheres exerted antioxidant effects by scavenging reactive oxygen species (ROS) induced by oxidative stress, thereby protecting neuronal cells from oxidative damage. This work presents a promising new approach for the treatment of neuronal oxidative damage.

Numerical study on the polydispersive effect of filler size distribution on the properties of thermal interface materials

Abstract Advanced thermal interface materials (TIMs) are indispensable for work reliability and lifespan assurance of high-power density electronic systems by facilitating timely and effective heat dissipation. A random algorithm consisting of diluting, dropping, and stirring processes is first proposed to simulate microstructures of TIMs with continuous particle size distribution, with an accessible maximum volume fraction of 55 vol%. Then the size polydispersity impact on the thermal performance and the fluidity of TIMs is numerically investigated. Simulation results reveal that as the particle size polydispersity increases, the thermal conductivity of TIMs improves, along with the improved fluidity. Therefore, it is necessary to consider the polydispersive impact of filler size distribution in actual production and optimize the material preparation process based on the actual distribution of particles. This work provides a deeper understanding of the influence of particle polydispersity on the co-optimization of the desired attributes of TIMs.

A Quality by Design Approach for Optimizing Solid Lipid Nanoparticles of Bedaquiline for Improved Product Performance.

Bedaquiline (BQ) solid lipid nanoparticles (SLNs), which have previously been formulated for parenteral administration, have a risk of patient non-compliance in treating tuberculosis. This research presents a strategy to develop BQ SLNs for oral delivery to improve patient adherence, The upper and lower levels for the formulation excipients were generated from screening experiments. Using 4 input factors (BQ, lecithin, Tween 80, and PEG), a full factorial design from 3 × 2x2 × 2 experiments was randomly arranged to investigate 3 response variables: Particle size distribution (PSD), polydispersity index (PdI), and zeta potential (ZP). High shear homogenization was used to mix the solvent and aqueous phases, with 15% sucrose as a cryoprotectant. The response variables were assessed using a zeta sizer while TEM micrographs confirmed the PSD data. Solid-state assessments were conducted using powdered X-ray diffraction and scanning electron microscopy (SEM) imaging. A comparative invitro assessment was used to determine drug release from an equivalent dose of BQ free base powder and BQ-SLN, both packed in hard gelatin capsules. The sonicated formulations obtained significant effects for PSD, PdI, and ZP. The p-values (0.0001 for PdI, 0.0091 for PSD) for BQ as an independent variable in the sonicated formulation were notably higher than those in the unsonicated formulation (0.1336 for PdI, 0.0117 for PSD). The SEM images were between 100 - 400nm and delineated nanocrystals of BQ embedded in the lipid matrix. The SLN formulation provides higher drug levels over the drug's free base; a similarity factor (f2 = 18.3) was estimated from the dissolution profiles.

Physical experiment and pore-scale investigation of the clogging of polydisperse particles in saturated porous media during artificial groundwater recharge

Groundwater recharge engineering practices are usually accompanied by the migration and deposition of polydisperse particles. Solid particles may be retained in the pore space leading to clogging of the porous media and reducing groundwater recharge efficiency. However, the mechanism behind this clogging phenomenon remains poorly understood. Specifically, the relation of particle clogging at pore-scale and macroscale is unclear. Here, the influence of polydisperse particle size on clogging development patterns was studied utilizing a series of laboratory-scale column experiments in conjunction with pore-scale scanning electron microscopy (SEM) experiments. Particles with median particle sizes (dp50) of 0.66, 4.05, 11.83 μm were injected separately into the sand column to simulate particle clogging that occurs during groundwater recharge. SEM was used to directly observe particles deposition on porous media grain surface after the column experiments. By counting the size distribution of the particles on the media grain surface, the response of the particle deposition to the surface morphology of the media grains was analysed. Compared to dp50 of 4.05 and 11.83 μm, the spatial distribution of particles deposited in the sand column was more uniform at dp50 of 0.66 μm. The smallest particles (dp50 = 0.66 μm) used in the experiments ultimately formed mixed clogging, which was the result of the combined effects of particle deposition and aggregation. The particle deposition with dp50 = 4.05 and 11.83 μm ultimately exhibited hyper-exponential distribution and formed mixed and superficial clogging, respectively. At the same time, the concave region of the media grain surface played a dominant role in particle deposition. For dp50 = 4.05 μm, 69.41 % of the particles were deposited in the concave region, and for dp50 = 11.83 μm, the proportion was 90.1 %. The results help to better manage particle clogging in groundwater recharge and other engineering applications (e.g., groundwater source heat pump, and filtration project). In addition, these findings provide a theoretical reference for the development of numerical models to help recognize the probability of particles of different sizes to be captured in porous media.

Two‐step simulation combining large eddy simulation and population balance Monte Carlo for nanoparticle synthesis in flame spray pyrolysis

AbstractA two‐step simulation approach combining large eddy simulation (LES) for turbulent flame and multidimensional/multivariate population balance Monte Carlo (PBMC) for nanoparticle dynamics is proposed to explore the detailed flame fields and particle dynamics of zirconia nanoparticles in a flame spray pyrolysis (FSP) reactor. The turbulent combustion of gas and spray are simulated by the nonlinear LES‐partially stirred reactor model. Thereafter, the differentially weighted PBMC is applied for the first time to describe the spatially resolved formation and growth of nanoparticles using the flame fields derived from LES as an input. An efficient submodel for particle spatial transport in multidimensional grids is adopted and tested to account for the effect of thermophoresis, convective and diffusion of the nanoparticles. This methodology is successfully applied to an FSP case, demonstrating a reliable level of fidelity when compared to experiments and other model. Simulation results are discussed, in particular the flame fields and the size, morphology, as well as polydisperse primary particle and aggregates size distribution.

Transport properties of 2D Lennard–Jones fluid: effect of particle size polydispersity

ABSTRACT We performed molecular dynamics simulation to investigate the transport coefficients of 2D size polydisperse Lennard–Jones fluids considering two size distributions, namely, Gaussian (G) and Uniform (U). In particular, we investigate how transport coefficients like viscosity (η), self-diffusion (D) and thermal conductivity (κ) are affected by particle size polydispersity (δ). For both systems, it is found that η is a non-monotonic function of δ, i.e. η gradually decreases and then increases as one vary δ across terminal polydispersity δ t . The re-entrant freezing at large δ due to increase fractionation may describe this behaviour. Dynamics of different size particles indicate that small particles tend to be more diffusive and contribute significantly to the collective diffusion according to SE relation. The self-diffusion coefficient obtained from the collective dynamics of the particles and the fluid's viscosity agree well with one another. It is noted that the thermal conductivity, κ, exhibits a decreasing trend with both δ and T as a result of the decreasing correlation in particle arrangement and the increase in defect such as vacancies or interstitials in the structure or composition due to polydispersity. Finally, it is shown that the particle size polydispersity of the developed material may be tuned to obtain the desired κ value.

Effect of distribution shape on the melting transition, local ordering, and dynamics in a model size-polydisperse two-dimensional fluid

Abstract We study the effect of particle size polydispersity (δ) on the melting transition (T *), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian (G) and uniform (U) distribution functions. For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity, the value of T * initially increases due to improved packing efficiency (ϕ) followed by a decrease and terminates at δ ≈ 8% (U-system) and 14% (G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which ϕ drops suddenly coincides with the peak of the heat capacity (CP ) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter (Q 6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T–δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems; however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Dispersion and Dosimetric Challenges of Hydrophobic Carbon-Based Nanoparticles in In Vitro Cellular Studies.

Methodologies across the dispersion preparation, characterization, and cellular dosimetry of hydrophilic nanoparticles (NPs) have been developed and used extensively in the field of nanotoxicology. However, hydrophobic NPs pose a challenge for dispersion in aqueous culture media using conventional methods that include sonication followed by mixing in the culture medium of interest and cellular dosimetry. In this study, a robust methodology for the preparation of stable dispersions of hydrophobic NPs for cellular studies is developed by introducing continuous energy over time via stirring in the culture medium followed by dispersion characterization and cellular dosimetry. The stirring energy and the presence of proteins in the culture medium result in the formation of a protein corona around the NPs, stabilizing their dispersion, which can be used for in vitro cellular studies. The identification of the optimal stirring time is crucial for achieving dispersion and stability. This is assessed through a comprehensive stability testing protocol employing dynamic light scattering to evaluate the particle size distribution stability and polydispersity. Additionally, the effective density of the NPs is obtained for the stable NP dispersions using the volumetric centrifugation method, while cellular dosimetry calculations are done using available cellular computational modeling, mirroring approaches used for hydrophilic NPs. The robustness of the proposed dispersion approach is showcased using a highly hydrophobic NP model (black carbon NPs) and two culture media, RPMI medium and SABM, that are widely used in cellular studies. The proposed approach for the dispersion of hydrophobic NPs results in stable dispersions in both culture media used here. The NP effective density of 1.03-1.07 g/cm3 measured here for black carbon NPs is close to the culture media density, resulting in slow deposition on the cells over time. So, the present methodology for dispersion and dosimetry of hydrophobic NPs is essential for the design of dose-response studies and overcoming the challenges imposed by slow particle deposition.

Formulation and Evaluation of Trimetazidine Hydrochloride Loaded Solid Lipid Nanoparticles

Objective The aim of the current study was to design trimetazidine hydrochloride solid lipid nano-particles SLNs and to evaluate them.Methods Hot homogenization technique was used for preparation of trimetazidine hydrochloride SLNs using different lipids Tristearin GMS and Compritol soy lecithin as stabilizers and Tween 80 Poloxamer as surfactants. Results The nano-particles were characterized for particle size polydispersity index PDI zeta potential entrapment efficiency and drug release patterns. Particle sizes ranged from 145.6 to 780.1 nm. All formulations showed PDI from 0.170 to 0.358. The zeta potential ranged from -24.2 to -38.0 mV trimetazidine SLNs demonstrated entrapment efficiency ranging from 84.42 to 93.82. The cumulative percentage release of drug from different trimetazidine hydrochloride nano- particles ranged from 75.43 to 93.59 depending upon nature and quantity of lipid used. Conclusion Among all the formulations F1 showed highest drug release of 93.59 and was considered as optimized formulation. Drug release was found to follow first order diffusion control and the lsquonrsquo value obtained from the Korsmeyer Pepparsquos model indicated anomalous diffusion non-Fickian type n value of F1 was 0.5716 as release mechanism. The particle size PDI and zeta potential of optimized formulation were found to be 153.8 nm 0.358 -38.0 mV respectively.

Unveiling Enhanced Electrostatic Repulsion in Silica Nanosphere Assembly: Formation Dynamics of Body-Centered-Cubic Colloidal Crystals.

We demonstrate the effective establishment of long-range electrostatic interactions among colloidal silica nanospheres through acid treatment, enabling their assembly into colloidal crystals at remarkably low concentrations. This novel method overcomes the conventional limitation in colloidal silica assembly by removing entrapped NH4+ ions and enhancing the electrical double layer (EDL) thickness, offering a time-efficient alternative to increase electrostatic interactions compared with methods like dialysis. The increased EDL thickness facilitates the assembly of SiO2 nanospheres into a body-centered-cubic lattice structure at low particle concentrations, allowing for broad spectrum tunability and high tolerance to particle size polydispersity. Further, we uncover a disorder-order transition during colloidal crystallization at low particle concentrations, with the optimal concentration for crystal formation governed by both thermodynamic and kinetic factors. This work not only provides insights into assembly mechanisms but also paves the way for the design and functionalization of colloidal silica-based photonic crystals in diverse applications.

Large eddy simulation-bivariate sectional model for non-spherical TiO2 nanoparticle synthesis in flame

Numerical simulation of nanoparticle synthesis in flame necessitates a high level of fidelity for turbulent flame, as well as delivers more detail insight into the evolution of structure and size distribution of particles undergoing various dynamic events. In the present work, a new simulation approach coupling large-eddy simulation (LES) and bivariate sectional model is proposed to explore the synthesis of nanoparticles in turbulent flame. More specifically, the nonlinear LES-partially stirred reactor model (NLES-PaSR) is utilized to simulate the turbulent flame, wherein the gradient-type structural subgrid-scale (SGS) model for turbulent flow and partially stirred reactor (PaSR) model for turbulent combustion are considered. In addition, the volume-based bivariate sectional model is thoroughly coupled with the LES model for the first time to describe the spatiotemporally resolved formation and growth of nanoparticles using particle number concentration and surface area concentration as two sets of variables. Compared directly with the LES-monodisperse (LES-Mono) and LES-univariate sectional (LES-UniSe) models, the LES-bivariate sectional (LES-BiSe) model has significant advantages in its ability to analyze and predict the size, morphology, as well as polydispersed particle size distribution (PSD) evolution of nanoparticles at a moderate computational cost simultaneously. In the LES framework, the proposed model successfully simulates the spatiotemporally resolved formation and growth of non-spherical TiO2 nanoparticle in turbulent diffusion burner. The predicted results derived from the LES-BiSe model are in good agreement with the experimental measurements. Also, the aggregate and primary particle size distribution shows highly temporal fluctuation, which mainly results from the continuous variations of particle path induced by the unsteady turbulent combustion. Furthermore, the present work demonstrates the profound dependence of particle morphological on both spatiotemporal evolution and their intrinsic size distribution. In particular, the large aggregates in the higher sections are commonly found as irregular structure with fractal-like dimensions.

Tunable Reflection through Size Polydispersity of Chiral-Nematic Liquid Crystal Polymer Particles

Micro-sized chiral-nematic liquid crystal (N* LC) polymer particles have attracted considerable interest as versatile reflective colorants with selective circularly polarized light (CPL) properties. However, challenges in achieving the desired size distribution of N* LC particles have led to an incomplete understanding of their reflective characteristics. In this study, we successfully synthesized N* LC particles via dispersion polymerization, enabling precise control over size polydispersity by manipulating the composition of the polymerization solvent. Our investigation revealed that monodisperse N* LC particles displayed distinct reflection bands with high CPL selectivity, while polydisperse particles exhibited broader reflection with lower CPL selectivity. These findings underscore the potential to synthesize N* LC particles with tailored reflective properties using identical monomeric compounds. Furthermore, we demonstrated the production of multifunctional reflective colorants by blending N* LC particles with varying reflection colors. These discoveries hold significant promise for advancing the development of reflective colorants and anti-counterfeiting printing techniques utilizing micro-sized N* LC particles.

Development of calculation tool for iodine 131 biodistribution depending on the aerosol particle distribution.

Radiation damage to tissues depends on radiation exposure levels. Therefore, we have studied accurate estimations of radiation exposure levels so far. Recently, we developed a tool that can calculate the respiratory tract deposition of radionuclides based on polydisperse particle size distribution. As a next step, there is a need for a new calculation tool for the biodistribution of radionuclides because a fraction of the radionuclides deposited in the respiratory tract is absorbed into the body. In this study, a calculation tool for iodine 131 biodistribution depending on aerosol size distribution was developed. The developed tool in this study is used with the former tool.

D-α-tocopherol polyethylene glycol 1000 succinate-based microemulsion delivery system: Stability enhancement of physicochemical properties of luteolin.

In the present study, D-α-Tocopherol polyethylene glycol 1000 succinate-based self-microemulsifying drug delivery systems (TPGS-SMEDDS) were introduced to enhance the solubility and stability of luteolin. The ternary phase diagrams were constructed to obtain the maximum area of microemulsion and suitable formulations of TPGS-SMEDDS. The particle size distribution and polydispersity index of selected TPGS-SMEDDS were analyzed to be less than 100nm and 0.4, respectively. The thermodynamic stability results suggested that the TPGS-SMEDDS was stable during the heat-cool and freeze-thaw cycle. Moreover, the TPGS-SMEDDS exhibited excellent encapsulation capacity (51.21±4.39 to 85.71±2.40%) and loading efficiency (61.46±5.27 to 102.86±2.88mg/g) to luteolin. In addition, the TPGS-SMEDDS showed an admirable vitro release ability with a ratio of more than 88.40±1.14% for luteolin in 24h. Therefore, TPGS-based SMEDDS might provide an effective role for the oral administration of luteolin and holds promise as a potential delivery for poorly soluble bioactive compounds.

A 1D Model for Nucleation of Ice From Aerosol Particles: An Application to a Mixed‐Phase Arctic Stratus Cloud Layer

AbstractMixed‐phase clouds (MPCs) have been identified as significant contributors to uncertainties in climate projections, attributable to model representation of processes controlling the formation and loss of supercooled water droplets and ice particles from the atmosphere. Arctic MPCs are commonly widespread and long‐lived, with sustained ice crystal formation processes that challenge current understanding. This study examines the ice‐nucleating particle (INP) reservoir dynamics governing immersion‐mode heterogeneous freezing in an observed case of Arctic MPCs using a simplified 1D aerosol‐cloud model. The model setup includes prescribed dynamical forcings and thermodynamic profiles, and represents INPs as multicomponent and polydisperse particle size distributions. Diagnostic and prognostic approaches to immersion freezing parameterization are compared, including time‐independent (singular) number‐ and surface area‐based descriptions and a time‐dependent description following classical nucleation theory (CNT). The choice of freezing parameterization defines the size of the INP reservoir. The CNT‐based description yields an orders of magnitude larger INP reservoir than the singular parameterizations, which is the dominant factor for sustained ice crystal formation. The efficiency of the freezing process and cloud cooling are of secondary importance. A diagnostic treatment neglecting INP loss is only accurate when the INP reservoir size is large and INP depletion weak. Since a larger INP reservoir sustains ice crystal formation substantially longer, and ice water path scales with ice crystal concentrations for the conditions considered, resolving the source of differences in INP reservoir dynamics due to model implementation is a high priority for advancing climate model physics.