Triangular Cells Research Articles

Lattice Induced Short-Range Attraction between Like-Charged Colloidal Particles.

We perform experiments and computer simulations to study the effective interactions between like-charged colloidal tracers moving in a two-dimensional fluctuating background of colloidal crystal. By a counting method that properly accounts for the configurational degeneracy of tracer pairs, we extract the relative probability of finding a tracer pair in neighboring triangular cells formed by background particles. We find that this probability at the nearest neighbor cell is remarkably greater than those at cells with larger separations, implying an effective attraction between the tracers. This effective attraction weakens sharply as the background lattice constant increases. Furthermore, we clarify that the lattice-mediated effective attraction originates from the minimization of free energy increase from deformation of the crystalline background due to the presence of diffusing tracers.

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh

We present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

Effect of Single Slat and Double Slat on Aerodynamic Performance of NACA 4415

This study uses a Computational Fluid Dynamics (CFD) approach. The main object in this study is NACA 4415 with slat variations. The airfoil used as the slat is Eppler 421. Reynolds number in this study is 3 Í 10 6 . This study uses an unstructured mesh with a triangular cell shape with 137824 elements. The use of slats can improve the aerodynamic performance of NACA 4415. NACA 4415 without slat stalled at AoA=16º. Stall on airfoils with a single slat and double slat occurred at AoA=20º. Slat can increase C l in NACA 4415; however, the difference in C l increase is not much different when using a single slat or double slat. An airfoil with a single slat, on average, can increase C l by 20.9129%. The average increase in C l for an airfoil with a double slat is 25 . 6878%. Single slat and double slat increase C d . A single slat increased C d with an average increase of 26 . 1109%, and the average increase in C d for airfoils with double slat was 54 . 6152%. Single slat can produce a better C l to C d ratio than double slat, but the optimum AoA of double slat is 1º higher than single slat. Visualization of fluid flow at AoA=16° shows the fluid flow separation in the airfoil without a slat. The fluid flow separation can be handled well when NACA 4415 is given a single slat or double slat .

Spinless fermions in a Z2 gauge theory on a triangular ladder

A study of spinless matter fermions coupled to a constrained ${\mathbb{Z}}_{2}$ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared with a previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (QPT) only for decorated couplings. At finite doping and in the static case, a staggered flux insulator at half-filling and vanishing magnetic energy competes with a uniform flux metal at elevated magnetic energy. As for the square lattice, a single QPT into a confined fermionic dimer gas is found vs electric coupling. Dimer resonances in the confined phase are, however, a second-order process only, likely reducing the tendency to phase separate for large magnetic energy. The results obtained employ a mapping to a pure spin model of ${\mathbb{Z}}_{2}$ gauge-invariant moments, adapted from the square lattice, and density matrix renormalization group calculations thereof for numerical purposes. Global scans of the quantum phases in the intermediate coupling regime are provided.

Anisotropic multi-level hp-refinement for quadrilateral and triangular meshes

This paper extends the multi-level hp -approach—previously introduced for the isotropic refinement of quadrilateral and hexahedral elements—to the anisotropic refinement of quadrilateral and triangular meshes. To this end, this work first introduces anisotropic split operators for the hierarchical refine-by-superposition concept. For quadrilateral cells, the well-known anisotropic h 2 -split is used. For the anisotropic refinement of triangular cells, a novel split along the barycentric mid-lines is introduced, which minimizes the number of new cells without distorting their shape. Second, it is shown that the isotropic multi-level hp -approach of handling hanging nodes is not directly applicable in the case of directional refinement. For this reason, this work analyses the requirements of a valid fe-basis on anisotropically refined, irregular multi-level meshes and by this generalizes the isotropic multi-level hp -concept. On this basis, an algorithmic realization is derived demonstrating that the applied refine-by-superposition idea carries the implementational simplicity and the native support of arbitrary irregular meshes to anisotropic refinements. A systematic study of benchmarks featuring vertex-, edge-, and edge-vertex singularities as well as boundary layers shows that these advantages come neither at the expense of the approximation quality, nor the sparsity or conditioning of the final equation system. Further, an ad hoc edge-based indication scheme is introduced that reliably guides the place and the direction of the anisotropic refinement process even on unstructured meshes. The presented results qualify the proposed approach as an automatic, anisotropic multi-level hp -refinement method for quadrilateral and triangular meshes, coming at a marginal implementational complexity and without any restrictions due to arbitrary hanging nodes and the associated dead-lock problems. • Generalization of multi-level hp-method to anisotropic refinement of triangles and quadrilaterals. • Dead-lock free directional refinement without limitations due to hanging nodes. • Formulation of an anisotropic split of triangles that is free of element distortions. • Automatically driven anisotropic refinement of unstructured, mixed meshes.

Crushing Behaviors and Energy Absorption Evaluation Methods of Hexagonal Steel Tubular Columns with Triangular Cells.

Under axial compression, multi-cell tubes are considered more effective than single-cell tubes. Regular hexagonal multi-cell tubes (HMT) were designed, tested, and analyzed by finite element modeling (FEM). The crushing mechanism of the HMT was revealed by compression testing and FEM. Experiments and FEM revealed that the mean crushing force of the HMT can be increased by 14% by adopting multi-cell topology, which shortens the folding wavelength and enables HMT progressive crushing. Thus, the HMT is more efficient in energy absorption compared with the conventional regular hexagonal thin-walled tube (HST). More triangular cells result in HMTs with much greater mean crushing force and specific energy absorption. Three evaluation methods were proposed and discussed to determine the effective crushing distance. A plastic model established according to classical simplified super-folding elements was shown to consistently predict the mean crushing force of the HMTs.

Buckling of regular and auxetic honeycombs under a general macroscopic stress state in symplectic system

A symplectic stiffness method, based on Hamiltonian variational principle and symplectic eigen expansion, is presented to investigate the buckling of honeycomb structures under a general macroscopic stress state. The analytical closed-form expressions of critical forces are obtained for the possible buckling modes, which satisfy the deformation compatibility conditions for the cell beams, and the lowest value in the stability surface corresponds to the actual buckling force for the honeycomb. The results show that the buckling strengths and modes for the regular and auxetic honeycomb structures depend strongly on the biaxial stress state but weakly on the relative density. For some complex honeycombs, e.g., the triangular and re-entrant cell, the buckling modes change with the increasement of the orders. Considerable attention is focused on the physical mechanism of phase transformation. There is no possibility of a swaying buckling mode when the beam buckles symmetrically, and the re-entrant geometry has an important influence on the auxetic honeycomb buckling patterns. The present symplectic stiffness method is believed to be beneficial for the stability analysis of some frontier engineering fields such as flexible electronics and soft robots.

Investigating the Impact of Triangle and Quadrangle Mesh Representations on AGV Path Planning for Various Indoor Environments: With or Without Inflation

In a factory with different kinds of spatial atmosphere (warehouses, corridors, small or large workshops with varying sizes of obstacles and distribution patterns), the robot’s generated paths for navigation tasks mainly depend on the representation of that environment. Hence, finding the best representation for each particular environment is necessary to forge a compromise between length, safety, and complexity of path planning. This paper aims to scrutinize the impact of environment model representation on the performance of an automated guided vehicle (AGV). To do so, a multi-objective cost function, considering the length of the path, its complexity, and minimum distance to obstacles, is defined for a perfect circular robot. Unlike other similar studies, three types of representation, namely quadrangle, irregular triangle, and varying-size irregular triangle, are then utilized to model the environment while applying an inflation layer to the discretized view. Finally, a navigation scenario is tested for different cell decomposition methods and an inflation layer size. The obtained results indicate that a nearly constant coarse size triangular mesh is a good candidate for a fixed-size robot in a non-changing environment. Moreover, the varying size of the triangular mesh and grid cell representations are better choices for factories with changing plans and multi-robot sizes due to the effect of the inflation layer. Based on the definition of a metric, which is a criterion for quantifying the performance of path planning on a representation type, constant or variable size triangle shapes are the only and best candidate for discretization in about 59% of industrial environments. In other cases, both cell types, the square and the triangle, can together be the best representation.

Development and Processing of Thermal-Hydraulic Model for GFR 2400 Fast Reactor Design and NESTLE Coupled Transient Code

Abstract The paper investigates the influence of the used thermal-hydraulic approximations on the coupled calculations of gas-cooled fast reactor design (hereby GFR 2400). The NESTLE code is used as coupled simulation tool and solves the multigroup neutron diffusion equation by the finite difference method that is internally coupled with a thermal-hydraulic subchannel code. The in-house developed tempin code and the computational fluid dynamics (CFD) code fluent (from ANSYS code system, Canonsburg, PA) are used to prepare the thermal-hydraulic data for the GFR 2400 calculations. The tempin code solves the steady-state heat balance equation with flowing coolant in triangular lattice cell together with temperature dependent thermal-hydraulic properties of the fuel, cladding, and coolant. Based on the calculated fuel bundle temperature distributions by the tempin code, the thermal-hydraulic material properties (approximations) suitable for the NESTLE coupled code are processed for the GFR 2400 design. The influence of the constant and radial heat generation term within the fuel pin is studied within the paper. The performance of the NESTLE code with thermal-hydraulic approximations processed by both (tempin and fluent) methods is compared with the findings of the GoFastR project. Moreover, both the thermal-hydraulic approximations were compared for one steady-state and one transient state, related to the rapid withdrawal of one control rod assembly from the core. Changes in thermal-hydraulic distributions are described and visualized in the paper.

Load characteristics of triangular honeycomb structures with self-similar hierarchical features

Hierarchical structures and materials have attracted extensive attention due to their advantage in improving mechanical properties. Therefore, to design lightweight structures with superior mechanical properties, a novel self-similar hierarchical triangular honeycomb (SHTH) is developed by sequentially arranging the similar sub-triangles on the side of an ordinary triangular honeycomb (OTH) in this study. The crushing mechanism of SHTHs is investigated using experimental, numerical, and theoretical methods. The numerical simulation is verified by the experimental data of metal 3D printed specimens. Firstly, comparative studies on the crushing performances of the SHTH and the OTH are performed. The results demonstrate that the hierarchical configuration has great improvement in deformation mode and crashworthiness indicator for triangular honeycombs. Then, the crushing performances of SHTHs with different hierarchy factors and relative densities are discussed. The results show that the relative density and the hierarchy factor have significant effects on the in-plane mechanical behaviors of SHTHs. Moreover, the SHTHs exhibit better crashworthiness in the X-direction (i.e., along the side direction of the primary triangular cell) than in the Y-direction (i.e., normal to the side direction of the primary triangular cell), and the crushing performances of SHTHs are tunable by relative density and hierarchy factors. Finally, the theoretical models on the crushing responses of SHTHs are first derived based on equivalent simplified collapse mode and then verified by experimental and numerical data. The results further reveal the influence mechanism of hierarchical arrangement in improving the crushing performance of honeycomb structures, and a novel design concept for engineering collision protection is developed in this study.

Patch loading resistance of steel plate girders stiffened with triangular cell flanges

This paper aims at investigating the patch loading resistance of steel plate girders with triangular cell flanges. This geometrical arrangement increases considerably the resistance of the web plates when subjected to concentrated loading. In this study, the patch loading resistance is studied by means of GMNI- analyses considering large displacements, elastoplastic material behavior, initial geometric imperfections, and an assumed pattern of residual stress distribution. The numerical model is validated against experimental results taken from the literature. Thereafter, a parametric study is conducted in order to investigate the influence of various geometric parameters such as the location in the web and flange as well as the thickness of the plates that forms the triangular cells, and the panel aspect ratio on the resistance of the stiffened girders. A design proposal is also presented following the guideline in the EC3:1–5. This proposal takes into account the influence of the stiffening effect provided by the triangular cell flanges. The results show that the use of triangular cell flanges enhances the resistance of steel plate girders to patch loading.

Arrangements of Approaching Pseudo-Lines

We consider arrangements of n pseudo-lines in the Euclidean plane where each pseudo-line ell _i is represented by a bi-infinite connected x-monotone curve f_i(x), x in mathbb {R}, such that for any two pseudo-lines ell _i and ell _j with i !<! j, the function x !mapsto ! f_j(x) !-! f_i(x) is monotonically decreasing and surjective (i.e., the pseudo-lines approach each other until they cross, and then move away from each other). We show that such arrangements of approaching pseudo-lines, under some aspects, behave similar to arrangements of lines, while for other aspects, they share the freedom of general pseudo-line arrangements. For the former, we prove:There are arrangements of pseudo-lines that are not realizable with approaching pseudo-lines.Every arrangement of approaching pseudo-lines has a dual generalized configuration of points with an underlying arrangement of approaching pseudo-lines. For the latter, we show:There are 2^{Theta (n^2)} isomorphism classes of arrangements of approaching pseudo-lines (while there are only 2^{Theta (n log n)} isomorphism classes of line arrangements).It can be decided in polynomial time whether an allowable sequence is realizable by an arrangement of approaching pseudo-lines. Furthermore, arrangements of approaching pseudo-lines can be transformed into each other by flipping triangular cells, i.e., they have a connected flip graph, and every bichromatic arrangement of this type contains a bichromatic triangular cell.

Ingensalinae subfam. nov. (Hemiptera: Fulgoromorpha: Fulgoroidea: Inoderbidae), a new planthopper subfamily from mid-Cretaceous Kachin amber from Myanmar

Abstract. The second genus and species of recently established planthopper family Inoderbidae, Ingensala xiai gen. et sp. nov., is described based on a well-preserved specimen from mid-Cretaceous Kachin (Burmese) amber, and it can be definitely attributed to Inoderbidae mainly based on its head structure, pronotum, and mesonotum without median and lateral carinae and tegmen venation. Ingensala gen. nov. is superficially similar to Eofulgoridium regarding its venation pattern, rather than to the Inoderbidae type genus Inoderbe, and further confirmed that Inoderbidae might descend from the Jurassic planthopper family Fulgoridiidae. The early fork of CuA and the stem CuA bearing many branches also can be found in Jurassic Qiyangiricaniidae and Eocene Weiwoboidae. Ingensala gen. nov. also superficially resembles some Tropiduchidae: Tropiduchinae. The new genus differs from the type genus Inoderbe to a large extent according to its wide head, frons without fastigium, antennae not so elongate, the tectiform condition of wings' position in repose, large, broad and translucent tegmen, triangular basal cell, single CuA1, legs covered with short setae, and the lack of filamentous wax on body. Therefore, two new subfamilies (Inoderbinae stat. nov. and Ingensalinae subfam. nov.) are established for these two genera respectively. The diversification in planthoppers could be the result of pressure of environmental changes during the mid-Cretaceous, and Inoderbidae provides more information for us to understand the Cretaceous stage of Fulgoroidea evolution and diversification.

Influencing Parameters on experimental and theoretical analysis of geocell reinforced soil

Soil reinforcement is one of the most popular ground improvement techniques used to improve the stiffness and strength of the soils for the past few decades. This would be achieved through different materials and techniques, and the recent versatile material is geocell reinforcement. Geocell is a three dimensional, polymeric honeycomb structure consisting of a square or triangular cells. Due to the confinement effect and honeycomb structure, geocell spreads the loads over its larger area, thus increasing the load-bearing capacity of the soil. Geocell is applied in various civil engineering fields namely enhancing the bearing capacity of retaining structures, foundations, roads and railways, controlling the erosion of steep slopes and river banks and reinforcing soft grounds. A good number of works have been carried out by the researchers to discuss the performance of geocell reinforcement through field studies and laboratory tests. In this paper, the possible utilization of geocell as reinforcement for pavement and its impact in geotechnical applications by studying the laboratory findings and case histories from the available literature are presented.

The influence of mounted assembly process on the stress-strain state of the lattice dome frame

The aim of the research - analysis of the stress-strain state of spherical lattice dome structure during mounted assembly process. The dome has a metal frame consisting of six repeating sectors with triangular grid cells. The mesh dome has five tiers in height. The study is devoted to establishing the dependence of the stress-strain state of the fully assembled frame of the lattice dome on the method mounted assembly. Methods. A computer model of the frame of the lattice dome made of steel I-beams in its design configuration has been developed. On its basis, assembly models of an incomplete frame for different stages of installation are created. For all models of the lattice dome frame, computer calculations were performed for the effect of the load from the own weight of its bars. As a result of calculations deformations, internal forces and stresses in the frame bars were determined at all stages of assembly, which were compared with those for the design configuration scheme. Results. Diagrams of deformations, moments and stresses in the bars of the dome frame at all stages of mounted installation are obtained. Comparative diagrams of installation and design stresses in the bars of the lattice dome are presented. The assessment of the installation stress state of the frame is given, and their inevitability and influence on the initial stress state of the lattice dome are noted.

A compact high-order gas-kinetic scheme on unstructured mesh for acoustic and shock wave computations

Following the development of a third-order compact gas-kinetic scheme (GKS) for the Euler and Navier-Stokes equations (Ji et al. (2020) [40]), in this paper a higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an unstructured triangular cell, which may involve the closest neighbors of neighboring cells. The compactness and high-order accuracy of the scheme are coming from the consistency between the high-order initial reconstruction and the high-order gas evolution model under GKS framework. The high-order evolution solution at a cell interface provides not only a time-accurate flux function, but also the time-evolving flow variables. Therefore, the cell-averaged flow variables and their gradients can be explicitly updated at the next time level from the moments of the same time-dependent gas distribution function. Based on the cell averaged flow variables and their cell-averaged derivatives, the nonlinear high-order compact reconstruction can be obtained for these variables in the evaluation of local equilibrium and non-equilibrium states. The current nonlinear reconstruction is a combination of WENO and ENO methodology, which is specifically suitable for compact GKS on unstructured mesh with a high-order (≥4) accuracy. The initial piecewise discontinuous reconstruction is used for the determination of non-equilibrium state and an evolved smooth reconstruction for the equilibrium state. The evolution model in GKS is based on a relaxation process from non-equilibrium to equilibrium state. The time-accurate gas distribution function provides the Navier-Stokes (NS) flux function directly without separating the inviscid and viscous terms, which simplifies the numerical discretization of the NS equations directly on unstructured mesh. Based on the time-accurate flux solver, the two-stage fourth-order time discretization can be applied to get a fourth-order time-accurate solution with only two stages, which reduces two reconstructions in comparison with the same order Runge-Kutta time stepping method. The current high-order GKS can uniformly capture acoustic and shock waves without identifying troubled cells and implementing additional limiting procedure. In addition, the fourth- up to sixth-order compact GKS can use almost the same time step as a second-order shock capturing scheme in most flow problems. The fourth-order GKS on unstructured mesh will be used in the computations from low speed incompressible viscous flow to the high Mach number shock interaction. The accuracy, efficiency, and robustness of the scheme have been validated. The main conclusion of the paper is that beyond the first-order Riemann solver, the use of high-order gas evolution model seems have advantages in the development of high-order schemes.

Preoperative design of flap based on computer-aided design technology: morphological flattening and analysis of three-dimensional wound

The shape of skin flaps is only described by swatches for preoperative design because of the irregular shape of skin wounds caused by trauma in the clinic. The method is rough, and the flaps cut often cannot match the wounds and affect their appearance. Computer-aided design technology helps to attain precise results in less time. This study proposes a skin wound morphological flattening algorithm based on hierarchical values. First, the skin wound is scanned by three-dimensional (3D) scanning technology to obtain a spatial mesh model consisting of triangular cells, and the mesh model is layered with a hierarchical value. Then, the layered mesh is topologically mapped to the plane. Subsequently, the stress and strain of the skin are simulated using a mechanical method, and the shape of the flattened skin wound is optimized layer by layer. Finally, the multiresolution smoothing technique is used to smooth the developed boundary contour and fit the curve to obtain a guidance plan for preoperative flap design. The results of the study showed that this method can accurately determine the shape of the skin wounds and quantitatively analyze the preoperative design results of the skin flaps. The average error of the area and edge length after flattening was reduced to less than 10%. The work is designed to realize the precise and individualized design of flap schemes before operation and to help standardize the preoperative design process.

Numerical and experimental study on the collapse of a triangular cell under compression

Lattice materials can be described as arrangements of cell walls such as beams with joints of high stiffness. Loads on the macroscopic level of the lattice material can cause a loss of structural stability on the microscopic level and lead to buckling of cell walls. In this study the buckling and post-buckling deformation of a triangular cell with elasto-plastic material behavior is investigated in finite element (FE) analyses under compressive loading. The triangular cell is discretized with beam elements and the outcome is compared to simulations using a fine mesh of continuum elements. Both discretizations are investigated in nonlinear FE simulations since regular linear stability analysis cannot consider elasto-plastic material behavior and contact. In addition, the collapse of the triangular cells is studied experimentally with selective laser melted samples. The beam element model is capable of predicting the collapse behavior as well as the reaction force determined in the experiments and FE analyses with continuum elements. By applying eigenmodes from buckling analyses as initial imperfection to the triangular cell the beam element model is able to predict mode changes in the post-buckling regime. The magnitude of imperfection is thereby in agreement with the geometrical deviation of the samples introduced by the selective laser melting (SLM) process. The outcome of the study is a methodology for investigating lattice materials computationally efficient with FE analyses and taking multiple nonlinearities into account. Consequently, it can be used to study two- or three-dimensional lattice structures with a large number of cell walls, nonlinear parent material and instability effects.

Crashworthiness optimization of a multicellular thin-walled tube with triangular cells

This article optimizes a multicellular thin-walled tube with N-equilateral triangles (MTTN), which was inspired from the microstructure of the cross-section of bamboo. The crashworthiness of MTTN under axial impact was analyzed, and the sensitivity analysis was conducted for the geometric parameters of MTT24, which exhibited the best crashing performance among MTTNs with N ≤ 30. It was found that the order in radial direction has a weak influence on the crashworthiness of MTT24, while the cell-wall thickness and the inner-tube diameter could significantly affect the crashworthiness of MTT24. Then, a multi-objective optimization was carried out for the MTT24 to further improve its crushing performance. The wall thickness and inner diameter of the thin-walled tube were selected as design variables, while the minimum peak crushing force (PCF) and the maximum specific energy absorption (SEA) were set as objectives. The obtained Pareto front enables the thin-walled tube to achieve the best possible crush resistance under the conditions of maximum SEA and minimum PCF. With a constraint of PCF ≤ 200 kN, the SEA and MCF of MTT24 were improved by 11.40% and 68.20%, respectively, compared with the benchmark.

Enhanced Fluid Dynamics in 3D Monolithic Reactors to Improve the Chemical Performance: Experimental and Numerical Investigation

Three-dimensional (3D) Fe/SiC monoliths with parallel interconnected channels and different cell geometries (square, troncoconical, and triangular) were manufactured by robocasting and used as catalytic reactors in hydroxylation of phenol using hydrogen peroxide to produce dihydroxybenzenes; the reaction was performed at Cphenol,0 = 0.33 M, Cphenol,0:CH2O2,0 = 1:1 M, WR = 3.7 g, T = 80–90 °C, and τ = 0–254 gcat·h·L–1 with water as a solvent. The values of the apparent kinetic rate constants demonstrated the superior performance of the triangular cell monoliths for hydrogen peroxide decomposition, phenol hydroxylation, and dihydroxybenzene production reactions. A computational fluid dynamic model was validated with the experimental results. It demonstrated that the triangular cell monoliths, with a lower channel hydraulic diameter and not-facing interconnections, provided a higher internal macrotortuosity that induced an oscillating flow of the liquid phase inside the channels, leading to an additional transverse flow between adjacent parallel channels. This behavior, not observed in the other two geometries, resulted in a better overall performance.