An assessment of branching asymmetry of the tracheobronchial tree.

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.

Optimal Branching Structure of Fluidic Networks with Permeable Walls.

Biological and engineering studies of Hess-Murray's law are focused on assemblies of tubes with impermeable walls. Blood vessels and airways have permeable walls to allow the exchange of fluid and other dissolved substances with tissues. Should Hess-Murray's law hold for bifurcating systems in which the walls of the vessels are permeable to fluid? This paper investigates the fluid flow in a porous-walled T-shaped assembly of vessels. Fluid flow in this branching flow structure is studied numerically to predict the configuration that provides greater access to the flow. Our findings indicate, among other results, that an asymmetric flow (i.e., breaking the symmetry of the flow distribution) may occur in this symmetrical dichotomous system. To derive expressions for the optimum branching sizes, the hydraulic resistance of the branched system is computed. Here we show the T-shaped assembly of vessels is only conforming to Hess-Murray's law optimum as long as they have impervious walls. Findings also indicate that the optimum relationship between the sizes of parent and daughter tubes depends on the wall permeability of the assembled tubes. Our results agree with analytical results obtained from a variety of sources and provide new insights into the dynamics within the assembly of vessels.

Penetration of inhaled aerosols in the bronchial tree.

It has long been recognized that the pattern of particle deposition in the respiratory tree affects how far aerosols penetrate into the deeper zones of the arterial tree, and hence contribute to either their pathogenic potential or therapeutic benefit. In this paper, we introduce an anatomically-inspired model of the human respiratory tree featuring the generations 0-7 in the Weibel model of respiratory tree (i.e., the conducting zone). This model is used to study experimentally the dynamics of inhaled aerosol particles (0.5-20µm aerodynamic diameter), in terms of the penetration fraction of particles (i.e., the fraction of inflowing particles that leave the flow system) during typical breathing patterns. Our study underline important modifications in the penetration patterns for coarse particles compared to fine particles. Our experiments suggest a significant decrease of particle penetration for large-sized particles and higher respiratory frequencies. Dimensionless numbers are also introduced to further understand the particle penetration into the respiratory tree. A decline is seen in the penetration fraction with decreasing Reynolds number and increasing Stokes number. A simple conceptual framework is presented to provide additional insights into the findings obtained.

Toward an optimal design principle in symmetric and asymmetric tree flow networks.

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies.

Physics' insights into pedestrian motion and crowd dynamics: reply to comments on "The emergence of design in pedestrian dynamic: locomotion, self-organization, walking paths and constructal law".

Pedestrians' world is not a static one, but rather one which is constantly in flux. The pedestrian dynamics is subject to a wide range of influences and displays an interesting phenomenology. Along with collective self-organization phenomena (e.g., streams of people, rivers of people, collective synchronization), there are also a multitude of applications in the context of crowd management, design of pedestrian facilities and urban planning. Here, I address comments from the discussants of my review paper from the viewpoint of elementary physics laws paying particular attention to the self-organization phenomena in crowds.

The emergence of design in pedestrian dynamics: locomotion, self-organization, walking paths and constructal law.

Gait is inherent to human life and hence its importance is often overlooked. But walking remains the most basic form of transportation and almost all journeys begin and end with a walk, regardless of the modes used in-between. Gaining a good understanding of pedestrian's dynamics is thus a crucial step in meeting the mobility and accessibility needs of people by providing safe and quick walking flows. This paper presents a critical and integrative review of research on pedestrian's dynamics and associated topics. The review focuses on comprehensive theories and models, with an emphasis on the advances made possible by the application of the constructal law. Constructal law points out that the emergence and evolution of design in pedestrian dynamics is analogous to that of animate flow systems. Most importantly, it also highlights that the basic features of pedestrian dynamics and supportive walking infrastructures can be optimally envisaged with the help of a few fundamental physics laws.

Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions.

This paper explores a new application of the constructal theory, namely in describing and predicting the formation of dissimilar patterns inside elements of the same species under different hydrodynamics conditions. Our study proposes an explanation for the differences found in morphology of stony corals, bacterial colonies and plant roots. It specially provides an answer to the following question: have their shapes (architecture) been developed by chance, or do they represent the optimum structure serving their ultimate purpose? We show that in order to persist in time, these systems must evolve in such a way that an easy access to nutrients is ensured: their shapes develop in such a way as to minimize the time to reach the nutrient source. Moreover, it is also shown that it is the combination of a dispersive (diffusive) and a convective mechanism that allows for the maximization of nutrient transfer through use of the best of these mechanisms at a specific time. In the light of this outcome, it is straightforward to conclude why the existence of an optimal architecture makes sense: it is because there is an overriding natural tendency and because the system has the freedom to morph its shape in the search for an optimal attainment of this goal within a set of constraints imposed by the situation.

Aerosol particle deposition and distribution in bifurcating ventilation ducts.

The quantitative information gained from detailed studies of particle deposition in ducts is important, for example, to evaluate human exposure to particles within buildings, implement cleaning strategies for ventilation ducts and also understand particulate deposition in the respiratory tree. For this purpose, an experimental study for aerosol particles of diameters ranging from 8.1 to 23.2 microm was conducted in a curved bifurcating ventilation duct. At the bend segment of the duct, the particle size, bend angle, curvature ratio and Reynolds number affect aerosol deposition significantly. On the other hand, tests conducted on the bifurcating segments show that deposition increases with particle size and Reynolds number. Accumulation of particles occurs mainly around the bend segment and the ridge of carina of the bifurcation. In all segments of the duct models, particle deposition is found to be enhanced with increasing humidity which increases from 66 to 95% (i.e., close the saturation). A physical interpretation of the results obtained is also presented.