Water Vapor Absorption and The Surface Law

Many of nature's crucial processes occur at surfaces. Nutrients, water vapor and other material are exchanged by cells at the surface of each cell. Liquid water evaporates into the air (as water vapor) from the surface of a body of water. Sunlight is absorbed at the surface of the leaf. 


Water vapor absorption and adsorption also requires surfaces. Thus, ignoring efficiency considerations for the moment, a larger amount of water vapor will be absorbed if a larger a surface area is available that is capable of absorbing water vapor.


The Surface Law

A cube with sides of length 's'
Source: tutornext.com

The ability to increase surface area is controlled by the Surface Law that states: As volume of a physical object increases, the object's relative surface area decreases. For example, consider the cube on the right:

• A cube 1 unit in size (s=1), has volume equal to1 and surface area equal to 6. Its ratio of surface area/volume is 6
• A cube 2 units in size (s=2), has volume equal to 8 and a surface area equal to 24. Its ratio of surface area/volume is 3
• A cube 4 units in size (s=4), has a volume equal to 64 and surface area equal to 96. Its ratio of surface area/volume is 1.5 

In the above example, the relative surface area reduces as the volume increases. From a biological perspective, this implies that it is relatively more difficult to supply nutrients to the cells at the center of each cube as the volume of cube increases. As expected, Nature has come up with interesting structures that increase surface area without increasing mass


Tracheal System

source: users.rcn.com. 

This is a grouping of tubes, air sacs and various geometries (such as loops or helices) that continuously bring air to tissues so that the tissues can directly exchange nutrients (oxygen, water vapor, carbon dioxide, etc) from the air.


Pores
Nature invented pores to increase surface area. 

source: the poultrysite.com

The typical chicken egg is perforated by about 10,000 pores (approx 1.5 pores per square millimeter of shell surface) that permit passage of respiratory gases and water vapor through the hard shell.


The pore size (17 micro-mm) has been optimized to provide the large amount of oxygen required just prior to hatching.


The Human Respiratory System

Source: Goldiesroom.org

As body size increases, the complexity of providing enough surface area to all the tissues and cells in the body increases.

• Oxygen is extracted from the air we breathe at the surfaces of miniature air sacs (alveoli) in the lungs
• This oxygen diffuses from the blood into a cell at the surface of a capillary

The human system to move oxygen into the body and remove carbon dioxide from the human body increases in complexity by creating new surface areas with specialized functionality that feeds nutrients to cells and extracts waste for disposal.


A Gram with Surface Area of 2 Basketball Courts

Source: physorg.com

MOF-74 is a porous crystalline powder developed at the University of California in Los Angeles that resembles a series of tightly packed straws comprised of mostly carbon atoms (white balls) with columns of zinc ions (blue balls) running down the walls.


The green balls are hydrogen molecules that this design is optimized for.


A gram of MOF-74 has the surface area of 2 basketball courts


Many many more examples exist of structures created by nature and mankind for supplying cells with nutrients and removing waste. So what would a structure look like that presents enough surface area to withdraw water vapor from unsaturated air?