Range Of Length Scales Research Articles

The stochastic response of fatigue crack growth in scaled components

In fatigue testing the number of cycles and crack length to failure are recognised to be stochastic quantities necessitating repetitive testing to draw out statistically meaningful measures. The origin of this phenomena is uncertainty in the detailed microstructure, where (from a microstructural perspective) there exists no two identical test pieces. The situation is further compounded under scaled testing of polycrystalline specimens due to a form of coarsening with scaled samples containing less grains than the full-size test piece with samples drawn from the same material stock. Although microstructural uncertainly impedes predictability, implying the need for a probabilistic framework, it is nonetheless important to capture deterministic aspects that feature in any stochastic model. The theory advanced in this paper builds on the finite similitude scaling theory and the two-experiment first-order rule that features length as an invariant. Length invariance is shown to be critically important for fatigue as it caters for the many aspects of the microstructure that are not scaled under scaled testing. A diffusional stochastic model is introduced in the paper that is constrained by the first-order finite similitude rule. The approach is shown to enforce necessary determinism despite the uncertainties present and unlike many of the rules that are currently applied in fatigue analysis, it is applicable over a large range of length scales. Popular growth laws for long cracks are examined under the new framework, which transpires to be remarkably straightforward to apply.

A structural investigation on the interactions of cotton fabric cellulose with olive oil and water

The cotton fabric consists of cellulose arranged in a complex structure with multiple levels of organization at different length scales. Understanding this structure and its interactions with water and oil is essential for developing efficient and environmentally friendly methods of cotton washing. In this study, the structure of raw cotton fabric cellulose and the effects of water and oil were examined across a broad range of length scales using spatially resolved synchrotron small-angle X-ray scattering (SAXS) and auxiliary techniques.Water was observed to penetrate the cotton fabric and interact across nearly all length scales. Although a certain amount of the material was not affected by water as seen by intact distance between microfibrils, fractal analysis of the scattering data indicated a loosening of the microfibril arrangement after contact with water. This process was hindered if the material had been pre-treated with oil and was not seen after subsequent washing with water or surfactant solution. Analyzing spatially resolved SAXS data using a bi-sinusoidal model and 2D maps of the oil-to-cotton ratio facilitates understanding the structure of the material and its interactions with oil on the molecular, nano and macrolevels.

A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing

In recent years, Runge-Kutta Discontinuous Galerkin (RKDG) methods have gained substantial attention in solving hyperbolic conservation laws, attributed to their high-order accuracy and adaptability to unstructured meshes. However, standard RKDG methods cannot capture discontinuities without oscillation unless they are supplemented with troubled cell indicators and limiters. Existing indicators, such as the total variation bounded (TVB) minmod indicator and the KXRCF indicator, typically depend on a critical parameter tied to the equation's solution, necessitating tuning for different cases. In terms of limiters, the popular limiters even fail to guarantee the high-order property in the smooth regions. The advent of Weighted Essentially Non-Oscillatory (WENO) schemes prompts the implementation of WENO limiters for RKDG methods, preserving high-order properties. However, WENO-family schemes exhibit significant numerical dissipation, potentially smearing small-scale flow structures. In this work, the Targeted Essentially Non-Oscillatory (TENO) indicator [1] is utilized, which leverages the nonlinear weighting strategy of the TENO scheme to separate high-wavenumber physical fluctuations and genuine discontinuities from smooth regions with a unified set of parameters. For troubled cells, a novel limiter is proposed for structured meshes, which combines a TENO scheme for resolving high-wavenumber physical fluctuations and a novel non-polynomial Tangent of Hyperbola for the INterface Capturing (THINC) scheme for resolving genuine discontinuities with extremely low numerical dissipation. Furthermore, the shifting between the TENO and THINC schemes is based on a new boundary variation diminishing (BVD) strategy, which only relies on compact neighborhoods and is significantly simpler than its predecessors. Meanwhile, a new strategy is proposed to ensure the consistency of the new limiter applied for 1D and 2D cases. A set of 1D and 2D benchmark cases including strong shockwaves and a broad range of flow length scales is simulated with uniform meshes for 1D cases and structured quadrilateral meshes for 2D cases to demonstrate the performance of the new numerical scheme. The indicator does not activate any limiters in the accuracy test cases to ensure the high-order property of the whole numerical scheme. Other cases with discontinuities demonstrate the low-dissipation properties of the new limiter in comparison to the simple WENO limiter.

Towards a universal analytical model for Population III star formation: interplay between feedback and fragmentation

ABSTRACT JWST has brought us new insights into Cosmic Dawn with tentative detection of the unique signatures of metal-free Population III (Pop III) stars, such as strong He II emission, extremely blue ultraviolet spectrum, and enhanced nitrogen abundance. Self-consistent theoretical predictions of the formation rates, sites, and masses of Pop III stars are crucial for interpreting the observations, but are challenging due to complex physical processes operating over the large range of length-scales involved. One solution is to combine analytical models for the small-scale star formation process with cosmological simulations that capture the large-scale physics such as structure formation, radiation backgrounds, and baryon-dark matter streaming motion that regulate the conditions of Pop III star formation. We build an analytical model to predict the final masses of Pop III stars/clusters from the properties of star-forming clouds, based on the key results of small-scale star formation simulations and stellar evolution models. Our model for the first time considers the interplay between feedback and fragmentation and covers different modes of Pop III star formation ranging from ordinary small ($\sim\!{10{-}2000}\ \rm M_\odot$) clusters in molecular-cooling clouds to massive ($\gtrsim\!{10^{4}}\ \rm M_\odot$) clusters containing supermassive ($\sim\!{10^{4}{-}3}\times 10^{5}\ \rm M_\odot$) stars under violent collapse of atomic-cooling clouds with large gas accretion rates of $\gtrsim\!{0.1}\ \rm M_\odot \ yr^{-1}$. As an example, the model is applied to the Pop III star-forming clouds in the progenitors of typical haloes hosting high-z luminous quasars ($M_{\rm h}\sim 10^{12}\ \rm M_\odot$ at $z\sim 6$), which shows that formation of Pop III massive clusters is common ($\sim\!{20{-}70}{{\ \rm per\ cent}}$) in such biased ($\sim\!{4}\sigma$) regions, and the resulting heavy black hole seeds from supermassive stars can account for a significant fraction of observed luminous ($\gtrsim\!{10^{46}}\ \rm erg\ s^{-1}$) quasars at $z\sim 6$.

Thermal and Mechanical Mechanisms of Polymer Wear at the Nanoscale.

Wear is a ubiquitous phenomenon that limits the life of many engineered components with sliding interfaces through the gradual removal of material. The wear of polymers is crucial in many applications, ranging from bearings to orthopedic implants to nanolithography processes. The wear rate of polymers is strongly affected by the stress and temperature at the interface. The effects of temperature and stress are often described empirically since the wear process involves complex interactions between multiple asperities on rough surfaces over a range of length scales. Nanoscale tribology experiments at the single-asperity level have provided new insights into the underlying mechanisms of wear. Experiments on hard covalently bonded materials, including silicon and diamond, have demonstrated that wear is an atomic attrition wear process that can be modeled using stress-assisted transition state theory. Here, we examine the wear of a common polymer, polymethylmethacrylate (PMMA), at the nanoscale as a function of stress and temperature and show that the polymer wear is controlled by a combination of atomic attrition and viscoelastic relaxation. While the wear experiments are conducted at the nanoscale via atomic force microscopy, the results show that accounting for the local stress distribution at the contact interface is critical to understanding the wear behavior, an effect that was not considered in earlier studies on hard materials. Using a model that accounts for the stress distribution, we demonstrate the ability to predict the wear volume within 8%.

Bio-Informed Porous Mineral-Based Composites.

Certain biominerals, such as sea sponges and echinoderm skeletons, display a fascinating combination of mechanical properties and adaptability due to the well-defined structures spanning various length scales. These materials often possess high density normalized mechanical properties because they contain well-defined pores. The density-normalized mechanical properties of synthetic minerals are often inferior because the pores are stochastically distributed, resulting in an inhomogeneous stress distribution. The mechanical properties of synthetic materials are limited by the degree of structural and compositional control currently available fabrication methods offer. In the first part of this review, examples of structural elements nature uses to impart exceptional density normalized Young's moduli to its porous biominerals are showcased. The second part highlights recent advancements in the fabrication of bio-informed mineral-based composites possessing pores with diameters that span a wide range of length scales. The influence of the processing of mineral-based composites on their structures and mechanical properties is summarized. Thereby, it is aimed at encouraging further research directed to the sustainable, energy-efficient fabrication of synthetic lightweight yet stiff mineral-based composites.

Multiscale simulation of spray and mixture formation for a coaxial atomizer

Coaxial atomization is an established atomization strategy for many stationary combustion systems. While modeling spray formation in coaxial atomization is challenging due to the existence of a wide range of length and time scales, typical models introduce a substantial uncertainty for Euler–Lagrange simulations of the actual application, e.g., a spray flame. To reduce uncertainties, a recently proposed multiscale approach is adopted for simulations of realistic applications in this work. The multiscale approach uses three one-way coupled simulation domainss that cover the internal nozzle flow, the interfacial flow of the near-field, and the dispersed flow of the far-field. The capabilities of the approach are explored by applying it to a standardized non-reacting experiment from the flame spray pyrolysis research community. In order to assess the relevance for application simulations, results are discussed in the context of mixture formation. The results are compared against shadowgraphy images of the near-field and measured droplet statistics in the far-field. It is found that the multiscale approach is capable of providing similarly accurate droplet statistics as experiments or models derived from them. In addition, it is found that the breakup dynamics in the near-field introduce substantial mixture fraction fluctuations. These fluctuations are only included because of the deterministic coupling of the multiscale approach and are typically neglected in conventional approaches.

Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability in high-curvature regions are inefficient elsewhere. To address this we present a delayed rejection (DR) variant: if an initial HMC trajectory is rejected, we make one or more subsequent proposals each using a step size geometrically smaller than the last. To reduce the cost of DR approaches, we extend the standard delayed rejection to a probabilistic framework wherein we do not make multiple proposals at every rejection, but allow the probability of a retry to depend on the probability of accepting the previous proposal. We test the scheme in several sampling tasks, including statistical applications and multiscale model distributions such as Neal’s funnel. Delayed rejection enables sampling multiscale distributions for which standard approaches such as HMC fail to explore the tails, and improves performance five-fold over optimally-tuned HMC as measured by effective sample size per gradient evaluation. Even for simpler distributions, delayed rejection provides increased robustness to step size misspecification.

Pushing the limits of accessible length scales via a modified Porod analysis in small-angle neutron scattering on ordered systems.

Small-angle neutron scattering is a widely used technique to study large-scale structures in bulk samples. The largest accessible length scale in conventional Bragg scattering is determined by the combination of the longest available neutron wavelength and smallest resolvable scattering angle. A method is presented that circumvents this limitation and is able to extract larger length scales from the low-q power-law scattering using a modification of the well known Porod law connecting the scattered intensity of randomly distributed objects to their specific surface area. It is shown that in the special case of a highly aligned domain structure the specific surface area extracted from the modified Porod law can be used to determine specific length scales of the domain structure. The analysis method is applied to study the micrometre-sized domain structure found in the intermediate mixed state of the superconductor niobium. The analysis approach allows the range of accessible length scales to be extended from 1 µm to up to 40 µm using a conventional small-angle neutron scattering setup.

Isolating effects of large and small scale turbulence on thermodiffusively unstable premixed hydrogen flames

Lean turbulent premixed hydrogen/air flames have substantially increased flame speeds, commonly attributed to differential diffusion effects. In this work, the effect of turbulence on lean hydrogen combustion is studied through Direct Numerical Simulation using detailed chemistry and detailed transport. Simulations are conducted at six Karlovitz numbers and four integral length scales. A general expression for the burning efficiency is proposed which depends on the conditional mean chemical source term and gradient of a progress variable, and the amount of superadiabatic burning. At a fixed Karlovitz number, the normalized turbulent flame speed and area both increase almost linearly with the integral length scale ratio. The effect on the mean source term profile is minimal, indicating that the increase in flame speed can solely be attributed to the increase in flame area. At a fixed integral length scale, both the flame speed and area first increase with Karlovitz number before decreasing. The qualitative observations and trends do not change when Soret effects are neglected. Specifically, neglecting Soret diffusion is shown to reduce the flame speed, area, and burning efficiency. At higher Karlovitz numbers, the diffusivity is enhanced due to penetration of turbulence into the reaction zone, significantly dampening differential diffusion effects.Novelty and SignificanceLean premixed hydrogen flames are subject to thermodiffusive instabilities, which can lead to system level instabilities such as flashback. A comprehensive study of the thermodiffusively unstable turbulent flames with detailed chemistry and detailed transport (including Soret diffusion) was conducted across a wide range of turbulent intensities and integral length scales. Varying these two parameters independently was necessary to isolate the effects of large- and small-scale turbulence. Using these results, we propose a general expression for the burning efficiency to explain the relationship between the turbulence intensity, flame speed, and flame area. This work is an important step in developing predictive models which can aid in the design of practical combustion devices.

Morphological analysis of polydisperse nanoplatelets using SAXS

Two-dimensional materials like graphene and boron nitride find applications in numerous innovations thanks to their high specific surface area and unusual electrical, thermal and optical properties. These materials are often produced via liquid-phase exfoliation, yielding nanoplatelets with a high degree of polydispersity. Unfortunately, methods for the characterization of both lateral dimension and thickness for dispersed polydisperse nanoplatelets are still lacking. In this work, a fast and quantitative method for the characterization of polydisperse nanoplatelets in dispersion is proposed using the example of graphene nanoplatelets (GNPs). The method is benchmarked using well-defined gibbsite nanoplatelets. Synchrotron small-angle X-ray scattering (SAXS) is used to probe the structure of the platelets over a wide range of length scales. The SAXS data are fitted with a polydisperse form factor for discs, which yields size distributions in both thickness and diameter. Benchmarking the procedure with the gibbsite model system shows excellent agreement between the SAXS results and previous transmission electron microscopy and atomic force microscopy data. The method is also successfully applied to GNPs from 1–60 layers in thickness and 20–2000 nm in diameter. We believe that this work brings reliable quantitative in situ characterization, for instance during preparation, of nanoplatelet dispersions within reach.

Grain size assessment using EBSD on heterogeneous additively manufactured microstructures

Abstract Grain microstructures are important for a whole range of materials properties. With the widespread use of additive manufacturing (AM), current standards for grain boundary evaluation, such as ASTM E2627-13, may not be fit for purpose due to their microstructural complexity. They are notoriously anisotropic across a range of length scales due to the non-equilibrium nature of the solidification process and the tracking of the heat source. In this work we examine the grain microstructure of a nickel superalloy produced by laser powder bed AM by electron back scatter diffraction. We find that the guidelines provided by the ASTM E2627-13 are not suitable for such heterogeneous and anisotropic materials and some modified guidelines are provided on the field of view and EBSD step size that should be used to characterise such materials.

A Coupled CFD-DEM Approach to Model Reactive Granular Beds

Packed and moving bed reactors are widely used in process industry to process granular material. Shaft furnaces are one example of this. Due to their counterflow layout, a high thermal efficiency can be achieved. Shaft furnaces have a wide range of length and time scales that makes them challenging to model. Geometric details, like injection nozzles, are smaller than the particle size, which need a computationally highly expensive resolved Discrete Element Method (DEM) approach. To overcome this problem, a computing technique called Volume Fraction Smoother (VFS) was developed. Since the time scales in those systems reach from milliseconds for the particle collisions to hours of process time, the process time scale must be separated to model a quasi-steady state with reasonable computing time. For this, the Time Scale Splitting Method (TSSM) was introduced. This method was also adapted to model the self-heating behaviour of direct reduced iron (DRI).

Curvature programming of freestanding 3D mesostructures and flexible electronics based on bilayer ribbon networks

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

A Vision for the Future of Neutron Scattering and Muon Spectroscopy in the 2050s.

Neutron scattering and muon spectroscopy are techniques that use subatomic particles to understand materials across a wide range of energy (μeV to tens of eV), length (Å to cm) and time (attosecond to hour) scales. The methods are widely used to study condensed phase materials in areas that span physics, chemistry, biology, engineering and cultural heritage. In this Perspective we consider three questions: (i) will neutron scattering and muon spectroscopy still be needed in the 2050s? (ii) What might the technology to produce neutron and muon beams look like in the 2050s? (iii) What will be the applications in the 2050s? Overall, the neutron/muon ecosystem in the 2050s will have less capacity than now, but greater capability because of the somewhat higher power sources, better instrumentation and data analysis.

Multi-Scale Flow Estimation Within Stereoscopic PIV Processing Based On Deep Learning

Classical methods of particle-image velocimetry (PIV) based on state-of-the-art cross-correlation algorithms constitute a spatial filtering operation that leads to a loss of spatial resolution of the estimated velocity fields. This is associated with numerous limitations, e.g., when it comes to aligning high-fidelity numerical simulations, since the detection of small turbulent scales is often precluded. An optical flow neural network adapted for PIV processing, called RAFT-PIV, can overcome the drawback of reduced spatial resolution while maintaining the reliability and robustness of the classical approach. The present work aims to extend the application of the aforementioned deep learning based method by integrating it within a stereoscopic PIV processing workflow. Experimental data from an optically accessible single-cylinder combustion engine the flow field of which is characterized by complex, three-dimensional flow structures and a broad range turbulent scales are processed using RAFT-PIV. The 2D-3C vector fields obtained from stereoscopic reconstruction are compared against a classical cross-correlation based PIV evaluation, providing insight into instantaneous quantities and turbulent structures. A qualitative comparison of the instantaneous in-plane and out-of-plane velocity components reveals that the reconstructed flow obtained from the deep learning based estimation includes a wide range of resolved turbulent length scales. It outperforms the classical method. Furthermore, the findings of the present study demonstrate that the pixel accuracy has an effect on both physical quantities and turbulence characteristics. In particular, an increase in turbulent kinetic energy is observed across the engine cycles of the investigated engine flow states. Moreover, a higher fraction of three-dimensional isotropic turbulent structures is derived from RAFT-PIV compared to the results from the cross-correlation based technique.

On the analysis of two-time correlation functions: equilibrium versus non-equilibrium systems.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of timescales and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, with subsequent extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as the diffusion coefficient remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections ('cuts') of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.

Wrinkling of fluid deformable surfaces.

Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic processes. We here consider wrinkling of fluid deformable surfaces. In contrast with thin elastic sheets, with in-plane and out-of-plane elasticity, these surfaces are characterized by in-plane viscous flow and out-of-plane elasticity and have been established as model systems for biomembranes and cellular sheets. We use this hydrodynamic theory and numerically explore the formation of wrinkles and their coarsening, either by a continuous reduction of the enclosed volume or bythe continuous increase of the surface area. Both lead to almost identical results for wrinkle formation and the coarsening process, for which a scaling law for the wavenumber is obtained for a broad range of surface viscosity and rate of change of volume or area. However, for large Reynolds numbers and small changes in volume or area, wrinkling can be suppressed and surface hydrodynamics allows for global shape changes following the minimal energy configurations of the Helfrich energy for corresponding reduced volumes.

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids.

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equationof motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Advancing Fuel Spray Characterization: A Machine Learning Approach for Directly Injected Gasoline Fuel Sprays

Compression ignition engines when operated on gasoline fuels cause significant reduction in NOx and particulate emissions. In such advanced combustion strategy, the fuel-oxidiser mixing process, intensified by the prolonged ignition delays of gasoline fuels, directly affects the stability and efficiency of combustion. Thus, optimising fuel spray characteristics leads to optimisation of injector design, engine performance and subsequent decrease in emissions. Since spray development is a complex process that involves wide range of length and time scales, computationally expensive modelling techniques can be replaced with machine learning (ML) models. These ML models are employed to predict spray characteristics utilizing datasets generated from comprehensive spray studies. In this work, a dataset of about 5400 instances taken from non-evaporating gasoline fuel spray imaging experiments under Gasoline Compression Injection (GCI) engine conditions is used to train various ML models with data split of 70 % and 30 % for training and testing, respectively, with five-folds cross-validation performed within the training. The fuel injection pressure (60 – 150 MPa), chamber pressure (0.1 – 2 MPa), nozzle diameter, nozzle hole conicity and injection duration are used as input features to the models for predicting the spray tip penetration and spray angle. The performance of four ML models was evaluated and compared under default and tuned hyperparameters against experimental data and available physics-based correlations in the literature. The models include random forest, extreme gradient boosting, multilayer perceptron, and elastic-net. The results show that the hyperparameter-tuned extreme gradient boosting model performs best in predicting the spray parameters. The overall model performance was evaluated using the coefficient of determination (R2), mean absolute error (MAE), and root mean squared error (RMSE), resulting in values of 0.884, 0.651, and 1.571, respectively. This study presents compelling evidence demonstrating the effectiveness of ML as a powerful tool for isolating non-linear behaviors from physical processes. By effectively decoupling these behaviors, ML enhances the accuracy of predicting spray characteristics while significantly reducing computational costs. The application of ML in fuel injector design has the potential to revolutionize engine performance and contribute to substantial reductions in emissions.