Ask A Scientist Physics Archive

name         PL Y.
status       other
age          50s

Question -   I see where surface tension can be measured in mN/m units. Can you identify 
mN/m units?
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Surface tension is measured as (Energy/Area) The amount of energy required to increase the area 
of a surface 1 square unit of distance. This is numerically equal (Force/Distance) in the same 
set of units. Now, the units of energy, force and distance in MKS is: Joules, Newtons, and meters 
respectively. The units of energy, force and distance in CGS is: ergs, dynes, and centimeters 
respectively. The conversions involved are:
1 Joule = 10^7 ergs, 1 meter = 100 cm, or 1 meter^2 = 10^4 cm^2, 1Newton = 10^5 dynes.
So the units of mN/m (this is really confusing notation) is 1 milli Newton/meter. The two "m's" 
stand for different things.

Expressing surface tension as (energy/area) I think is an easier way of thinking about it.

Vince Calder
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PL Y.,
I read the unit mN/m to be milliNewtons per meter.  Surface tension can be described as a force 
per unit length pulling on the edge of an object.  For a flat object setting on the surface of a 
liquid, the length of the edge multiplied by the surface tension value is the upward force 
provided by surface tension.  For an object that is not quite flat, use the edge of the portion 
of the object actually in contact with the liquid.


It is actually surface tension that holds a bubble in the shape of a sphere as it rises through 
a liquid.  The value of this force toward the center of the bubble, holding the surface 
"together".  As this value is more a function of pressure and radius than force and edge length, 
it requires more complex mathematics to understand.


Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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m is a common prefix meaning 10^-3 = 0.001.  Thus, for example, the coefficient of surface 
tension for water is 0.073 N/m = 73 mN/m = 73 milli-Newtons/meter.

There are a large number of such symbols.  For example f means femto = 10^-15,
G = giga = 10^9, M = mega = 10^6, etc.

I recommend the following web site.  Not only do you get a fascinating ride through our universe 
from the very largest objects known to the to the very smallest, but at each stage the size 
scale is given using powers of ten as well as all size prefixes.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Doing a search for "powers of ten" will find you many similar sites.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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