Tracer Particles Research Articles

Film characteristics of atmospheric pressure plasma-treated chitosan solution

Chitosan (Cs) is a biopolymer that can be used to create films with high swelling capacity. Its application, however, is restricted by its weak mechanical strength. To address this limitation, atmospheric pressure plasma (APP) treatment was integrated into the Cs film synthesis. This was done by exposing the Cs solution to air plasma at varying times—2, 4, and 6 min. Improved dissolution of Cs was observed in the scanning electron microscope images where no traces of excess Cs particles were found on the surface. Spectroscopic techniques such as optical emission spectroscopy, Fourier transform infrared spectroscopy, and Raman spectroscopy suggested that chain scission and cross-linking synergistically occurred to establish the network of the Cs films. This possible reaction mechanism of film formation was manifested as changes in the peak intensities of the different Cs attributes such as the pyranose ring, –OH, the C–O–C glycosidic, and the amide linkages. Shorter treatment time (2 min) resulted in the dominance of degradation where scission occurred to open the Cs rings. When using a longer treatment time (>4 min), cross-linking reactions occurred along the scission sites, which acted as initiation points. As a result, the hydrophilicity and swelling behavior of the Cs films were influenced by the APP treatment. The fabricated Cs films were generally hydrophilic. However, utilizing a longer treatment time decreased the hydrophilic nature of the film. A decreased swelling capacity for APP-treated Cs films also accompanied the decreased hydrophilicity. This observed phenomenon was attributed to the addition of Cs chains possibly caused by cross-linking. The study revealed that the water absorption ability of the Cs films was based on the relaxation of the Cs chains upon interaction with water. The integration of APP treatment for film synthesis may provide easier processing of Cs films.

Impact of ceiling fan and room air cleaner on air mixing and fate of particulate matter in a multiroom residence

We are exposed to airborne particles of health concern in residences, and Room Air Cleaners (RACs) can remove these particles. However, they are often limited to treating local air in the room or near vicinity of the device. RAC performance in multi-room residences may be improved by ceiling fan whole-house air mixing with a minor increase in energy use. This study analyzed air quality and energy efficiency from experimental measurements using combinations of ceiling fan and RAC operation. We measured removal rates of tracer gas and particles from ultrafine to 5 µm after their release in the kitchen area of a multiroom test house. Results show that the air mixing by ceiling fans increased ultrafine and > 1 µm particle removal over the baseline – with no ceiling fans and no RAC – suggesting increased deposition onto the ceiling fan blades and house surfaces. Also, ceiling fan mixing increased particle removal in all size bins over the RAC performance with no ceiling fans. The removal rate with ceiling fans and the RAC was greater than the sum of the rates from each operating alone, indicating that synergistic interactions between the ceiling fans and the RAC increased the RAC filtration rate.

Improved Particle Spray Algorithm for Modeling Globular Cluster Streams

Abstract Stellar streams that emerge from globular clusters (GCs) are thin stellar structures spread along the orbits of progenitor clusters. Numerical modeling of these streams is essential for understanding their interaction with the host galaxy's mass distribution. Traditional methods are either computationally expensive or oversimplified, motivating us to develop a fast and accurate approach using a particle spray algorithm. By conducting a series of N-body simulations of GCs orbiting a host galaxy, we find that the position and velocity distributions of newly escaped stream particles are consistent across various GC masses and orbital parameters. Based on these distributions, we develop a new algorithm that avoids computing the detailed internal cluster dynamics by directly drawing tracer particles from these distributions. This algorithm correctly reproduces the action space distribution of stream particles and achieves a 10% accuracy in stream morphology and velocities compared to N-body simulations. To facilitate broader use, we have implemented this algorithm in galactic dynamics codes agama, gala, galax, and galpy.

Influence of Photoemission Geometry on Timing and Efficiency in 4D Ultrafast Electron Microscopy.

Broader adoption of 4D ultrafast electron microscopy (UEM) for the study of chemical, materials, and quantum systems is being driven by development of new instruments as well as continuous improvement and characterization of existing technologies. Perhaps owing to the still-high barrier to entry, the full range of capabilities of laser-driven 4D UEM instruments has yet to be established, particularly when operated at extremely low beam currents (~fA). Accordingly, with an eye on beam stability, we have conducted particle tracing simulations of unconventional off-axis photoemission geometries in a UEM equipped with a thermionic-emission gun. Specifically, we have explored the impact of experimentally adjustable parameters on the time-of-flight (TOF), the collection efficiency (CE), and the temporal width of ultrashort photoelectron packets. The adjustable parameters include the Wehnelt aperture diameter (DW), the cathode set-back position (Ztip), and the position of the femtosecond laser on the Wehnelt aperture surface relative to the optic axis (Rphoto). Notable findings include significant sensitivity of TOF to DW and Ztip, as well as non-intuitive responses of CE and temporal width to varying Rphoto. As a means to improve accessibility, practical implications and recommendations are emphasized wherever possible.

Computational Fluid Dynamics as a Digital Tool for Enhancing Safety Uptake in Advanced Manufacturing Environments Within a Safe-by-Design Strategy.

In modern manufacturing environments, pollution management is critical as exposure to harmful substances can cause serious health issues. This study presents a two-stage computational fluid dynamic (CFD) model to estimate the distribution of pollutants in indoor production spaces. In the first stage, the Reynolds-averaged Navier-Stokes (RANS) method was used to simulate airflow and temperature. In the second stage, the Lagrangian method was applied for particle tracing. The model was applied to a theoretical acrylonitrile butadiene styrene (ABS) filament 3D printing process to evaluate the factors affecting the distribution of ultrafine particles (30 nm). Key parameters such as ventilation system effects, the presence of cooling fans and the print bed, and nozzle temperatures were considered. The results show that the highest flow velocities (1.97 × 10-6 m/s to 3.38 m/s) occur near the ventilation system's inlet and outlet, accompanied by regions of high turbulent kinetic energy (0.66 m2/s2). These conditions promote dynamic airflow, facilitating particulate removal by reducing stagnant zones prone to pollutant buildup. The effect of cooling fans and thermal sources was investigated, showing limited contribution on particle removal. These findings emphasize the importance of digital twins for better worker safety and air quality in 3D printing environments.

Mixing by internal gravity waves in stars: assessing numerical simulations against theory

ABSTRACT Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multidimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localized flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20\, \mathrm{M}_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for time-scales typically considered by 2D numerical simulations.

One- and two-particle microrheology of soft materials based on optical-flow image analysis.

Particle-tracking microrheology probes the rheology of soft materials by accurately tracking an ensemble of embedded colloidal tracer particles. One-particle analysis, which focuses on the trajectory of individual tracers is ideal for homogeneous materials that do not interact with the particles. By contrast, the characterization of heterogeneous, micro-structured materials or those where particles interact directly with the medium requires a two-particle analysis that characterizes correlations between the trajectories of distinct particle pairs. Here, we propose an optical-flow image analysis as an alternative to the tracking-based algorithms to extract one and two-particle microrheology information from video microscopy images acquired using diverse imaging contrast modalities. This technique, termed optical-flow microrheology (OFM), represents a high-throughput, operator-free approach for the characterization of a broad range of soft materials, making microrheology accessible to a wider scientific community.

Density-dependent flow generation in active cytoskeletal fluids

The actomyosin cytoskeleton, a protein assembly comprising actin fibers and the myosin molecular motor, drives various cellular dynamics through contractile force generation at high densities. However, the relationship between the density dependence of the actomyosin cytoskeleton and force-controlled ordered structure remains poorly understood. In this study, we measured contraction-driven flow generation by varying the concentration of cell extracts containing the actomyosin cytoskeleton and associated nucleation factors. We observed continuous actin flow toward the center at a critical actomyosin density in cell-sized droplets. The actin flow exhibited an emergent oscillation in which the tracer advection in the bulk solution periodically changed in a stop-and-go fashion. In the vicinity of the actomyosin density where oscillatory dynamics occur, the velocity of tracer particle motion decreases with actomyosin density but exhibits superdiffusive motion. Furthermore, the increase or decrease in myosin activity causes the oscillatory flow generation to become irregular, indicating that the density-dependent flow generation of actomyosin is driven by an interplay between actin density and myosin force generation.

Impact of Flat-Surfaced Pins on Material Flow and Particle Distribution in Friction Stir Processing: A CEL Method Analysis

Abstract This study investigates the impact of Flat-Surfaced Pin geometry on temperature, strain, particle distribution, and material flow during Friction Stir Processing (FSP) using a Coupled Eulerian-Lagrangian (CEL) formulation. Various models incorporating different pin shapes—cylindrical, square, and hexagonal—were developed for this purpose. To investigate material flow during the FSP, Tracer particles were employed as a methodological tool. A comparison between experimental and numerical results concerning the distribution of reinforcing particles in the base metal reveals a strong correlation, highlighting the model's effectiveness in accurately predicting material flow patterns. The findings indicate that the circular tool was less effective in achieving a uniform distribution of particles, with a significant accumulation observed on the retreating side. In contrast, both square and hexagonal tools demonstrated improved performance regarding particle distribution. Quantitative measurements show that the areas occupied by the reinforcing particles are 14.3 mm² for the circular pin, 34.4 mm² for the square pin, and 37.9 mm² for the hexagonal pin. This variation can be attributed to the design of the pin profiles, as the flat surfaces facilitate a pulsating effect that enhances material flow. Moreover, in samples processed with square and hexagonal pins, particles located near the upper surface of the plate tend to rotate with the pin, subsequently stretching toward the advancing side. Finally, the square and hexagonal tools exhibited higher average hardness values of 68.88 HV and 66.84 HV, respectively, compared to the circular tool, which yielded an average hardness of 57.17 HV.

Temporally resolved concentration profiling via computationally limited, distributed sensor nodes

AbstractAccurate mapping of chemical concentrations in reactor networks remains an obstacle to establish complete systems‐level insight and control. This issue extends beyond traditional reactor design to biological and other inaccessible systems of interest. Recent developments in novel materials with non‐volatile memory allow autonomous sensor nodes to record information with minimal external supervision. Integrating these materials in solution suspended particles demonstrates the unique potential for diffuse measurements of chemical data at the microscale. In this study, we establish a generalized workflow for the simulated deployment of time aware particle sensors (TAPS) in ideal reactor systems to measure analyte profiles, using Gillespie kinetic Monte Carlo algorithms (KMC). Our results show that computationally‐limited, chemically sensitive tracer particles capable of timestamping an analyte detection event can provide accurate analyte profiles throughout multistage reactors in an ensemble fashion.

Using tracer particle kinematics to sense particle size in rotating drums

Comminution is an energy intensive process. In SAG-mills, it is achieved by rotating a drum in which large metal balls crush ore particles. In-situ monitoring of particle size would be of considerable interest to optimize their operation. However, there is no established solution to measure particle size in such a harsh mechanical environment. We show here that the acceleration of the grinding media, which can be monitored using embedded accelerometers, can be used to sense the particle size and size distribution during operation. In DEM simulations, we find that a machine learning classifier is able to detect the size and distribution of small particles solely based on the knowledge of the acceleration of larger grinding media particles. Results show that this kinematic sensing is effective over a wide range of particle size ratios, size distribution, mixture ratio and mill charge. Beyond their potential applications in mineral processing, these results point out that the kinematics of large particles is affected by the size of the smaller particles, an observation which can help advance rheological models for bi-disperse granular flows.Graphical

Modeling and simulation of dielectrophoretic sorting of tenogenically differentiating mesenchymal stem cells for high throughput

Mesenchymal stem cell (MSC)-based regenerative therapies are promising for healing tendon injuries and tears, due to their potential to differentiate into tenogenic cells. However, generating homogeneous populations of tenogenically differentiated stem cells remains a big challenge, as non-differentiated cells can lead to post-transplantation complications. Therefore, a homogenous sample of tenogenically differentiated MSCs is critical for advancing tendon therapies and avoiding uncontrolled cell growth or non-tendon tissue formation (e.g., ectopic bone). This work is focused on designing and simulating a dielectrophoretic (DEP)-based label-free, microfluidic platform to selectively sort and enrich tenogenically differentiated MSCs (tMSCs) from undifferentiated MSCs. Using particle tracing, creeping flow (transport of diluted species model), and electric current physics modules in the COMSOL Multiphysics simulation software package, the sorting was simulated within a two-stage microfluidic device operating at a sinusoidal frequency of 160 kHz. The optimal separation efficiency and purity are achieved at an inlet velocity of 400–1000 μm/s, with specific voltage configurations, enabling recovery of one million tMSCs in ∼3 h. Results demonstrate a near-linear relation between recovery time and particle count at the outlet boundaries and selected surfaces, indicating consistent throughput across varying conditions. This study demonstrates that DEP can offer a scalable, efficient, and label-free method for enriching tMSC populations with high selectivity, enhancing more prospects for MSC-based tendon therapies and advancing the development of microfluidic sorting devices for regenerative medicine applications.

Four-dimensional flow characteristics of air-entrained turbulent impinging waterjet onto quiescent water surface

This paper presents a time-resolved three-dimensional (4D) flow fields measurement of the continuous phase of a turbulent impinging jet inducing foam formation using the Lagrangian particle tracking velocimetry utilizing the Shake-The-Box algorithm. With the systems equipped with four high-speed cameras, time-series of images of fluid tracer particles were acquired. The Vortex-In-Sharp (VIC#) method was used to reconstruct the Eulerian flow fields of the particle tracks. The impinging jet was characterized as plume-like along the vertical direction with two distinct layers: developing shear and fully developed shear. The streamwise vortex structures of the continuous phase were influenced by the bubble plume motion, and the results showed high amplitude oscillations of the acceleration and deceleration near the jet source resulting in the formation of ring-like vortices, which break down as the jet moves downstream with its momentum dissipated. The flow of the continuous phase of impinging jet was self-similar both at the developed shear layer and the fully developed diffusion layer beneath the water pool and is characterized as homogeneous shear flow with anisotropy turbulence. The classical assumption of self-similarity with Gaussian profiles for continuous phase velocity is verified experimentally. We found that the results show a huge potential of blue energy harvesting from the low frequency (∼2 Hz) dissipating kinetic energy of the turbulent plume-like jet underneath the impinging water surface using triboelectric nanogenerator.

Flow analysis of steady state forward flow of aortic valve prostheses using Particle Image Velocimetry

Abstract Transcatheter aortic valve replacement (TAVR) has become the standard therapy for aortic valve stenosis in patients with high surgical risk. Understanding the flow dynamics in TAVR is crucial for its evaluation and optimization. Experimental flow measurement by means of Particle Image Velocimetry (PIV) is increasingly applied alongside numerical analyses. This study introduces a novel test rig concept enabling the determination of velocity fields using Stereo-PIV under steady forward flow conditions through a TAVR during the peak systole matching the ISO 5840-1:2021 requirements. The experimental setup utilized an impeller pump to generate steady forward flow through a silicone aortic root model with implanted TAVR. A Stereo-PIV setup captured velocity fields in both ventricular inflow and aortic outflow regions. Test conditions were based on physiological flow rates determined from pulsatile measurements. Illumination of the added particles in the test fluid was achieved using an Nd:YAG laser. Fluorescent polystyrol particles (size: 50 μm) were used for flow visualization. Results showed characteristic flow patterns: a central jet flow entering the TAVR in the ventricular flow field. A jet flow directed towards the sinus side and a recirculation zone forming on the opposite side of the sinus could be detected in the aortic outflow. The width of the recirculation zone increases with distance from the TAVR. Maximum flow velocities were detected at 0.78 m/s for the ventricular flow field and 0.94 m/s for the aortic flow field. This study provides a comprehensive approach for fluid dynamic analysis of TAVR under steady flow conditions, offering insights into flow mechanics performance crucial for device optimization. Further investigations could enhance the PIV - measurement procedure by increasing both the spatial resolution and the tracer particle density within the acquired images for a comprehensive characterization of TAVR flow dynamics.

Simulation of the charged particle deflection from the sweeping magnet array in the Lunar Environment heliospheric X-ray imager.

The Lunar Environment heliospheric X-ray Imager (LEXI) is an instrument built to image x-rays from solar wind charge exchange in Earth's magnetosheath. Monitoring the position of the magnetopause at the inner boundary of the magnetosheath allows us to understand how magnetic reconnection regulates how energy from the solar wind is deposited into Earth's magnetosphere. LEXI is part of an upcoming lunar lander mission set to land in Mare Crisium. To repel unwanted charged particles, the instrument carries a permanent magnet array composed of 48 neodymium magnets. The array was designed to maximize charged particle deflection while minimizing stray magnetic fields, which could impact other instruments or spacecraft operation. A Runge-Kutta-based fully kinetic particle tracing model was created to evaluate the effectiveness of LEXI's unique charged particle deflector array. Combined with the other particle suppression measures of the instrument, including physical structures and filters, the simulations show proton and electron transmission to the LEXI detector is expected to be sufficiently reduced to allow successful imaging. The flexible simulation model can be generalized to be used in examining the magnetic deflector array effectiveness of other instruments whose signals could be compromised by unwanted charged particle contamination.

Promoting Polarization and Differentiation of Primary Human Salivary Gland Stem/Progenitor Cells in Protease-Degradable Hydrogels via ROCK Inhibition.

Towards the goal of in vitro engineering of functional salivary gland tissues, we cultured primary human salivary stem/progenitor cells (hS/PCs) in hyaluronic acid-based matrices with varying percentages of proteolytically degradable crosslinks in the presence of Rho kinase (ROCK) inhibitor. Single cells encapsulated in the hydrogel grew into organized multicellular structures by day 15, and over 60% of the structures developed in the non-degradable and 50% degradable hydrogels contained a central lumen. Importantly, ROCK inhibition led to the establishment of multicellular structures that were correctly polarized, as evidenced by apical localization of a Golgi marker GM130, apical/lateral localization of tight junction protein zonula occludens-1 (ZO-1), and basal localization of integrin β1 and basement membrane proteins laminin α1 and collagen IV. Cultures maintained in 50% degradable gels with ROCK inhibition exhibited an increased expression of acinar markers AQP5 and SLC12A2 (at the transcript level) and AQP5 and NKCC1 (at the protein level) as compared to those without ROCK inhibition. Upon stimulation with isoproterenol, α-amylase secretion into the lumen was observed. Particle-tracking microrheology was employed to analyze the stiffness of cells using mitochondria as the passive tracer particles. Our results indicated that cells grown in 100% degradable gels were stiffer than those maintained in non-degradable gels, and cells cultured with the ROCK inhibitor were softer than those maintained without the inhibitor. We conclude that reducing cellular contractility via ROCK inhibition while retaining some degree of matrix confinement promotes the establishment of multicellular structures containing pro-acinar cells with correct apicobasal polarization.

Divertor Tokamak Test: Impact of NBI shine-through and beam-plasma interaction on Divertor Tokamak Test facility

IntroductionIn this work, we aim to explore numerically the behavior of beam energetic particles in the Divertor Tokamak Test (DTT), a superconductive device equipped with a Neutral Beam Injection (NBI) system capable of injecting neutrals up to 510 keV.MethodWe explore beam ionization and beam slowing down for different DTT plasma scenarios. Numerical simulations are performed using the ASCOT suite of codes, including a wide-range scan of plasma density and beam injection energy. For different plasma conditions, we estimate shine-through losses, including the heat fluxes on the first wall thanks to dedicated particle tracing simulations. Orbits of newly-born fast ions are characterized by means of the constant of motion phase space, showing how trapped energetic particles’ population and prompt losses change with plasma density and NBI energy.Results and discussionSlowing down simulations show that NBI injection at 510 keV is well coupled to DTT plasmas. DTT NBI will be one of the sources of auxiliary ion heating, with an absorbed power ratio of up to ∼50% depending on plasma and beam parameters. At low plasma densities, energetic particle confinement is less efficient, and NBI power and/or energy reduction is expected.

Hematological Response to Particle Debris Generated During Wear-Corrosion Processes of CoCr Surfaces Modified with Graphene Oxide and Hyaluronic Acid for Joint Prostheses.

Various surface modifications to increase the lifespan of cobalt-chromium (CoCr) joint prostheses are being studied to reduce the wear rate in bone joint applications. One recently proposed modification involves depositing graphene oxide functionalized with hyaluronic acid (a compound present in joints) on CoCr surfaces, which can act as a solid lubricant. This paper analyzes the biological alterations caused by wear-corrosion phenomena that occur in joints, both from the perspective of the worn surface (in vitro model) and the particles generated during the wear processes (in vivo model). The analysis of the inflammatory response of macrophage was performed on CoCr surfaces modified with graphene oxide and functionalized with hyaluronic acid (CoCr-GO-HA), before and after wear-corrosion processes. The wear particles released during the wear-corrosion tests of the CoCr-GO-HA/CoCr ball pair immersed in 3 g/L hyaluronic acid were intra-articularly injected into the experimental animals. The hematological analysis in vivo was made considering a murine model of intra-articular injection into the left knee in male adult Wistar rats, at increasing concentrations of the collected wear particles dispersed in 0.9% NaCl. Non-significant differences in the inflammatory response to unworn CoCr-GO-HA surfaces and control (polystyrene) were obtained. The wear-corrosion of the CoCr-GO-HA disk increased the inflammatory response at both 72 and 96 h of material exposure compared to the unworn CoCr-GO-HA surfaces, although the differences were not statistically significant. The pro-inflammatory response of the macrophages was reduced on the worn surfaces of the CoCr modified and functionalized with graphene oxide (GO) and hyaluronic acid (HA), compared to the worn surfaces of the unmodified CoCr. The hematological analysis and tissue reactions after intra-articular injection did not reveal pathological damage, with average hematological values recorded, although slight reductions in creatinine and protein within non-pathological ranges were found. Some traces of biomaterial particles in the knee at the highest concentration of injected particles were only found but without inflammatory signs. The results show the potential benefits of using graphene in intra-articular prostheses, which could improve the quality of life for numerous patients.

Sensitivity of wavelet-based optical flow velocimetry (wOFV) to common experimental error sources

Abstract The influence of several potential error sources and non-ideal experimental effects on the accuracy of a wavelet-based optical flow velocimetry (wOFV) method when applied to tracer particle images is evaluated using data from a series of synthetic flows. Out-of-plane particle displacements, severe image noise, laser sheet thickness reduction, and image intensity non-uniformity are shown to decrease the accuracy of wOFV in a similar manner to correlation-based particle image velocimetry (PIV). For the error sources tested, wOFV displays a similar or slightly increased sensitivity compared to PIV, but the wOFV results are still more accurate than PIV when the magnitude of the non-ideal effects remain within expected experimental bounds. For the majority of test cases, the results are significantly improved by using image pre-processing filters and the magnitude of improvement is consistent between wOFV and PIV. Flow divergence does not appear to have an appreciable effect on the accuracy of wOFV velocity estimation, even though the underlying fluid transport equation on which wOFV is based implicitly assumes that the motion is divergence-free. This is a significant finding for the broader applicability of planar velocimetry measurements using wOFV. Finally, it is noted that the accuracy of wOFV is not reduced notably in regions of the image between tracer particles, as long as the overall seeding density is not too sparse i.e. below 0.02 particles per pixel. This explicitly demonstrates that wOFV (when applied to particle images) yields an accurate whole field measurement, and not only at or adjacent to the discrete particle locations.

A novel 3D uniformity measurement method in mechanical stirring systems

AbstractAccurate assessment of mixing uniformity is crucial in industrial mixing processes. This study proposes an evaluation method for three‐dimensional (3D) mixing processes that combines dual‐camera positioning and point pattern density fluctuation (PD) based on disordered hyperuniformity. This study employs a positioning method using dual‐camera to achieve precise capture and reconstruction of tracer particles in 3D space. The 3D reconstruction data is then evaluated for mixing performance using the PD method. A relationship model between |k| and time I values with mixing time was established for λ = 1. The results indicate that mixing time decreases with the increase of |k| and decreases with the decrease of I values. To ensure the accuracy of the PD method, feasibility analysis was conducted using conductometry. Additionally, the superiority of the PD method was validated by comparing it with the 3D‐Q method. The impact of bottom height of stirring paddle and motor speed on mixing effect were also investigated. This study establishes a fundamental groundwork and theoretical framework for optimizing parameters of stirring systems and assessing 3D mixing uniformity. It also offers important references and insights for engineering practices and theoretical research in related fields.