Surface area to volume ratio

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In chemical reactions involving a solid material, the surface area to volume ratio is an important factor for the reactivity, that is, the rate at which the chemical reaction will proceed. In some industries it is abbreviated sa/vol.

1 Physical Chemistry
2 Biology
3 Examples
4 See also
5 References
6 External links

[edit] Physical Chemistry

Materials with high surface area to volume ratio (e.g., very small diameter, or very porous or otherwise not compact) react at much faster rates than monolithic materials, because more surface is available to react. Examples include grain dust; while grain isn't typically flammable, grain dust is explosive. Finely ground salt dissolves much more quickly than coarse salt.

High surface area to volume ratio provides a strong "driving force" to speed up thermodynamic processes that minimize free energy.

Surface to Volume Ratio causes a cell to be limited in size due to the fact that when the volume increases so does the surface area.

[edit] Biology

The ratio between the surface area and volume of cells and organisms has an enormous impact on their biology. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure.

If you have 3 cubes: one 2cm squared, one 1cm squared and one 0.5cm squared, the SA/Vol ratio will double every single time. I.E.: the 2cm cube would be 3:1, the 1 cm cube would be 6:1 and the 0.5cm cube would be 12:1. This shows that each time, the surface area doubles. Humans cannot rely on diffusion for their whole body; however, animals such as flatworms and leeches can, as they have less volume.

An increased surface area to volume ratio also means increased exposure to the environment. The many tentacles of jellyfish and anemones are the result of increased surface area for the acquisition of food. Greater surface area allows more of the surrounding water to be sifted for food.

Individual organs in animals are often based on the principle of greater surface area. The lung is an organ with numerous internal branchings that increase the surface area through which oxygen is passed into the blood and carbon dioxide is released from the blood. The intestine has a finely wrinkled internal surface, increasing the area through which nutrients are absorbed by the body. This is done to increase the surface area in which diffusion of oxygen and carbon dioxide in the lungs and diffusion of nutrients in villi of the small intestine can occur.

Cells can get around having a low surface area to volume ratio by being long and thin (nerve cells) or convoluted (microvilli)

Increased surface area can also lead to biological problems. More contact with the environment through the surface of a cell or an organ (relative to its volume) increases loss of water and dissolved substances. High surface area to volume ratios also present problems of temperature control in unfavorable environments.

[edit] Examples

Example Table
side of cube	side²	Area of side	6*side²	Area of Cube's Surface	side³	Volume	Ratio of Surface Area to Volume
2	2x2	4	6x2x2	24	2x2x2	8	3:1
4	4x4	16	6x4x4	96	4x4x4	64	3:2
6	6x6	36	6x6x6	216	6x6x6	216	3:3
8	8x8	64	6x8x8	384	8x8x8	512	3:4
12	12x12	144	6x12x12	864	12x12x12	1728	3:6
20	20x20	400	6x20x20	2400	20x20x20	8000	3:10

[edit] See also

Compactness measure of a shape

[edit] References

Schmidt-Nielson, K (1984). "Scaling: Why is Animal Size so Important?" Cambridge University Press, New York, NY.
Vogel, S (1988). "Life's Devices: The Physical World of Animals and Plants". Princeton University Press, Princeton, NJ.