Macroscopic Transport Properties Research Articles

Examining Solvent Motion in Polarized Concentrated Electrolytes

Historically, ion transport in electrolytes has been described in terms of current – potential response. This behavior is often explained using macroscopic transport properties such as ionic conductivity, transference number, and salt diffusivity.1,2 In contrast, recent X-ray3 and magnetic resonance4 techniques capture ion motions at smaller yet continuum scales. Interestingly, some of these measurements observe the directed motion of solvent in polarized electrolytes, while traditionally solvent is assumed to be a stationary species. Driven by this mismatch of two interpretations, we revisit Newman’s concentrated solution theory1,2,5–8 to examine the role of solvent motion in polarized electrolytes (Figure 1(a)). We use LiTFSI in PEO as an exemplar electrolyte since it is one of the few electrolytes with a full set of transport properties measured previously.9 We find that as the electrolyte is polarized, salt concentration gradients can create a thermodynamic drive for the solvent to travel against the salt motion. Time evolution of voltage (a macroscopic quantity), as well as velocity fields for each species (Figure 1(b)), are examined. We study polarizations at various currents and concentrations to identify when and how the solvent motion contributes to electrolyte response. We find that the solvent, even if it is a charge-neutral species, moves in the direction of ionic current. Apart from these new insights into electrolyte transport dynamics, the results help rationalize recent direct measurements of ion fluxes.Figure 1. (a) A schematic showing physical situation of interest. x=0 is the left interface between Li electrode and electrolyte, while x=L is the right interface. As time passes by, the electrolyte fields evolve as well as the interfaces move equally in the opposite direction of current density, iapp. (b) Example distribution of cation, anion, and solvent velocities in the polarized electrolyte. Directions of these velocities are shown when current flows along the positive coordinate. In this scenario, ions pile up close to the left electrode, while they deplete near the right electrode.(1) Newman, J.; Thomas-Alyea, K. E. Electrochemical Systems; John Wiley & Sons, 2012.(2) Newman, J.; Bennion, D.; Tobias, C. W. Mass Transfer in Concentrated Binary Electrolytes. Berichte der Bunsengesellschaft für Phys. Chemie 1965, 69 (7), 608–612. https://doi.org/10.1002/bbpc.19650690712.(3) Steinrück, H. G.; Takacs, C. J.; Kim, H. K.; MacKanic, D. G.; Holladay, B.; Cao, C.; Narayanan, S.; Dufresne, E. M.; Chushkin, Y.; Ruta, B. et al. Concentration and Velocity Profiles in a Polymeric Lithium-Ion Battery Electrolyte. Energy Environ. Sci. 2020, 13 (11), 4312–4321. https://doi.org/10.1039/d0ee02193h.(4) Bazak, J. D.; Allen, J. P.; Krachkovskiy, S. A.; Goward, G. R. Mapping of Lithium-Ion Battery Electrolyte Transport Properties and Limiting Currents with In Situ MRI. J. Electrochem. Soc. 2020, 167 (14), 140518. https://doi.org/10.1149/1945-7111/abc0c9.(5) Liu, J.; Monroe, C. W. Solute-Volume Effects in Electrolyte Transport. Electrochim. Acta 2014, 135, 447–460. https://doi.org/10.1016/j.electacta.2014.05.009.(6) Dees, D.; Gunen, E.; Abraham, D.; Jansen, A.; Prakash, J. Alternating Current Impedance Electrochemical Modeling of Lithium-Ion Positive Electrodes. J. Electrochem. Soc. 2005, 152 (7), A1409. https://doi.org/10.1149/1.1928169.(7) Pollard, R.; Comte, T. Determination of Transport Properties for Solid Electrolytes from the Impedance of Thin Layer Cells. J. Electrochem. Soc. 1989, 136 (12), 3734–3748. https://doi.org/10.1149/1.2096540.(8) Nyman, A.; Behm, M.; Lindbergh, G. Electrochemical Characterisation and Modelling of the Mass Transport Phenomena in LiPF6-EC-EMC Electrolyte. Electrochim. Acta 2008, 53 (22), 6356–6365. https://doi.org/10.1016/j.electacta.2008.04.023.(9) Villaluenga, I.; Pesko, D. M.; Timachova, K.; Feng, Z.; Newman, J.; Srinivasan, V.; Balsara, N. P. Negative Stefan-Maxwell Diffusion Coefficients and Complete Electrochemical Transport Characterization of Homopolymer and Block Copolymer Electrolytes. J. Electrochem. Soc. 2018, 165 (11), A2766–A2773. https://doi.org/10.1149/2.0641811jes. Figure 1

Quantum Transport in a Crystal with Short-Range Interactions: The Boltzmann\u2013Grad Limit

We study the macroscopic transport properties of the quantum Lorentz gas in a crystal with short-range potentials, and show that in the Boltzmann–Grad limit the quantum dynamics converges to a random flight process which is not compatible with the linear Boltzmann equation. Our derivation relies on a hypothesis concerning the statistical distribution of lattice points in thin domains, which is closely related to the Berry–Tabor conjecture in quantum chaos.

Atomic-state-dependent screening model for hot and warm dense plasmas

An ion embedded in warm/hot dense plasmas will greatly alter its microscopic structure and dynamics, as well as the macroscopic radiation transport properties of the plasmas, due to complicated many-body interactions with surrounding particles. Accurate theoretically modeling of such kind of quantum many-body interactions is essential but very challenging. In this work, we propose an atomic-state-dependent screening model for treating the plasmas with a wide range of temperatures and densities, in which the contributions of three-body recombination processes are included. We show that the electron distributions around an ion are strongly correlated with the ionic state studied due to the contributions of three-body recombination processes. The feasibility and validation of the proposed model are demonstrated by reproducing the experimental result of the line-shift of hot-dense plasmas as well as the classical molecular dynamic simulations of moderately coupled ultra-cold neutral plasmas. Our work opens a promising way to treat the screening effect of hot and warm dense plasma, which is a bottleneck of those extensive studies in high-energy-density physics, such as atomic processes in plasma, plasma spectra and radiation transport properties, among others.

Misestimation of the ITZ Thickness around Non-Spherical Aggregates

The ITZ (interfacial transition zone) in concrete has very high porosity and permeability, which affects concrete’s macroscopic mechanical properties and transport properties. Two-dimensional (2D) areal analysis and one-dimensional (1D) linear analysis are usually used to study ITZ’s microstructure. However, 3D microstructure is difficult to be characterized by 1D and 2D information. For example, 2D cross-section planes do not always intercept both the ITZ and the corresponding aggregate, which causes some ITZ regions are ignored by researchers. Therefore, ITZ’s volume and thickness will be misestimated, and leads to the misestimation of the diffusivity. In this paper, the effect of aggregate’s shape on the misestimation of ITZ thickness t is studied. The results reveal that the misestimation increases with the increasing sphericity s of aggregates.

Reduced Thermal Conductivity in Ultrafast Laser Heated Silicon Measured by Time-Resolved X-ray Diffraction

We investigate the effect of free carrier dynamics on heat transport in bulk crystalline Silicon following femtosecond optical excitation of varying fluences. By taking advantage of the dense 500 MHz standard fill pattern in the PLS-II storage ring, we perform high angular-resolution X-ray diffraction measurements on nanosecond-to-microsecond time-scales with femtometer spatial sensitivity. We find noticeably slowed lattice recovery at increasingly high excitation intensities. Modeling the temporal evolution of lattice displacements due to the migration of the near surface generated heat into the bulk requires reduced thermal diffusion coefficients. We attribute this pump-fluence dependent thermal transport behavior to two separate effects: first, the enhanced nonradiative recombination of free carriers, and, second, reduced size of the effective heat source in the material. These results demonstrate the capability of time-resolved X-ray scattering as an effective means to explore the connection between charge carrier dynamics and macroscopic transport properties.

Correlation between backbone and pyridine dynamics in poly(2‐vinyl pyridine)/silica polymer nanocomposites

AbstractPolymer segmental dynamics in polymer nanocomposites (PNCs) can be significantly perturbed from bulk and underlie macroscopic mechanical and transport properties, but fundamental studies are necessary to build correlations between dynamics and properties. To elucidate a mechanistic description of this perturbation and isolate different molecular motions, we present quasi‐elastic neutron scattering (QENS) measurements on PNCs with attractive interactions comprised of colloidal silica nanoparticles (NPs) uniformly dispersed in poly(2‐vinyl pyridine) (P2VP) with and without backbone deuteration. Measurements of fully‐protonated P2VP probe the dynamics of both the polymer backbone and pyridine pendant group; whereas measurements of backbone‐deuterated P2VP isolate the dynamics of only the pyridine ring. On the small length scales (~1 nm) and fast time scales (~1 ns) captured by QENS, we show that the backbone and pyridine ring dynamics are highly coupled at high temperatures and both are slowed by about 35% relative to neat polymer in 25 vol% PNCs. This observation implies that the backbone and pendant interfacial dynamics are perturbed similarly in PNCs, which further develops our fundamental understanding of microscopic properties in PNCs.

Discrete modelling of hydro-chemo-mechanical performance of clay materials

The truncated octahedron cellular assemblies are used to represent the clay materials which align with experimentally characterised microstructures. The cellular assembly is divided into two interacting graphs: one is the mechanical graph which is developed to describe the deformation behaviour of the material, and the other is physical/chemical graph which is developed to demonstrate the reactive transport in the material. This setting is realistic especially when the mechanically-driven cracking has an impact on the transport pathways. Both graphs can represent the anisotropy and heterogeneity of the materials. The model performance is demonstrated using experimental data on the diffusion of species through Opalinus clay (OPA) – a complex process that involves elastic response, diffusion and anionic exclusion. The accuracy of the model is validated by the simulating the confining pressure and reactions dependency of different species transport through OPA. The model improves the understanding of the microstructure influence on the macroscopic transport properties of porous materials. The developed model can be applied to a variety of scientific and engineering problems, such as hydraulic cracking of gas-bearing shale, radioactive nuclear waste geo-disposal, contaminated soil remediation and geological carbon storage.

Step-edge assisted large scale FeSe monolayer growth on epitaxial Bi2Se3 thin films

Enhanced superconductivity of FeSe in the 2D limit on oxide surfaces as well as the prediction of topological superconductivity at the interface to topological insulators makes the fabrication of Fe-chalcogenide monolayers a topic of current interest. So far superconductive properties of the latter are mostly studied by scanning tunneling spectroscopy, which can detect gaps in the local density of states as an indicator for Cooper pairing. Direct macroscopic transport properties, which can prove or falsify a true superconducting phase, are yet widely unexplored due to the difficulty to grow monolayer films with homogeneous material properties on a larger scale. Here we report on a promising route to fabricate micron-scale continuous carpets of monolayer thick FeSe on Bi2Se3 topological insulators. In contrast to previous procedures based on ultraflat bulk Bi2Se3 surfaces, we use molecular beam epitaxy grown Bi2Se3 films with high step-edge densities (terrace widths 10–100 nm). We observe that step edges promote the almost strainless growth of coalescing FeSe domains without compromising the underlying Bi2Se3 crystal structure.

Collective intracellular cargo transport by multiple kinesins on multiple microtubules.

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Hydrodynamic slip can align thin nanoplatelets in shear flow

The large-scale processing of nanomaterials such as graphene and MoS2 relies on understanding the flow behaviour of nanometrically-thin platelets suspended in liquids. Here we show, by combining non-equilibrium molecular dynamics and continuum simulations, that rigid nanoplatelets can attain a stable orientation for sufficiently strong flows. Such a stable orientation is in contradiction with the rotational motion predicted by classical colloidal hydrodynamics. This surprising effect is due to hydrodynamic slip at the liquid-solid interface and occurs when the slip length is larger than the platelet thickness; a slip length of a few nanometers may be sufficient to observe alignment. The predictions we developed by examining pure and surface-modified graphene is applicable to different solvent/2D material combinations. The emergence of a fixed orientation in a direction nearly parallel to the flow implies a slip-dependent change in several macroscopic transport properties, with potential impact on applications ranging from functional inks to nanocomposites.

The effect of contact resistance on electrical conductivity in filled elastomer materials

This paper is focused on studying the charge transport between the particles in filled elastomer composites, and suggests a new modeling approach that would allow predicting the electrical conductivity of this material. Our approach is based on a combination of non-equilibrium Green's function (DFTB-NEGF) analysis for atomic-level electron quantum transport, and effective medium theory for calculating the said macroscopic transport properties of the material. The model can be used for predicting macroscopic material conductivity based on the information of material microstructure received by electron microscopy; explain changes of conductivity in deformed material and with temperature variation, and finally it can assist in finding the optimal material parameters such as particle shape, size distribution, and volume fraction to maximize the performance. The results of our modeling re-attest the known phenomenon that the electrical conductivity in percolated network is always dominated by direct particle-to-particle charge transport. We studied the electrical conductivity in a medium of high volume fraction of metallic particles dispersed in polymer matrix where thin polymer matrix layer covalently attached to the metallic particle contacts, and the thin polymer layer undergoes high local shear strain when hard particles slide along each other during deformation. These conditions allow the redistribution of electron density from metal to the polymer, and the conductance through normally insulating matrix can become comparable with the pinpoint conductance through the metal. These conditions can only occur in the place of direct particle contacts, therefore all criteria for percolated conductive network hold valid in this case. The integral conductance of thin “sandwiched” polymer layer strongly, but predictably depends on local contact geometry, mostly on particle surface curvature at place of contact. This allows predicting composite conductivity from the properties of each phase, loading, and particle shape and size distributions. Further, the conductance of polymer chain can significantly increase with the fluctuations of molecular shape caused by temperature and/or deformation. We infer that this effect is responsible for the major part of strain and temperature dependence of the conductivity that has been reported in the literature, although particle orientation and stacking at larger deformations may also contribute to the strain dependence.

Vorticity of viscous electronic flow in graphene

In ultra-pure materials electrons may exhibit a collective motion similar to the hydrodynamic flow of a viscous fluid, the phenomenon with far reaching consequences in a wide range of many body systems from black holes to high-temperature superconductivity. Yet the definitive detection of this intriguing behavior remains elusive. Until recently, experimental techniques for observing hydrodynamic behavior in solids were based on measuring macroscopic transport properties, such as the ‘nonlocal’ (or ‘vicinity’) resistance, which may allow alternative interpretation. Earlier this year two breakthrough experiments demonstrated two distinct imaging techniques making it possible to ‘observe’ the electronic flow directly. We demonstrate that a hydrodynamic flow in a long Hall bar (in the absence of magnetic field) exhibits a nontrivial vortex structure accompanied by a sign-alternating nonlocal resistance. An experimental observation of such unique flow pattern could serve a definitive proof of electronic hydrodynamics.

New exact results for the two-phase model with several conserved currents

We consider the macroscopic transport properties of two-dimensional random binary mixtures with identical spatial distributions of the two phases. Previous studies have obtained exact analytical results for the electrical conductivity of a single layer with and without a magnetic field, as well as for the thermoelectric response of a magnetic field-free double-layer. Here, we generalize these exact solutions to the magneto-thermoelectric response of a single layer and to the thermoelectric response of a double-layer. The magneto-thermoelectric transport coefficients of the double-layer are calculated perturbatively for weak magnetic field.

Macroscopic transport properties of Gyroid structures based on pore-scale studies: Permeability, diffusivity and thermal conductivity

Gyroid structure is a kind of triply periodic minimum surface, which presents several advantages such as free-standing, highly ordered and interconnected pore network and high specific surface area. Understanding transport processes inside the Gyroid structure is important for its application. In this study, porous structures of the Gyroid are reconstructed, and then pore-scale studies of fluid flow, diffusion and heat transfer in the two phases of Gyroid structures are numerically implemented using the lattice Boltzmann method (LBM). Pore-scale velocity, concentration and temperature fields inside the Gyroid structures are discussed, based on which macroscopic properties including permeability, effective diffusivity, effective thermal conductivity, and tortuosity are predicted. There are two phases in the Gyroid structures, and both phases are continuous, leading to the bicontinuous characteristic of Gyroid structures. The results show that transport resistance in one phase is lower than that in the other phase. Thus from the perspective of enhancing transport process, it is desirable to choose the phase with higher transport properties for transporting the slower process. The present study provides guidance for subsequent applications of Gyroid structure.

Multi-scale pore network modelling of fluid mass transfer in nano-micro porous media

It is widely accepted that pore size distribution and spatial pore connectivity directly impact on the macroscopic porous medium transport properties. Therefore it is indispensable to characterize nano-micro porous media like shale with multi-scale pore structure to accurately assess fluid transport properties. In this study, we propose a multi-scale pore network model to estimate the fluid transport properties. A 3D binary inorganic porous structure model is constructed from a section of scanning electron microscopy (SEM) image which only images large scale inorganic pores and its corresponding inorganic pore network is extracted by the maximal ball fitting method. The nano-porous organic matter is treated as the virtual throat which is embedded in series or parallel connection with the inorganic throat on the original inorganic pore network. Three parameters namely the ratio of total amount of the virtual throat to the total amount of the inorganic throat, the proportion of virtual throat in parallel connection with the inorganic throat and average organic pore radius inside the organic matter are applied to analyze the impact of multi-scale pore structure characteristic on fluid transport properties. The constructed multi-scale pore network model accounts for the organic matter distribution, organic matter total volume, organic pore size, inorganic pore structure and connectivity characteristic between organic and inorganic system all together. Nano-micro scale fluid transport mechanisms are considered in modelling fluid mass transfer. Key analysis results indicate that the fluid mass transfer in nano-micro porous media is influenced by the nano-porous organic matter distribution pattern and it’s local volume. The series connection of nano-porous organic matter and the increase of virtual throat amounts significantly decrease the fluid transport ability. Furthermore, the established multi-scale pore network model is used to interpretate laboratory pressure pulse decay response curve.

Nanoparticle dispersion in porous media in viscoelastic polymer solutions

Flow of viscoelastic fluids in porous media is ubiquitous in biological and industrial processes, and the choice of viscoelastic fluids is of foremost importance for their effect on macroscopic flow and transport properties. In this paper we study the macroscopic properties of flow and transport of viscoelastic fluids through a model porous media by means of Direct Numerical Simulation (DNS). We show that flow of a viscoelastic fluid modeled via a FENE-P constitutive model features three distinct regimes of flow resistance: a plateau at low Deborah numbers, and a shear-thinning phase followed by an abrupt flow thickening above a critical Deborah number, consistent with experimental observations. Congruous to this shear-thickening, we observe the onset of hydrodynamic instabilities resulting in fluctuations in pressure drop and flow resistance. These fluctuations intensify with increasing the fluid elasticity. Finally, we investigate Lagrangian attributes of viscoelastic flow and transport through porous media. We find that although the fluid elasticity broadens the Lagrangian velocity distributions, it does not alter the long-term particle dispersion in disordered porous media.

Level-expansion: A statistical sequential design methodology with application to nanomaterial synthesis

Nanotechnology is an era-defining breakthrough across science and engineering. For example, one-dimensional nanostructures such as nanowires, nanotubes, and nanobelts are widely regarded as critical building blocks for creating the next generation of devices in electronics, optics, energy, and biomedicine. Motivated by a practical problem of sequential synthesis of nanowires, we propose a new statistical design augmentation method, called level-expansion. For a fractional factorial design at two levels, this method creates a follow-up design by expanding some of the factors in the initial design to four elaborately chosen levels and reversing the signs of the remaining factors. The augmented design produced as such strikes a fine balance between dealiasing and entertaining nonlinear effects. Some statistical properties of the proposed method are derived. The effectiveness of the proposed method is successfully illustrated with a case study for growing a type of zinc-oxide nanowire. The use of level-expansion in the case study unveils some previously unknown nonlinear relationships between the concentration of polyethyleneimine and the length of nanowires. This finding is important for nanoscientists to invent new zinc-oxide nanowires with better macroscopic transport properties. Besides nanotechnology, the proposed method applies broadly to problems in many other scientific fields with similar traits where a follow-up design is needed for the dual purposes of investigating nonlinear effects and dealising.

Effect of MCl3 (M=La, U or Sc) component on the local structures and transport properties of LiCl–KCl–MCl3 eutectic: A molecular dynamics study

LiCl–KCl eutectic material is a crucial waste reprocessing candidate for use in molten salt reactors and the major component of spent nuclear fuel. Investigating the structure and thermodynamic transport properties of this eutectic mixed with fission waste cations will provide a better understanding of the reprocessing progress. In this study, molecular dynamic simulations were performed on the molten salts of a LiCl–KCl eutectic mixed with La3+, U3+, or Sc3+ cations, and the mole fractions of the trivalent cations ranged from 0% to 50% at 773 K, 873 K, and 973 K. The local structures (in nearest neighbor distance and coordination numbers) and macroscopic transport properties (self-diffusion, electrical conductivity, and viscosity coefficients) of the three systems have been studied. When the trivalent cation concentration varied from 0 mol% to 50 mol%, the mean nearest neighbor distance of La3+–Cl- and U3+–Cl- increased and the mean nearest neighbor distance of Sc3+–Cl- decreased, and the coordination numbers of La3+ and U3+ increased while the coordination numbers of Sc3+ decreased as the trivalent cation concentrations increased. The trivalent cations were primarily present in the form of [MClx]3−x in diluted mixtures, and they linked to form a network in the viscous regions. The viscosity was primarily affected by the network and followed by a nearly linear increase with the degree of the network in the arbitrary trivalent mixtures. Additional investigation predicted the electrical conductivity and self-diffusion over a broader range; the results indicated that the electrical conductivities were hardly affected by the radius of the given trivalent cation.

Hydrodynamic and Electrophoretic Properties of Trastuzumab/HER2 Extracellular Domain Complexes as Revealed by Experimental Techniques and Computational Simulations.

The combination of hydrodynamic and electrophoretic experiments and computer simulations is a powerful approach to study the interaction between proteins. In this work, we present hydrodynamic and electrophoretic experiments in an aqueous solution along with molecular dynamics and hydrodynamic modeling to monitor and compute biophysical properties of the interactions between the extracellular domain of the HER2 protein (eHER2) and the monoclonal antibody trastuzumab (TZM). The importance of this system relies on the fact that the overexpression of HER2 protein is related with the poor prognosis breast cancers (HER2++ positives), while the TZM is a monoclonal antibody for the treatment of this cancer. We have found and characterized two different complexes between the TZM and eHER2 proteins (1:1 and 1:2 TZM:eHER2 complexes). The conformational features of these complexes regulate their hydrodynamic and electrostatic properties. Thus, the results indicate a high degree of molecular flexibility in the systems that ultimately leads to higher values of the intrinsic viscosity, as well as lower values of diffusion coefficient than those expected for simple globular proteins. A highly asymmetric charge distribution is detected for the monovalent complex (1:1 complex), which has strong implications in correlations between the experimental electrophoretic mobility and the modeled net charge. In order to understand the dynamics of these systems and the role of the specific domains involved, it is essential to find biophysical correlations between dynamics, macroscopic transport and electrostatic properties. The results should be of general interest for researchers working in this area.

A STUDY ON NUMERICAL DETERMINATION OF PERMEABILITY AND INERTIA COEFFICIENT OF ALUMINUM FOAM USING X-RAY MICROTOMOGRAPHY TECHNIQUE: FOCUS ON INSPECTION METHODS FOR RELIABILITY (PERMEABILITY AND INERTIA COEFFICIENT BY TOMOGRAPHY)

The volume-averaged (i.e., macroscopic) transport properties such as permeability and inertia coefficient of two aluminum foams with 10 and 20 pores per inch (PPI) pore density are found using microtomography images. It is shown that a comparison between the numerical values and the experimental results may not be sufficient to prove the correctness of the obtained results. Hence, in addition to traditional validation methods such as grid independency and comparison with reported results in literature, further inspections such as (a) checking the development of flow, (b) inspection of Darcy and non-Darcy regions, (c) conservation of flow rate through the porous media, (d) sufficiency of number of voxels in the narrow throats, and (e) observation of transverse velocity gradients in pores for high and low Reynolds numbers can be performed to further validate the achieved results. These techniques have been discussed and explained in detail for the performed study. Moreover, the obtained permeability and inertia coefficient values are compared with 19 reported theoretical, numerical, and experimental studies. The maximum deviation between the present results and the reported studies for 10 PPI is below 25%, while for 20 PPI it is below 28%.