The unstable fluid–fluid displacement patterns in porous media with rough invasion fronts and trapping of the defending phase are often observed in drainage, i.e. when the solid is non-wetting to the ...invading phase. On the other hand, during imbibition, compact and faceted growth is expected in regular porous media with geometrically homogeneous pore structure. Here, we report the irregular growth of invading fluid during the imbibition process in two-dimensional regular porous media. The ramified invasion morphology associated with thin fingers is reminiscent of capillary fingering. Through examining the capillary pressure signals and the type of pore-scale invasion mechanisms, the fundamental differences between faceted growth and irregular invasion are revealed. By analysing the pore-scale invasion mechanisms, a phase diagram describing the dominance of different invasion events is proposed. Through conducting systematic quasi-static radial injection simulations across a wide range of porosity and wettability, excellent agreement is observed on the transition boundary from faceted and compact displacement patterns to irregular and dendritic invasion morphologies. This is reflected by the overlap of the transition boundaries from analytical prediction, type of pore-scale invasion events, and macroscopic morphology quantified by the fractal dimension. This work provides new insights on the role of geometrical features of solid structures during multiphase flow with emphasis on the porosity and wettability. The findings could assist in guiding the design of microfluidic devices to control deterministically the multiphase flow, transport and reaction processes.
We study numerically the characteristics of fluid–fluid displacement in simple mixed-wet porous micromodels using a dynamic pore network model. The porous micromodel consists of distinct water-wet ...and oil-wet regions, whose fractions are varied systematically to yield a variety of displacement patterns over a wide range of capillary numbers. We find that the impact of mixed-wettability is most prominent at low capillary numbers, and it depends on the complex interplay between wettability fraction and the intrinsic contact angle of the water-wet regions. For example, the fractal dimension of the displacement pattern is a monotonically increasing function of wettability fraction in flow cells with strongly water-wet clusters, but it becomes non-monotonic with respect to wettability fraction in flow cells with weakly water-wet clusters. Additionally, mixed-wettability also manifests itself in the injection pressure signature, which exhibits fluctuations especially at low wettability fraction. Specifically, preferential filling of water-wet regions leads to reduced effective permeability and higher injection pressure, even at vanishingly small capillary numbers. Finally, we demonstrate that scaling analyses based on a weighted average description of the overall wetting state of the mixed-wet system can effectively capture the variations in observed displacement pattern morphology.
Migratory cells transition between dispersed individuals and multicellular collectives during development, wound healing, and cancer. These transitions are associated with coordinated behaviors as ...well as arrested motility at high cell densities, but remain poorly understood at lower cell densities. Here, we show that dispersed mammary epithelial cells organize into arrested, fractal-like clusters at low density in reduced epidermal growth factor (EGF). These clusters exhibit a branched architecture with a fractal dimension of Df
= 1:7, reminiscent of diffusion-limited aggregation of nonliving colloidal particles. First, cells display diminished motility in reduced EGF, which permits irreversible adhesion upon cell–cell contact. Subsequently, leader cells emerge that guide collectively migrating strands and connect clusters into space-filling networks. Thus, this living system exhibits gelation-like arrest at low cell densities, analogous to the glass-like arrest of epithelial monolayers at high cell densities. We quantitatively capture these behaviors with a jamming-like phase diagram based on local cell density and EGF. These individual to collective transitions represent an intriguing link between living and nonliving systems, with potential relevance for epithelial morphogenesis into branched architectures.
Permeability is a required parameter for studying aquifer properties. However, for sandstone aquifers with low permeability, it is difficult to measure permeability directly through experiments. ...Based on fractal theory and the J function, a new method to calculate the permeability of a sandstone aquifer is derived. This work first solves the J function under each water saturation according to its definition. Combined with mercury pressure data, the J function and logarithmic curve equation of water saturation are then fitted by the drawing method, and the fractal dimension and tortuosity of the aquifer are further solved. Finally, the aquifer's permeability is calculated using the new permeability calculation method. To verify the accuracy of the proposed method, 15 rock samples from the Chang 7 Group, Ordos Basin, are taken as research objects. The permeability is calculated using the new method combined with mercury injection data and aquifer characteristic parameters, and the results are compared with the real permeability. The relative error of most samples is <20%, which shows the permeability calculated by this method is accurate and reliable. The effects of fractal dimension, tortuosity, and porosity on permeability are also analyzed.
Surface texture of an image plays an imperative role in understanding objects such as aggregates, woods, grains, soils, trees, and houses. Fractal dimension (FD) helps to characterise these objects ...by quantifying their complex texture patterns. Differential box counting (DBC) is one of the popularly used methods to measure FD of a gray-scale image. However, it suffers from several limitations. So, this study introduces three improved DBC methods using three box heights based on eigenvalue, kurtosis, and skewness of an image respectively. These methods also use a new xy-plane shifting mechanism and a modified formula for computing nr. Moreover, weighted least squares (WLS) regression is adopted, where a trapezoidal membership function (TMF) based rule is proposed for assigning weights to each grid size. The image surface exhibits multifractal nature, hence two multifractal analysis methods are also analysed and included in the experiments. All the experiments are performed on three gray-scale image databases viz., the synthesized Fractal Brownian motion (FBM) images, natural texture images of Brodatz database, and images of Outex database that are captured at different rotations. Experimental results show that the proposed methods outperform some of the state-of-the-art methods.
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•Surface texture analysis of an image is done based on fractal dimension (FD).•FD is computed using an improved differential box counting method.•This work addresses the over-counting problem along z-direction.•The under-counting problem along xy-directionis is also solved using a xy-plane shiftiting mechanism.•Weighted least squares regression is utilized to obtain a better fitted line.
We investigate the dynamics of cohesive particles in homogeneous isotropic turbulence, based on one-way coupled simulations that include Stokes drag, lubrication, cohesive and direct contact forces. ...We observe a transient flocculation phase, followed by a statistically steady equilibrium phase. We analyse the temporal evolution of floc size and shape due to aggregation, breakage and deformation. Larger turbulent shear and weaker cohesive forces yield smaller elongated flocs. Flocculation proceeds most rapidly when the fluid and particle time scales are balanced and a suitably defined Stokes number is $O(1)$. During the transient stage, cohesive forces of intermediate strength produce flocs of the largest size, as they are strong enough to cause aggregation, but not so strong as to pull the floc into a compact shape. Small Stokes numbers and weak turbulence delay the onset of the equilibrium stage. During equilibrium, stronger cohesive forces yield flocs of larger size. The equilibrium floc size distribution exhibits a preferred size that depends on the cohesive number. We observe that flocs are generally elongated by turbulent stresses before breakage. Flocs of size close to the Kolmogorov length scale preferentially align themselves with the intermediate strain direction and the vorticity vector. Flocs of smaller size tend to align themselves with the extensional strain direction. More generally, flocs are aligned with the strongest Lagrangian stretching direction. The Kolmogorov scale is seen to limit floc growth. We propose a new flocculation model with a variable fractal dimension that predicts the temporal evolution of the floc size and shape.
Experimental parameters have direct influences on materials properties and therefore their applications. The effect of plasma power on the properties of cobalt oxide thin films, prepared using ...plasma-enhanced chemical vapor deposition technique, on stainless steel substrates have been addressed in this paper. The structural, morphological, and compositional properties of these films were investigated by means of X-ray diffraction (XRD), atomic force microscopy (AFM), and X-ray photoelectron spectroscopy (XPS) technique. The XRD patterns demonstrated the growth of polycrystalline Co
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thin film with a cubic spinel structure such that the intensity of (511) and (311) peaks increase as the plasma power increases to 100 W. It is observed that crystallite size increases by increasing the plasma power and the maximum crystallite size is found to be 64.8 nm for 100 W. The AFM results illustrate that the surface roughness and grain size increase by increasing the plasma power, and the film deposited at lower plasma power has more uniform and smoother surface, mainly owing to the increase in surface diffusion that in turn causes the coalescence of the grains. The results of XPS spectra indicated the formation of Co
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thin films on stainless steel substrates and there were no other elements other than Co, O in the XPS spectra. Additionally, stereometric analysis and fractal dimension of the 3-D surface microtexture of the AFM micrographs were analyzed and the Kolmogorov–Smirnov test was used to assess the normal distribution of quantitative variables. The results of statistical analysis corroborated the experimental results and proved that the surface roughness increased upon an increase in plasma power. Moreover, the corrosion behavior and the surface morphology of the cobalt oxide thin films were investigated using the potentiodynamic method and scanning electron microscopy. The results of these analysis proved that as the plasma power increases the corrosion resistance improves against the H
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. The sample which deposited at 100 W plasma power has the minimum corrosion current and the corrosion resistance of steel substrate was improved by controlling the anodic reactions resulted from a protective Co
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thin film. These results are useful for building and designing stainless steel devices in corrosive environments.
After an earthquake, the residual stiffness and strength of structural elements are typically estimated based on a qualitative visual inspection of cracks that is prone to error. In this paper a new ...approach is proposed to automatically estimate the updated stiffness and strength of damaged unreinforced masonry walls by characterization of crack patterns by a mathematical index. It is shown that structural and textural fractal dimensions of a crack pattern reflect the extent of cracking and the type of cracking or crushing, i.e., whether the cracks pass through joints or whether bricks have been damaged and crushed. Using results of six quasi-static cyclic tests on unreinforced brick masonry walls with different failure modes at various drift ratios, it is shown that the structural and textural fractal dimensions of the crack patterns are an accurate predictor of the stiffness and strength degradation. This procedure seems therefore a promising approach for replacing the traditional assessment methods that are based on visual inspection and engineering judgment by an analytical procedure based on image processing that can eventually be completely automated.
•Crack branching is a phase in asphalt mixture crack propagation.•The diagonal crack and the splitting crack coexist in the crack propagation phase of asphalt mixture.•There were eight crack ...branching modes in the asphalt mixtures.•The fractal dimension of crack branching paths ranged from 1.14 to 1.64.
Crack branching is a multi-crack propagation problem. Singular crack tip elements are frequently encountered, and defining the multi-crack tips’ enrichment functions is difficult. To overcome these drawbacks, this study used an already developed ordinary state-based peridynamics method to simulate crack branching in AC-13, AC-20, and PAC-13 asphalt mixtures. These asphalt mixtures’ digital images were acquired by an X-ray computed tomography method. Next, the Prony series coefficients of the fine asphalt mixtures were obtained by the dynamic modulus test. After that, the fracture energy of the fine asphalt mixtures was measured by the semi-circular bending test. Finally, the measured asphalt mixture properties were input into the ordinary state-based peridynamics method in order to simulate crack branching in the AC-13, AC-20, and PAC-13 asphalt mixtures. The simulation results indicate that the diagonal crack first emanates in asphalt mixtures. Then, the diagonal crack continues to branch into a wing crack, splitting crack, and branched crack. These four types of cracks can generate eight crack branching categories in asphalt mixtures. The crack branching trajectory was quantified by the fractal dimension, whose value ranged from 1.14 to 1.64. The physical significance of the fractal dimension explains the changes of crack branching paths in the asphalt mixtures.
Thanks to the continuous development of light-curing resin composites it is now possible to print permanent single-tooth restorations. The purpose of this study was to compare resin composites for ...milling -Gandio Blocks (GR), Brilliant Crios (CR) and Enamic (EN) with resin composite for 3D printing—Varseo Smile Crown plus (VSC). Three-point bending was used to measure flexural strength (σf) and flexural modulus (Ef). The microhardness was measured using a Vickers method, while fractographic, microstructural, texture and fractal dimension (FD) analyses were performed using SEM, optical microscope and picture analysis methods. The values of σf ranged from 118.96 (±2.81) MPa for EN to 186.02 (±10.49) MPa for GR, and the values of Ef ranged from 4.37 (±0.8) GPa for VSC to 28.55 (±0.34) GPa for EN. HV01 ranged from 25.8 (±0.7) for VSC to 273.42 (±27.11) for EN. The filler content ranged from 19–24 vol. % for VSC to 70–80 vol. % for GR and EN. The observed fractures are typical for brittle materials. The correlation between FD of materials microstructure and Ef was observed. σf of the printed resin depends on layers orientation and is significantly lower than σf of GR and CR. Ef of the printed material is significantly lower than Ef of blocks for milling.
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