Constructal theory

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Design in nature is flow. The two sides of the constructal law: we predict the occurrence of design in nature, and we design devices for human use.

The constructal law puts forth the idea that the generation of design (configuration, pattern, geometry) in nature is a physics phenomenon that unites all animate and inanimate systems, and that this phenomenon is covered by the Constructal Law. The constructal law was stated by Adrian Bejan in 1996 as follows: "For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it."

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The tree is the natural design for achieving flow access between one point and a volume. Alternating trees achieve flow access between two planes. Natural porous media exhibit multi-scale flow structures consistent with the multiple scales and performance of alternating trees.

Constructal Law

The constructal law was stated by Bejan in 1996 as follows: "For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it."

"Constructal" is a word coined by Adrian Bejan, coming from the Latin verb construere, to construct, in order to designate the natural tendency of flow system (rivers, trees and branches, lungs and also the engineered forms) to morph in a constructal evolutionary process toward greater and greater flow access in time.

The constructal law was proposed in 1996 as a summary of all design generation and evolution phenomena in nature. The constructal law represents three steps toward making “design in nature” a concept and law-based domain in science:

1. Life is flow: all flow systems are live systems, the animate and the inanimate.
2. Design generation and evolution is a phenomenon of physics.
3. Designs have the universal tendency to evolve in a certain direction in time.

The constructal law is a first principle of physics that accounts for all design and evolution in nature. It holds that shape and structure arises to facilitate flow. The designs that arise spontaneously in nature reflect this tendency: they allow entities to flow more easily – to measurably move more current farther and faster for less unit of useful energy consumed. Rain drops, for example, coalesce and move together, generating rivulets, streams and the mighty river basins of the world because this design allows them to move more easily. The constructal law asks the question: Why does this design arise at all? Why can't the water just seep through the ground? The constructal law provides this answer: Because the water flows better with design. The constructal law covers the tendency of nature to generate designs to facilitate flow.

The constructal law proclaims that this is why we find a similar tree-like structure in all designs that move a current from a point to an area or an area to a point. The lightning bolts that flash across the sky generate a tree-like structure because this is a good design for moving a current (electricity) from an area (the cloud) to a point (a church steeple or another cloud). The circulatory and nervous systems of biological creatures generate a similar tree-like design because they too are moving currents from a point to an area and from an area to a point.

Although treelike structures are a very common design in nature, they are only one manifestation of the constructal law. In a simple example, logs floating on a lake or icebergs at sea orient themselves perpendicular to the wind in order to facilitate the transfer of motion from the moving air body to the water body. A more complex example is the design of animals that have evolved to move mass better and better (to cover more distance per unit of useful energy) across the landscape.

This includes the seemingly “characteristic” sizes of organs, the shape of bones, the rhythm of breathing lungs and beating hearts, of undulating tails, running legs, and flapping wings. The constructal law proclaims that all these designs have arisen—and work together—to allow animals, like raindrops in a river basin, to move more easily across a landscape. Because human beings are not separate from but a part of nature, their designs are also governed by the constructal law.

The constructal law defines the time direction of all evolutionary design phenomena. It states that designs should evolve, acquiring better and better configurations to provide more access for the currents that flow through them. It defines in physics terms what it means to be “fittest”, to “survive”, and to be efficient. Not all changes are improvements, but those that stick measurably enhance flow. The constructal law states that design generation and evolution are macroscopic physics phenomena that arise naturally to provide better and better flow access to the currents that run through them. This occurs at every scale. Each component of an evolving flow system—each rivulet, each tree, each road—acquires evolving designs to facilitate flow access. As these elements coalesce into larger and larger structures (into evolving river basins, forests and transport networks), a hierarchy emerges such that the varying sized components work together so that everything flows more easily. This is seen in the shape and structure of the neural networks in the brain, of the alveoli in the lung, the size and distribution of vegetation in the forest and of human settlements on the map.

In the big picture, all the mating and morphing flows on the largest system that surrounds us, the Earth itself, evolve to enhance global flow. For example, trees and other forms of vegetation that move moisture from the ground to the air are components of the larger global system, including forests, river basins and weather patterns, that have the tendency to equilibrate all the moisture on Earth. The constructal law states that every flow system is destined to remain imperfect. The direction of design evolution is toward distributing the imperfections of the system, such that the “whole” flows easier (e.g., river basin, animal body, human vehicle). Evolution never ends. Optimality statements (minimum, maximum, optimum, end design, destiny), have no place in constructal theory. Nature does not move toward an optimal end design. The natural phenomena is not the elimination but the distribution (better and better over time) of imperfection. The distribution of imperfection generates the geometry (shape, structure) of the system.

For example, in point-area and point-volume flows, constructal theory predicts tree architectures, such flows displaying at least two regimes: one highly resistive and one with lower resistivity. The constructal-law tendency manifests itself at every scale.

Some domains of application

Application	What flows	Tree channels: Low Resistivity	Interstitial spaces: High Resistivity
Packages of electronics	Heat	High-conductivity inserts (blades, needles)	Low conductivity substrate
Urban traffic	People	Low-resistance street car traffic	Street walking in urban structure
River basins	Water	Low-resistance rivulet and rivers	Darcy flow through porous media
Lungs	Air	Low-resistance airways, bronchial passages	diffusion in alveoli tissues
Circulatory system	Blood	Low-resistance blood vessels, capillaries, arteries, veins	diffusion in capillaries tissues

The constructal law provides a unifying theory of evolution. It holds that inanimate and animate phenomena generate evolving configurations to move more easily. The constructal law also provides a new definition of what it means to be alive. It states that life means flow and the free generation of design. If the flows stop, the system is dead (in thermodynamic equilibrium). The constructal law is the physics law of life and evolution.

Constructal Thermodynamics

Thermodynamics rests on two laws. Both are first principles: The first law commands the conservation of energy, and the second law summarizes the tendency of all currents to flow from high (temperature, pressure) to low. These two laws are about systems in the most general sense, viewed as black boxes, without shape and structure.

The two laws of thermodynamics do not account for nature completely. Nature is not made of black boxes. Nature’s boxes are filled with configurations—even the fact that they have names (rivers, blood vessels) is due to their appearance, pattern, or design. Where the second law commands that things should flow from high to low, the constructal law commands that they should flow in configurations that flow more and more easily over time.

Classical thermodynamics versus constructal thermodynamics

Thermodynamics	Constructal theory
State	Flow architecture (flow structure)
Process	Change of structure (design change)
Properties	Global objective and global constraints
Equilibrium state	Equilibrium flow architecture
Fundamental relation	Fundamental relation
Constrained equilibrium states	Nonequilibrium architectures
Removal of constraints	Increased freedom to morph
Energy minimum principle	Evolution toward greater flow access

In contrast to fractal models of observed objects in nature, the constructal law is predictive and thus can be tested experimentally. Many natural designs, animate and inanimate, have been explained and unified by the constructal law, for example:

• Global circulation and climate
• River basin design: Horton's rules of stream numbers (~4) and lengths (~2), and all the other scaling rules (e.g., Melton, Hack) of river basins all over the world.
• The distribution of city sizes and numbers, i.e. the "Zipf" line of log (size) versus log (rank).
• The distribution of tree sizes and numbers on the forest floor, which is also a Zipf line of log (size) versus log (rank).
• The flow of education as a morphing vasculature on the globe, and the rigidity of university rankings.
• Vision, cognition, and the "golden ratio" phenomenon.
• The entire architecture of vegetation: roots, trunks, canopies, branches, leaves, and the forest, including the prediction of Leonardo da Vinci's rule, Huber's rule, and the Fibonacci sequence.
• Pedestrian movement, speeds, and patterns
• The emergence of urban traffic design
• The entire morphogenesis of dendritic crystals (e.g., snowflakes), as a flow structure that facilitates the flow of the heat of solidification
• The scaling law of all animal locomotion (running, flying, swimming): speeds, frequencies, forces and the work spent per unit of mass moved and distance traveled.
• The evolution of speed in sports.
• Kleiber's law, the relationship between metabolic rate and body size
• the relationship between breathing and heart beating times and body size
• the relationship between the mass transfer contact area and body mass
• The human bronchial tree with 23 levels of bifurcation.
• the dimensions of the alveolar sac,
• the total length of the airways,
• the total alveolar surface area,
• the total resistance to oxygen transport in the respiratory tree.

Criticisms of constructal theory

The main criticism of constructal theory is that its formulation is vague. The constructal law states that “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it”, but there is neither a mention of what these “currents” are nor an explicit definition of what “providing easier access” means. As a result, constructal theory is very versatile, but often unconvincing: depending on the choices made for the currents and the “access” to them, it can lead to extremely different results.

The second criticism of constructal theory is that there has been no attempt to prove it from first principles. Contrarily to alternative theories of non-equilibrium thermodynamics, there is no proof of constructal theory based on simplified systems of statistical physics. The claim that constructal theory is a fundamental principle of thermodynamics itself has also been disputed .

Alternative theories include:

• Non-equilibrium thermodynamics
• Self-organization
• And various extremal principles in non-equilibrium thermodynamics

Responses to criticisms of the constructal law

Bejan has responded to this criticism by noting that the constructal law is not about what flows, but about the physics phenomenon of how any flow system acquires its evolving configuration (design) in time. The constructal law is not about optimality (max, min, opt)—it is the definition of “life” in physics terms, and of the time direction of the changes in flow configuration.

Bejan also noted that the phenomenon governed by the constructal law (design in nature) is macroscopic (finite size, not infinitesimal). It is the birth of design and evolution of design in all the parts together. It is dynamic, not static. The evolution never ends. There is no end design, no destiny (max, min, opt).

Bejan and Lorente expanded on this by explaining the difference between a law of physics (e.g., the constructal law) and the many invocations of the law, which underpin many theories based on the law. In the section titled “The constructal law versus the second law of thermodynamics” they noted that the constructal law and the second law are first principles. The constructal law is a useful reminder not only of what was missing in physics and thermodynamics (the law of design and evolution) but also of what is present. For example, contrary to the critic’s view, the first and second laws of thermodynamics did not require any “proof based on simplified systems of statistical physics.”

The constructal law is a statement of a natural tendency—the time direction of the phenomenon. It is as non-mathematical as the original statements of the second law:

Clausius: No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

Kelvin: Spontaneously, heat cannot flow from cold regions to hot regions without external work being performed on the system.

A new law does not have to be stated in mathematical terms. The mathematization of the second law statement (and of thermodynamics) came later. The constructal law underwent the same evolution. The 1996 statement was followed in 2004 by a complete mathematical formulation of constructal-law thermodynamics [13].

Like any other law of physics, the constructal law is a concise summary of observed facts: the natural tendency of flow systems to evolve toward configurations that provide easier access over time. The word “access” means the ability to move through a confined space such as a crowded room. This mental viewing covers all the flow design and evolution phenomena, animate and inanimate, because they all morph to enter and to flow better, more easily .

External links

• Constructal Law web portal: publications, events, links, etc.
• Unified Physics Theory Explains Animals' Running, Flying And Swimming: Duke University article.
• Is Einstein the last genius? [1]
• Tree branching key to efficient flow in nature and novel materials, [2]
• Unifying The Animate And Inanimate Designs Of Nature, [3]
• The bigger they get, the faster they go, The Guardian, UK, [4]
• Size matters: bigger athletes dwarf efforts of smaller rivals [5]
• ABC News, Are giants taking over sports? [6]
• Why the golden ratio pleases the eye, The Guardian, UK, [7]
• Le secret de la beaute demystifiee, Le Devoir, Montreal, [8]
• Behind the NFL's Touchdown Binge, The Wall Street Journal, [9]
• Collaboration of soloists makes the best science, [10]
• Pseudo-Science of Constructal Theory (Hierarchy) in Heat Transfer Modeling, [11]

Popular literature

• Maggie Wittlin, "A Finger on the Pulse of the World", SEED Magazine, January 13, 2006.
• H. Poirier, Une théorie explique l’intelligence de la nature, Science & Vie, 1034, 2003, pp. 44–63.
• YouTube, A new "constructal" law of nature? [12]
• Video: Design in Nature, [13]
• Video: Constructal Theory explains why a river looks like a tree, [14]
• Natural Design with Constructal Theory, Mechanical Engineering magazine, [15]
• The many and the few, Mechanical Engineering magazine, [16]
• Laufen = Fliegen = Schwimmen, [17]