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Articles 31 - 60 of 366

Full-Text Articles in Mechanical Engineering

Advancing Multi-Physics Modeling For Microwave Heating: Application In Micro-Reactor Design And Optimization, Raghav Adhikari Aug 2025

Advancing Multi-Physics Modeling For Microwave Heating: Application In Micro-Reactor Design And Optimization, Raghav Adhikari

All Theses

Microreactors are a type of small-scale chemical reactors for achieving reduced volume, improved product selectivity and higher reaction rate. It allows precise temperature control, which is crucial for sensitive chemical processes. Microreactors can be employed as key components of conducting small-scale reactions with improved reactor configuration and process efficiency. It is important to identify a localized and precise heating mechanism to trigger and control the corresponding chemical reactions.

In fact, microwave heating has gathered significant attention in recent years due to its ability to deliver efficient, rapid, and localized heating, which can accelerate reaction rates and enhances the reaction selectivity. …


Advancing Life Cycle Assessment For Environmental Sustainability Of Carbon Fiber-Reinforced Polymer Composites (Cfrps)), Hao Chen Aug 2025

Advancing Life Cycle Assessment For Environmental Sustainability Of Carbon Fiber-Reinforced Polymer Composites (Cfrps)), Hao Chen

All Dissertations

Carbon fiber-reinforced polymer composites (CFRPs) have emerged as promising materials, particularly for lightweight applications, with the potential to reduce environmental impacts across multiple sectors, including automotive, aerospace, and renewable energy. However, fully realizing their sustainability potential requires a more comprehensive and context-specific understanding of their environmental performance throughout the entire life cycle—from raw material production to end-of-life management.

This dissertation advances life cycle assessment (LCA) practices for CFRPs by addressing key challenges across multiple phases of the CFRP life cycle. First, I conducted a critical review and meta-analysis of carbon fiber manufacturing, revealing substantial variability in reported data on energy …


Application Of Polymer Nanocomposites In The Design Of Prosthetic Sockets That Feature Auxetic Meta-Structures, Sumit Suryakant Kolte, Vinayak Vijayan, Lihua Lou Jul 2025

Application Of Polymer Nanocomposites In The Design Of Prosthetic Sockets That Feature Auxetic Meta-Structures, Sumit Suryakant Kolte, Vinayak Vijayan, Lihua Lou

Publications

This research evaluates the response of prosthetic sockets constructed using polymer nanocomposites and incorporating auxetic meta-structures. The prosthetic sockets feature lightweight meta-structures between the inner and outer walls of the socket. Three different prosthetic designs featuring chiral, reentrant hexagon, and honeycomb meta-structures are evaluated in this study. The prosthetic sockets were designed in SolidWorks and compared using finite element analysis. The polymer nanocomposites used in this study include polypropylene and ultra-high molecular weight polyethylene containing uniformly distributed inclusions of either titanium dioxide, zinc oxide, or graphene nanoplatelets. Our results show a favorable pressure profile at the interface between the prosthetic …


Collecting Human Subject Data For Modeling Maximum Potential Power At Specific Cadence And Fatigue Levels, Alexander John Minnich May 2025

Collecting Human Subject Data For Modeling Maximum Potential Power At Specific Cadence And Fatigue Levels, Alexander John Minnich

Honors College Theses

The overarching goal of this research project was to investigate the relationship between a participant's maximum power (Watts) at a given cadence (RPM) on a specific fatigue level. Before conducting any experiments, we hypothesized that maximum power and cadence would decay linearly with fatigue. To do this, six days of testing for each of 4 human subjects were split across two phases. The first 4 days were devoted to Phase one, which focuses on determining the physical abilities of each unique participant and finding metabolic constants such as Critical Power and Anaerobic Work Capacity. Phase two then tests maximal power …


Cloud-Native Mucad For Design Reviews, Emily C. Petty May 2025

Cloud-Native Mucad For Design Reviews, Emily C. Petty

All Theses

This research explores the potential of a cloud-native multi-user computer-aided design (MUCAD) system to improve communication and efficiency during engineering design reviews and shorten the design timeline for military tools. First, a literature review is used to generate a list of thirty-five collaboration-oriented requirements that aim to ensure concurrency, annotations, heterogeneity, security, IP protection, version control, and viewing within a MUCAD system. A comparative evaluation of existing collaborative CAD system architectures, including cloud-native, cloud-enabled, and a single-user system with external file sharing, is conducted to determine how well each system architecture fulfills the generated collaboration-oriented requirements. Following this, a survey …


Tradespace Exploration With Statistical Modeling Techniques And Immersive Visual Representation In Virtual Environments, Nikhil Raj May 2025

Tradespace Exploration With Statistical Modeling Techniques And Immersive Visual Representation In Virtual Environments, Nikhil Raj

All Theses

Statistical modeling techniques combined with virtual reality (VR) visualization offer powerful new approaches to tradespace exploration in engineering design. The research presented addresses the challenge of analyzing and communicating insights from complex multidimensional datasets, particularly for autonomous ground vehicle systems.

Beginning with a review of statistical methods—including Principal Component Analysis (PCA), Analysis of Variance (ANOVA), and correlation analysis—the study examines their applications in tradespace exploration. Building on this foundation, three distinct visualization pathways connecting MATLAB data to virtual environments are developed and evaluated: VRML representation, STL conversion, and Blender integration. Each approach is assessed for its ability to maintain data …


Investigation Of Plm Utilities And Concepts In Engineering Curriculum: Challenges And Opportunities, Frederick Rowell May 2025

Investigation Of Plm Utilities And Concepts In Engineering Curriculum: Challenges And Opportunities, Frederick Rowell

All Theses

The implementation of Product Lifecycle Management (PLM) tools and concepts in engineering education has gained increasing significance as manufacturing and engineering industry shifts towards digital engineering workflows to enhance collaboration, efficiency, and innovation. Despite its typical application in engineering industries, many mechanical engineering programs have not integrated PLM software into their curriculums. The Product Lifecycle Management Center (PLMC) at Clemson University offers PLM workshops and research opportunities to students. Despite these initiatives, PLM education remains largely extracurricular and is not fully incorporated into required coursework within the mechanical engineering curriculum. The objective of this thesis is to explore the role …


Ultrafast Laser Surface Structuring For Wettability Control On Copper, Akshay Arvind Nagvenkar May 2025

Ultrafast Laser Surface Structuring For Wettability Control On Copper, Akshay Arvind Nagvenkar

All Theses

Wettability is a crucial surface property influencing various phenomena, including heat transfer, cell adhesion, and corrosion. Engineering devices can achieve superior performance by precisely manipulating surface wettability. As a result, extensive research has focused on developing surfaces that exhibit either extreme water attraction (superhydrophilic) or strong water repellency (superhydrophobic). Tailoring surface wettability paves the way for numerous applications, such as drag reduction in marine vessels, controlled drug delivery, efficient water collection, advanced liquid transport systems, oil-water separation, anti-corrosion coatings, friction reduction, and self-cleaning materials. Ultrafast laser surface structuring is a promising approach for engineering multifunctional surfaces, effectively modifying material properties …


Tsunamigenesis On A Buoyant Granular Layer As A Model Of Ice Mélange In Ice-Choked Fjords, Nathan F. Reyner May 2025

Tsunamigenesis On A Buoyant Granular Layer As A Model Of Ice Mélange In Ice-Choked Fjords, Nathan F. Reyner

All Theses

Glacial calving events can often create destructive tsunami waves in ice-choked fjords in the arctic region, posing a threat to local inhabitants and damaging coastlines. Here the sea is covered by a polydisperse granular material called ice mélange, whose properties can affect the wave characteristics. To investigate the role of a buoyant granular layer, as a model of ice mélange, on tsunami generation, or tsunamigenesis, a series of laboratory experiments were conducted by collapsing a column of dense granular material into a body of water with a layer of buoyant particles distributed across the liquid surface. Experiments were performed over …


Deciphering And Translating Bioinspired Structures For Engineering Materials Design Via Computational Modeling And Machine Learning, Zhangke Yang May 2025

Deciphering And Translating Bioinspired Structures For Engineering Materials Design Via Computational Modeling And Machine Learning, Zhangke Yang

All Dissertations

Nature has evolved extraordinary structural materials—such as nacre, bone, and the mantis shrimp’s dactyl club—that achieve remarkable combinations of strength, toughness, and impact resistance. These properties arise from sophisticated synergies between structure and composition. Inspired by these biological systems, this dissertation presents a comprehensive investigation into bioinspired materials, uncovering fundamental mechanisms and providing guidance on designing materials with superior mechanical properties.

This dissertation begins by examining the "brick-and-mortar" structure of nacre, which informs the design of layered polymer-graphene nanocomposite films. Using coarse-grained molecular dynamics simulations, I elucidate mechanisms of dynamic wave propagation and energy dissipation in these systems, providing critical …


Reinforcement Learning For High-Dimensional Tradespace Exploration In Multi-Objective Optimization, Aaditya Kothavade May 2025

Reinforcement Learning For High-Dimensional Tradespace Exploration In Multi-Objective Optimization, Aaditya Kothavade

All Theses

Engineering design optimization often requires balancing multiple competing objectives while navigating complex, high-dimensional tradespaces. Despite significant advances in tradespace exploration techniques, current methods face critical challenges in efficiently navigating high-dimensional design spaces. As the number of design variables and competing objectives increases, traditional multi-criteria decision-making and optimization methods struggle to explore the vast solution space comprehensively. The curse of dimensionality exacerbates this issue, making it impractical to analyze all possible solutions and effectively identify trade-offs between objectives. Additionally, the computational complexity of high-dimensional spaces further complicates optimization, making exhaustive solution analysis infeasible. Traditional multi-objective optimization methods rely on static Pareto-front …


Stability Of Holes In Granular Raft, Plabon Kumar Saha May 2025

Stability Of Holes In Granular Raft, Plabon Kumar Saha

All Theses

A granular raft at an oil–water interface exhibits unique mechanical properties, including the ability to form and sustain stable holes. In this study, we experimentally investigate the formation, stability, and collapse dynamics of holes in particle rafts composed of micrometer-sized particles. Holes are created using a hollow cylinder, which generates a meniscus that inhibits particle motion, thus stabilizing the hole. Stable holes are formed when their size reaches a critical value, which depends upon the capillary length. The critical hole size does not depend upon the circularity of the hole. We show that capillary forces due to the presence of …


Micro Wind Turbine - Modelling And Testing, Mohammad Uzair Bhati May 2025

Micro Wind Turbine - Modelling And Testing, Mohammad Uzair Bhati

All Theses

The global energy demand continues to rise as people consume more electricity to power their personal electronics, electric vehicles, and consumer products such as outdoor tools. To generate renewable energy, large scale solar and wind farms continue to receive the most commercial attention. However, portable wind energy turbines have the potential to generate sufficient power for cell phones and other electronic devices. There are two types of wind turbines, horizontal and vertical axis each having their pros and cons. Vertical-axis wind turbines are the main focus of this thesis, with a reduction in their form factor or size and portable …


An Experimental And Computational Study Of High-Temperature Creep Behavior In Fully Lamellar Titanium Aluminide Alloys, Karel M. Ziminsky May 2025

An Experimental And Computational Study Of High-Temperature Creep Behavior In Fully Lamellar Titanium Aluminide Alloys, Karel M. Ziminsky

All Theses

Titanium aluminide alloys have seen increased aerospace applications in recent years, especially in aircraft jet engines. They can offer benefits such as improved high-temperature strength compared to titanium alloys and reduced density compared to nickel alloys. These alloys also can exhibit high creep resistance due to their fully lamellar microstructure. These mechanical properties are desirable for components like turbine blades, where tight tolerances must be maintained for optimal performance. This research examines the high-temperature creep behavior of a fully lamellar two-phase titanium aluminide alloy, TNM® (Ti-43.5Al-4Nb-1Mo-0.1B), through experimental and computational methods. Scanning electron microscopy studies reveal the presence of large …


Developing Reduced Order Models For Gas Bubble Formation In Irradiated Metals Using Integrated Phase Field Modeling And Koopman Operator Theory, John M. Eggemeyer V May 2025

Developing Reduced Order Models For Gas Bubble Formation In Irradiated Metals Using Integrated Phase Field Modeling And Koopman Operator Theory, John M. Eggemeyer V

All Theses

Irradiation damage in materials is prevalent in nuclear components, posing significant risks in the safety and reliability of nuclear reactors. Phase field models offer a versatile framework for modeling irradiation damage in materials at mesoscales. Such high fidelity method has been used to model the formation of fission gas bubbles superlattice, a microstructure array occurs at certain irradiation conditions (dose, dose-rate, and temperature). To overcome the high computational cost of phase field modeling, Koopman operator theory is applied to create reduced order models, allowing for instantaneous simulations of fission gas bubble behaviors. These low fidelity models are integrated into machine …


Defining Fidelity For Tradespace Application, Aditya Agrawal May 2025

Defining Fidelity For Tradespace Application, Aditya Agrawal

All Theses

This research proposes a definition of tradespace fidelity and presents a study on its effectiveness in the tradespace. Tradespace exploration helps evaluate various design options, allowing engineers to make informed decisions in early design stages. Fidelity generally refers to how closely a model approximates reality. However, the definition of fidelity has been inconsistently defined and interpreted in various contexts concerning particular problems. In some cases, it is a measure of accuracy; in others, information; in another, uncertainty; and in others, computational complexity. Fidelity is poorly and inconsistently defined in the literature. In general, higher fidelity models tend to be more …


Mechanistic Insights Into Polymer-Assisted Graphene Exfoliation: The Roles Of Velocity, Adhesion, Cohesion, Temperature, Peeling Mode, And Edge Defect Via Coarse-Grained Molecular Dynamics, Linjiale Dai May 2025

Mechanistic Insights Into Polymer-Assisted Graphene Exfoliation: The Roles Of Velocity, Adhesion, Cohesion, Temperature, Peeling Mode, And Edge Defect Via Coarse-Grained Molecular Dynamics, Linjiale Dai

All Theses

Graphene exfoliation is a critical step in the fabrication of high-quality graphene

layers. However, the underlying fracture mechanisms remain poorly understood. In this

work, I employed coarse-grained (CG) molecular dynamics (MD) simulations to

investigate how factors such as interfacial binding energy, substrate cohesion, temperature,

peeling mode, and edge defects influence the outcome of the exfoliation process. To model

polymer-assisted mechanical exfoliation, I used a finite-size system in which multilayer

graphene (MLG) is sandwiched between two thin polymer films. Leveraging the

spatiotemporal efficiency of the CG model, I performed fifty simulation iterations per

parameter set and analyzed the results from a …


Foundational Robotics, Akshit Lunia, Ananya Nagabhushana Rao, Yue Wang Jan 2025

Foundational Robotics, Akshit Lunia, Ananya Nagabhushana Rao, Yue Wang

Robotics

This textbook is a product of Co-DREAM OER (Collaborative Development of Robotics, Mechatronics, and Advanced Manufacturing Open Educational Resources), a US Department of Education-funded initiative to develop Open Educational Resource textbooks on robotics, mechatronics, and advanced manufacturing processes. It has been created by a diverse team of scholars and graduate students from across the country and is intended for higher-level robotics courses offered by 4-year undergraduate programs.


Investigating Challenges Of Converting Cad Models To Game Ready Assets, Vathsa Pawar Dec 2024

Investigating Challenges Of Converting Cad Models To Game Ready Assets, Vathsa Pawar

All Theses

This thesis explores the challenges associated with converting detailed CAD models into game-ready assets optimized for use in virtual reality (VR) environments using game engines, focusing on enhancing using mechanical engineering models. The primary goal is to establish a toolchain that allows the integration of CAD models into game engines for immersive applications, enabling engineers and stakeholders to interact with 3D models in a synthetic environment. The study employs several test cases ranging from simple door models to complex automotive vehicle prototypes, elaborating the process of exporting CAD models through intermediate formats (such as STEP, STL, GLB) using tools like …


Influence Of Hygrothermal Conditions Of The Bistability Of Asymmetric Carbon Fiber Laminate Composites, Celia Hill Dec 2024

Influence Of Hygrothermal Conditions Of The Bistability Of Asymmetric Carbon Fiber Laminate Composites, Celia Hill

All Theses

Carbon fiber-reinforced polymer (CFRP) laminates have widespread use in many industries because of their exceptional strength-to-weight ratio. Carbon fiber laminates following an asymmetric layup orientation can exhibit bistability meaning the laminate can exist at two stable geometric configurations. The morphing characteristics of bistable CRFP has a growing level of interest because of its potential in various applications including space aircraft structures for easy repair, automotive structures for energy dissipation and ergonomics, robotics for flexible motion and energy harvesting. Existing research shows that both moisture and temperature affect the material properties and behavior of CFRP laminates, however, the influence of moisture …


Deformation Mechanism In Gold Nanoparticles Under Compressive Loading: Insights From Atomistic Modelling And Unsupervised Machine Learning, Tanuj Gupta Dec 2024

Deformation Mechanism In Gold Nanoparticles Under Compressive Loading: Insights From Atomistic Modelling And Unsupervised Machine Learning, Tanuj Gupta

All Dissertations

Gold nanoparticles (AuNPs) offer exciting possibilities due to their inertness, malleability, and tunable structures, making them valuable for applications ranging from nanomedicine to electronics. Their optical, mechanical, and other properties can be tailored by modifying shape and structure, underscoring the importance of understanding their deformation behaviour at the nanoscale. This study used classical molecular dynamics simulations with LAMMPS to investigate the deformation mechanisms of gold nanospheres (AuNS) under uniaxial compression. Employing the embedded atom method (EAM) potential to model atomic interactions, AuNS with 20 nm in diameter were compressed along the z-direction using planar indenters moving at a constant …


Neural Operator And Physics-Informed Deep Learning Approaches For Inverse Design Of Composites And Manufacturing Processes, Minglei Lu Dec 2024

Neural Operator And Physics-Informed Deep Learning Approaches For Inverse Design Of Composites And Manufacturing Processes, Minglei Lu

All Dissertations

In this dissertation, artificial intelligence (AI) models are designed and used to accelerate inverse design of composites and manufacturing processes. The critical bottlenecks in machine learning (ML) including data availability, data quality, model generalization and adaptation, interpretability, physical consistency, and the ’black box’ nature of models for the inverse design are addressed. And the proposed AI models are tested under different engineering scenarios. Firstly, a fast deep neural operator (DNO) structure was developed to significantly reduce training time. This model was tested in the context of additive manufacturing, a transformative industrial technology that allows for the creation of materials with …


Prediction Of Dislocation Density During Casting Of 316 Stainless Steel Based Alloys As A Function Of Chromium And Nickel Composition, Abhishek Chitradurga Ranganath Dec 2024

Prediction Of Dislocation Density During Casting Of 316 Stainless Steel Based Alloys As A Function Of Chromium And Nickel Composition, Abhishek Chitradurga Ranganath

All Theses

By the 1990s, computational methods were beginning to be used to study dislocation density in mental casting. Prior to that time research was based heavily on laboratory studies. This move was encouraged by the need to overcome limitations that experimental approaches had, including high costs and time-consuming processes, and needs of researchers to understand atomic-scale phenomena. Computational techniques allow complex materials to be simulated in cost effective way and can provide insight into behaviour that could never be determined through experimental methods alone.

This work utilized molecular dynamics (MD) simulations along with machine learning approaches to examine the dislocation density …


Magnetic Nano And Micro Rods As Tools For Characterizing Materials Mechanical Properties: Fundamentals And Applications, Artis Brasovs Dec 2024

Magnetic Nano And Micro Rods As Tools For Characterizing Materials Mechanical Properties: Fundamentals And Applications, Artis Brasovs

All Dissertations

The focus of this dissertation is insect blood (Hemolymph). Hemolymph is analyzed by taking a materials science approach. Rheological characterization of hemolymph has been performed for the first time. Owing to a minute amount of available material, a new protocol was established where Magnetic Rotational Spectroscopy (MRS) with ferromagnetic nanorods was employed. The challenge was examining the microliter droplets' viscosity in less than a few minutes. This challenge was successfully resolved.

Blood is critical for the insect's survival: after wounding, the insect has to seal the wound quickly, in a few minutes. As the mechanism of fast clotting has never …


An Efficient Computational Frameworks For Design And Analysis Of Metamaterials, Raj Pradip Khawale Dec 2024

An Efficient Computational Frameworks For Design And Analysis Of Metamaterials, Raj Pradip Khawale

All Dissertations

Advancement in additive manufacturing helps in building artificial lattice structures with unique properties that are not available in naturally occurring materials or in continuum structures. Specifically, beam-based lattices are well known for producing lightweight structures with very high strength, auxetic behavior, and energy absorption capabilities. In recent years, numerous research studies have been conducted on generating algorithms and frameworks to obtain unusual properties based on the variation in the cell geometry and material properties. However, the exploration of the full design space is hampered in practice primarily due to restrictions on cell tiling variation. Additionally, the lattices are very intricate, …


Convex Approach To Data-Driven Optimal Control With Safety Constraints Using Linear Transfer Operator, Joseph Raphel Moyalan Aug 2024

Convex Approach To Data-Driven Optimal Control With Safety Constraints Using Linear Transfer Operator, Joseph Raphel Moyalan

All Dissertations

This thesis is concerned with the data-driven solution to the optimal control problem with safety constraints for a class of control-affine nonlinear systems. Designing optimal control satisfying safety constraints is a problem of interest in various applications, including robotics, power systems, transportation networks, and manufacturing. This problem is known to be non-convex. One of this thesis's main contributions is providing a convex formulation to this non-convex problem. The second main contribution is providing a data-driven framework for solving the control problem with safety constraints. The linear operator theoretic framework involving Perron-Frobenius and Koopman operators provides the convex formulation and associated …


Understanding The Microstructure And Tribological Performance Of Cocrfeni-Based High Entropy Alloys, Ali Azarmi Aug 2024

Understanding The Microstructure And Tribological Performance Of Cocrfeni-Based High Entropy Alloys, Ali Azarmi

All Theses

Due to their higher wear resistance compared to conventional alloys, high entropy alloys (HEAs) are now being considered as candidates for parts undergoing sliding contact during their lifetimes. While the engineering field has built some knowledge related to the performance of selected high entropy alloys, such as the CoCrFeNi alloy, more research is needed to determine if (how) expansions from four to five principal alloying elements alter the performance compared to the initial alloy. In this study, we started this research effort by investigating the relative performance of CoCrFeNiMn and CoCrFeNiTi with respect to CoCrFeNi. The two primary alloying elements …


Predicting The Ductility Of Tungsten Based Bcc Refractory High Entropy Alloys: A Computational Science Driven Study, Akshay Korpe Aug 2024

Predicting The Ductility Of Tungsten Based Bcc Refractory High Entropy Alloys: A Computational Science Driven Study, Akshay Korpe

All Theses

Bcc refractory high entropy alloys (HEAs) are a relatively new category of metallic alloys that promise excellent irradiation resistance and strength retention at high temperatures but exhibit brittle behavior at room temperatures limiting their formability. Understanding the deformation mechanisms and predicting their ductility at room temperature is a topic of interest in contemporary research.

In this work, multiple independent ductility criteria for quantifying the ductility of these HEAs were studied, calculated and compared using Density Functional Theory (DFT) calculations and continuum mechanics frameworks. These ductility parameters were calculated for various W-Ta-Cr-V alloys and the trends were analyzed for each criteria …


Developing An Assessment Tool For Ideation Effectiveness: A Survey-Based Approach For The Shah’S Method Of Design Space Exploration, Venkat Jaya Deep Jakka Aug 2024

Developing An Assessment Tool For Ideation Effectiveness: A Survey-Based Approach For The Shah’S Method Of Design Space Exploration, Venkat Jaya Deep Jakka

All Theses

The research is focused on creativity in engineering design. The goal is to understand if creativity in engineering design can be assessed using a less resource-intensive approach, specifically a survey, compared to design exercises. The survey builds on the metrics established by Shah and colleagues. The four metrics are Novelty, Quality, Variety and Quantity. The metrics are measured with the help of a design activity that is deployed to the participants. These metrics have been used in comparative analysis to assess treatments such as new design methods and personality types. However, the downside of the metrics is that they require …


Fundamental Study Of Nonlinear Electrophoresis, Joseph Armakan Bentor Aug 2024

Fundamental Study Of Nonlinear Electrophoresis, Joseph Armakan Bentor

All Dissertations

Classical electrophoretic theory describes the linear response of particles suspended in Newtonian fluids under weak electric fields. When the electric field exceeds this weak limit, a nonlinear response arises due to non-uniform surface conduction over the curved particles. This nonlinear behavior introduces dependencies on fluid and particle properties not considered in the classical theory, offering potential advantages for microfluidic particle manipulation. While this phenomenon has been extensively studied theoretically and numerically in Newtonian fluids, experimental investigations have been relatively limited.

Fluid rheology can significantly alter particle dynamics under applied electric fields. Rheological properties like shear-thinning and elasticity which are not …