This study presents a comprehensive methodology, based on physics laws, for predicting the architecture of symmetric and asymmetric dendritic flow networks. These flow networks, found in vascular systems and respiratory trees, exhibit prefractal patterns that can be described by using recursive processes based on the concept of self-similarity, and the definition of a dimension that represents the degree of the system occupancy in space. Prefractal dendritic networks are thought that ensure the best possible access to flow transport. According to the second law of thermodynamics, the path with the lowest impedance uses the least amount of energy to perform its task. The methodology employed in this study is the minimizing of flow impedance within constraints. The constraints are defined as the path's volume and lateral area. The homothety ratios for sizes of the network that ensure maximum flow access are presented. We also examine the relationship between the fractality of dendritic flow networks and the design obtained from physical laws in this study. Based on the homothetic relations obtained here, the prefractal dimension is defined in terms of physics quantities, giving it meaning beyond the degree of space occupation and potentially shedding light on predicting issues in specific systems when the measured fractality differs from the predicted. Our study can be also very valuable in designing flow networks, which are crucial in the bioengineering sciences.

Volcanism is a fundamental planetary process, and understanding the dynamics of lava flows is critical for both hazard mitigation and geological studies. The final length and morphology of a lava flow are governed by a complex interplay between effusion rate, total volume, topography, and the lava's evolving thermo-rheological properties. While empirical power laws relating flow length to effusion rate or volume have proven useful, they do not fully capture the physical processes driving flow behavior, particularly the effects of crust formation and fragmentation. This paper presents an integrated theoretical framework that links macroscopic flow dynamics with the microscale processes of fragmentation. We begin by deriving scaling laws for flow length and width based on a Herschel-Bulkley fluid model. We then introduce a novel component to this framework by postulating that key rheological parameters evolve as a function of the flow's developing prefractal dimension, which quantifies its fragmentation and complexity. Finally, we propose a modified power law for the final flow length that accounts for energy dissipation due to both viscous shearing and the creation of new prefractal surfaces. By analyzing observational data from various basaltic to rhyolitic lava flows, we calibrate and discuss the model's empirical coefficients. The results demonstrate that highly fragmented lava flows like 'a'ā have their runout distance significantly reduced by the energetic cost of their increasing complexity, consistent with field observations. This framework provides a more physically robust foundation for forecasting lava flow behavior and interpreting their final morphologies.

This study presents a cohesive physical model that predicts lava flow morphology by establishing a quantitative link between a lava’s yield strength and its geometric complexity, measured by a prefractal dimension. The model is founded on the principle of symmetry, where the potential for fracturing and complexity peaks at an intermediate yield strength. This peak in complexity, observed with a predicted prefractal dimension (Dpf) of 1.15 for terrestrial ‘a’ā-like lava, arises from a critical state where a balance between gravitational driving forces and internal resistance allows for the formation of intricate margins. The model demonstrates that as lavas deviate from this optimal strength, becoming either too fluid (pāhoehoe, Dpf = 1.05) or too rigid (rhyolite, Dpf = 1.07), their morphology becomes progressively simpler, representing a symmetrical decline in complexity. Our approach also incorporates the overriding influence of topographic confinement and the temporal evolution of complexity as the lava cools. Validated against terrestrial lavas and successfully applied to lower-gravity environments, the model predicts a reduction in complexity for similar flows on Mars (Dpf = 1.13) and the Moon (Dpf = 1.09), providing a tool for interpreting volcanic processes grounded in the fundamental principles of symmetry and complexity.

The study of pedestrian dynamics, both individually and in groups, has been a highly active field for the last few decades. Dimensionless numbers in fluid dynamics are used to characterize flow patterns, identify the dominant forces, and predict results. Here, we argue that these dimensionless numbers can be also relevant to obtaining basic features of pedestrian dynamics. In this study, pedestrians moving freely and in an environment with other pedestrians are analyzed using dimensionless numbers. The development of a comfortable walking speed, the range of velocities that characterize walking and running forms of human gait, and the impact of pedestrian density on pedestrian speed are all investigated. Another important feature studied is the self-organization of a group of individuals, which is a vital concept in understanding crowd dynamics. Crowd dynamics and the interactions with other pedestrians are also investigated.

This study investigates the asymmetric effects applying heat transfer as a diagnostic tool in dendritic networks with symmetrical branching, characterized by the geometric property of self-similarity. Using a Computational Fluid Dynamics (CFD) model, we analyze five structural isomers of a three-level dichotomous branching network to evaluate the relationship between fluid dynamics, heat transfer, and geometric configuration. The main constraints are geometrical; that is, the volume at each branching level remains constant, and homothetic relationships respect the Hess–Murray law both for diameters and angles between sister tubes. The model considers an incompressible and stationary Newtonian fluid flow with Reynolds numbers ranging from 10 to 2000 and heat transfer in the range 1 to 1000 W/m2. Our results show that significant asymmetries in flow distribution and temperature profiles emerge in these symmetric structures, primarily due to the successive alignment of tubes between different branching levels. We found that the isomer with the lowest pressure drop is not the same as the one providing the most uniform flow distribution. Crucially, thermal analysis proves to be more sensitive than fluid dynamic analysis for detecting flow asymmetries, particularly at low Reynolds numbers less than 50 and q″ = 1000 W/m2. While heat transfer does not significantly alter the fluid dynamic asymmetry, its application as a diagnostic tool for identifying flow asymmetries is effective and crucial for such purposes.

The branching topology of tree networks has a considerable influence on the distribution of fluid flow inside them. Fluid flow asymmetry (an unequal distribution of fluid flow between the daughter tubes) can arise in geometrically symmetric branches. It is important to be able to pinpoint the reason for this, which is still not fully understood. This study compares tree flow network designs with the same number of tubes of equal sizes but attached to one another various directions, i.e., network isomers. The flow resistance and fluid flow distribution assessment within the networks are calculated based on the computational fluid dynamics results. This study shows, among other results, that the flow asymmetries are more noticeable at higher bifurcation levels, and the performance of tree designs is highly dependent on how the tubes are arranged in the network, especially how they are aligned at different levels of bifurcation. Practical guidelines that can immediately produce significant insights into the relationship between the incidence of asymmetry in the flow and alignments of the tubes between levels are defined. The findings of this study will be useful to designers in improving the design and management of these networks.

In this paper, a numerical study of fluid flow through perforated panels with square holes and open-cell material with cubic cells is presented. Structures with a wide variety of porosities (0.15<φ<0.94) and Reynolds numbers (0.01

Because arteries transport blood that is rich in nutrients and oxygen to cells, its narrowing or obstruction can affect how well tissues are nourished. The hemodynamic patterns of these vessels have a significant impact on their structural stability and long-term patency. Bypass grafts are used to circumvent stenotic arteries. Here, blood flow through a stenosed coronary bypass with size constraints is studied. The effect of graft-vessel(host) diameter ratio, degree of stenosis, and blood flow ranging from resting to active conditions is examined. A three-dimensional computational fluid dynamics study was performed to examine a stenosed artery with different bypass designs. The absence of a volume constraint for the graft can lead to unrealistic predictions. Therefore, in the present study, we carefully accounted for the restriction on graft volume, recognizing that the space available for the bypass graft is not boundless. In addition, the Carreau-Yasuda model was used to study blood flow. Blood velocity and shear stress profiles and blood flow resistance are investigated in a grafted blood vessel with varying degrees of stenosis and graft-to-vessel diameter ratios at various Reynolds numbers. The velocity and distribution of shear stress distributions for various blood flow rates are obtained, and blood flow resistances are calculated. It can be observed that recirculation zones can form in stenosed vessels, especially in more severe degrees of stenosis. It is only safe for lower degrees of stenosis to keep the stenosed region of the vessel permeable to blood flow, both in terms of not being significantly different from flow conditions in a healthy vessel and the structural integrity of the graft. The appropriate design for the bypass graft must consider not only the value of resistance to blood flow but also the stresses that are produced in the walls. Therefore, both these key quantities have a significant impact on abidance and patency following artery bypass surgery.

The branching topology of tree networks has a considerable influence on the distribution of fluid flow inside them. Fluid flow asymmetry (an unequal distribution of fluid flow between the daughter tubes) can arise in geometrically symmetric branches. It is important to be able to pinpoint the reason for this, which is still not fully understood. This study compares tree flow network designs with the same number of tubes of equal sizes but attached to one another in various directions, i.e., network isomers. The flow resistance and fluid flow distribution assessment within the networks are calculated based on the computational fluid dynamics results. This study shows, among other results, that the flow asymmetries are more noticeable at higher bifurcation levels, and the performance of tree designs is highly dependent on how the tubes are arranged in the network, especially how they are aligned at different levels of bifurcation. Practical guidelines that can immediately produce significant insights into the relationship between the incidence of asymmetry in the flow and alignments of the tubes between levels are defined. The findings of this study will be useful to designers in improving the design and management of these networks.

A blood vessel bypass is a common way to restore blood flow due to blocked or narrowed arteries allowing oxygen-rich blood to be routed to the tissues. Herein, using a three-dimensional numerical simulation, the response of various vessel bypass designs to blood flow under size-limiting constraints is explored and compared to the flow in healthy arteries. Finding the best design requires a size constraint in the analysis; otherwise, the result is a configuration with excessive size in a limited allocated space, which represents a waste of material and an unnecessary space occupied by it. This study unveils the geometrical features of bypass grafts that have structural integrity while also minimizing the rate of entropy generation under volume constraint (constructal design). In a stenosed vessel with a bypass, the effect of bypass geometry, graft-vessel(host) diameter ratio, and stenose degree is analyzed and compared to a healthy vessel. This study concludes, among other things, that leaving the stenosed region of the vessel permeable to blood flow is only safe if the degree of stenosis is less than 0.5, both in terms of not being significantly different from flow conditions in a healthy vessel and also in terms of the structural integrity of the graft. The results presented here can be applied to any bypass graft and provide designers and practitioners with basic information.

The tracheobronchial tree is commonly seen to have a systematic branching symmetry, despite being known to have an asymmetrical design. Branching asymmetry allows for uniform airflow and provides robustness against the morphogenesis-related size variability. Here, a constructal approach is used to tracheobronchial tree analysis, and a general model based on entropy generation during breathing process is provided, which holds with asymmetric characteristics of the tree, and the change for inhaling and exhaling air. In contrast to traditional models available in the literature, the entropy generation of inspiration and expiration processes is compared for symmetry and asymmetric designs. This approach unravels the fundamental consequences of asymmetric constraint in the process of breathing and provides justification for the tracheobronchial tree having the same number of bifurcation levels as optimized symmetrical trees.

The ability and efficiency to dissipate heat is strongly dependent on the design of heat exchanger. Bifurcating systems are the solutions to fundamental access-maximisation problems. The performance of a forced-air heat sink with single Y-shaped, double Y-shaped and X-shaped configurations of tubes is investigated in this work. A 3-D numerical study is performed at Reynolds numbers (Re) ranging from 5 to 1,500, under a constant heat source. The study mainly focuses effect of the design of tube configurations on both the thermal and hydraulic performances. Among these configurations the optimal thermo-hydraulic performance against Re is determined. The deposition of particles from flowing air on wall of tubes may be detrimental for both thermal and hydraulic performances. The effect of particle size and Re number on deposition rates is also investigated.

Flow networks with dendritic tube organization are common in natural systems. Although the Hess-Murray law has been extensively reported in the literature, there have also been reports of systems that deviate from this law. Using 3D dendritic flow networks of tubes, this study compares designs with various homothety reduction factor for diameters and lengths of tubes. The geometric constraint that is applied to these networks is equal tube volume at each branching level. The assessment is based on the flow resistance of networks calculated based on the Computational Fluid Dynamics (CFD) results. This study shows, among other things, that the performance of dendritic designs is highly dependent on the geometric features such as the svelteness of the network, and on tube alignment at different levels of bifurcation. It is also worth mentioning that flow asymmetry can develop in the dendritic networks that are symmetrical in terms of design. These findings should be considered while designing networks for engineering systems.

Studies suggest that both the size of airways and the number of bifurcations of the respiratory tree provide the best structural design to accomplish its function. However, constrictions and occlusions due to inflammation and pulmonary edema of the airways can inhibit normal air flowing through the respiratory tree, affecting gas exchange. It results in heterogeneity in gas exchange (and pulmonary perfusion) with adverse risk factors. In this study, we propose a methodology based on the airway tree admittance (reciprocal of impedance) to study this problem. This methodology is distinct from the traditional quantification, based on overall impedance using lump parameter models, and applies to a matrix formed by admittances of each airway of the entire conducting part of the bronchial tree. The generated system admittance matrix is highly sparse in nature, and thus to solve the same system, a modified block-based LU decomposition method is proposed to improve the space-time tradeoff. Our approach enables the determination of the local ventilation pattern and reduces the misevaluation, mainly in the cases that characterize the early-stage obstructive disorders. The key finding of the present study is to show that how the position and intensity of local obstruction in an airway can affect the overall as well as regional ventilation which can lead to impaired gas exchange.

In this article, the significant characteristics of wave transmission and boundary layer influence are studied for an incompressible fluid flowing through a long elastic tube using lumped parameter model. An ameliorated version of the lumped parameter model is derived, where the flow impedance is linked with Womersley number to understand the phenomena of fluid wall interaction, especially in human airways. To analyze the flow phenomena through tubes, the flow governing equations are transformed through the Bessel series. We have observed that for the low value of Womersley number, there is a phase difference between pressure and flowrate, which produces a frequency-dependent flow impedance. The physiological relevance of this result is especially shown in the nasal-pharynx during breathing. The results are validated by ansys-based numerical simulation as well as by experimental results.

Microfluidic devices have many attractive qualities such as low cost, small size, and in-field use. Micromixers are very important components of these devices because affect their efficiency. In a passive mixer, the structural characteristics of the mixer are crucial and must be analyzed. This paper presents a numerical study of the mixing in passive Y-shaped micromixers with a spherical mixing chamber for a volume constrained system. The effect of asymmetric bifurcated ducts, the angle in between the inflow ducts, eccentricity and, obstacles inserted in the mixing sphere, on the mixing efficiency and flow impedance is evaluated. Vortical structures characteristics and the possible occurrence of engulfment are also identified. The results show that flow impedance (pressure drop for unit volumetric flow rate) can be decreased greatly for the same mixing efficiency as the volume of the spherical mixing chamber is 20% of the total volume. Insertion of the obstacles into the sphere mixing chamber decreases the mixing efficiency while they increase the flow impedance. The results also show that spherical mixing chamber enhances mixing efficiency while decreasing flow impedance if the volume reserved for it is greater than a limit value which depends on the diameter and length scale ratios in between the mother and daughter ducts as well as the total volume. Overall, the paper documents the variation of mixing efficiency and flow impedance based on the geometrical parameters of three-dimensional asymmetric passive micromixer with sphere mixing chamber.

The occurrence of flow pattern can be predicted based on constructal law. Scale analysis is a method for deriving the essential information based on the basic principles of fluid flow and heat transfer. It provides order-of-magnitudes but also the form of the functions that describe the quantities understudy. In flow systems, patterns (configuration, design, architecture) arise from competition between competing trends, at least two modes of transport or locomotion: slow (diffusion, walk, etc.) and fast (streams, run, etc.). Optimal patterns mean the best flow access and the best balance between these trends. The study presented here follows from the scale analysis together with constructal and, is illustrated by examples from simple water heating to human locomotion.

Liquid-cooled hot plates require effective thermal management which can be accomplished by implementing appropriate cooling architectures. This investigation is about high heat-generating systems and reports the performance of heated plates with various cooling flow configurations: Serpentine flow, parallel tubes flow, and two tree-shape flow systems. Single and double objectives with size constraint are studied to obtain the best design. The influence of fluid inlet position is also studied. The results are presented in terms of hydraulic and thermal characteristics for plates that is subject to a constant heat flux, and contain tubes with fixed total lateral area for cooling. A 3D numerical study is conducted to analyze the performance of these systems for Reynolds numbers ranging from 1000 to 33,000. The results obtained include temperatures of the plate, uniformity of temperature of the plate, fluid flow resistance and heat dissipation. Dimensionless parameters are identified to characterize the thermal performance, hydraulic performance, and hydrothermal performance as a function of the Reynolds number. The results show that a tree-shaped flow network of tubes inserted in the plate with inlet placed at the center of the plate presents the best cooling performance, with more cooling capacity and less flow resistance (and pumping power).

Evidence supports the interpretation that natural dendritic networks are described by fractal theory. It is recognised that the fractal description alone is not a complete description of nature of space filling. This study addresses the fundamental question of what the size of dendritic flow networks should be, in order to perform with the least irreversibilities, in addition to what fractal features-based pattern should have. Optimal shapes of symmetric and asymmetric networks for viscous flow and diffusion with junction loss effects are analysed based on exergy minimisation rate. Global size constraints included in the analysis are the volume and surface area. The optimal sizes of the flow networks are obtained, and prefractal dimensions that characterise these networks are computed. It is shown that the prefractal dimensions depend on both fluid transport mechanisms and space constraints. The physics link between prefractal regularity and optimal flow performance is clear presented.