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Surface Tension measurement 2
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btrueblood
Mechanical
Use a capillary tube. From my old CRC handbook,
"If a liquid of density d rises a height h in a tube of internal radius r, the surface tension is:
T = rhdg/2
The surface tension will be in dynes/cm if r and h are in cm, d in g/cm3, and g in cm/s2."
Note that surface tension is dependent on the interface fluid (usually it's air, and assumed to be air unless specified otherwise), and there are some who believe it can depend on the tube wall material as well...
"If a liquid of density d rises a height h in a tube of internal radius r, the surface tension is:
T = rhdg/2
The surface tension will be in dynes/cm if r and h are in cm, d in g/cm3, and g in cm/s2."
Note that surface tension is dependent on the interface fluid (usually it's air, and assumed to be air unless specified otherwise), and there are some who believe it can depend on the tube wall material as well...
A very simple method is to use a so called stalagmometer: basically it is a pipette with a sort of rounded outlet. For a known volume of a liquid you count the number of drops and then calculate the radius and surface of a drop: it is proportional to the surface tension of your liquid/air system. It works even with two inmiscible liquids (water/oil,..). The method is somehow obsolete, you will loose your eyes counting droplets, but you may improve the method by employing some optical pulse counting device or similar. It is a good practice to make a comparative test with a substance with well documented surface tension data like water.
m777182
m777182
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This is to comment on trueblood's excellent advice.
Books say that a more accurate capillarity equation for the estimation of surface tension would have to bring into account the difference between the densities of the liquid and the vapor at the top of the column ([ρ]l-[ρ]v), and the fact that at the top of the liquid column the surface is not flat, meaning that the radius of curvature of the meniscus should be accounted for when measuring h.
The more accurate equation with highlighted corrections would then be:
While the typical capillarity equation generally in use:
where [θ] is the angle of wetting. With a "perfectly wetting liquid" this angle is zero (cos [θ] =1); most common liquids wet glass having the angle ~zero, and the formula becomes equal to that brought by trueblood.
For example: at 20oC, ethyl acetate (EA) considered a glass-wetting liquid, rises 4.12 cm in a capillary tube of radius 0.01294 cm. The density of EA at this temperature is 0.9005 g/cm3.
The estimated surface tension, applying the more "accurate" formula, assuming [θ] = 0, g = 9.81 m/s2, and [ρ]air=0.00117 g/cm3:
The value, as estimated by the simplified equation, would be:
Which tells us that if the liquid in hand "wets" the capillary, trueblood's advice on the measuring procedure would be applicable and the results accurate enough.
Books say that a more accurate capillarity equation for the estimation of surface tension would have to bring into account the difference between the densities of the liquid and the vapor at the top of the column ([ρ]l-[ρ]v), and the fact that at the top of the liquid column the surface is not flat, meaning that the radius of curvature of the meniscus should be accounted for when measuring h.
The more accurate equation with highlighted corrections would then be:
[σ] = 0.5 (rg/cos [θ])([ρ]l-[ρ]v)[h + (r cos [θ])/3]
While the typical capillarity equation generally in use:
[σ] = 0.5 rg[ρ]lh/cos [θ]
where [θ] is the angle of wetting. With a "perfectly wetting liquid" this angle is zero (cos [θ] =1); most common liquids wet glass having the angle ~zero, and the formula becomes equal to that brought by trueblood.
For example: at 20oC, ethyl acetate (EA) considered a glass-wetting liquid, rises 4.12 cm in a capillary tube of radius 0.01294 cm. The density of EA at this temperature is 0.9005 g/cm3.
The estimated surface tension, applying the more "accurate" formula, assuming [θ] = 0, g = 9.81 m/s2, and [ρ]air=0.00117 g/cm3:
[σ] = 0.5(4.12+0.01294/3)(0.9005-0.00117)(981)(0.01294) ~ 23.54 dyne/cm
The value, as estimated by the simplified equation, would be:
[σ] = 0.5(4.12)(0.9005)(981)(0.01294) ~ 23.54 dyne/cm
Which tells us that if the liquid in hand "wets" the capillary, trueblood's advice on the measuring procedure would be applicable and the results accurate enough.
btrueblood
Mechanical
Thanks for the ego boost 25362 
. I mentioned the wall effect, which you have described in much more accurate detail. Wish I'd had that knowledge lo these many years ago, when a colleague (a very cute one too) was trying to measure surface tension, and not getting very repeatable results, nor could she correlate her tests to "book" values. Turned out she had drawn her own glass capillary tubes, by using a wire as a mandrel. She had coated the wire with something (silicone?) that affected how the liquid wetted the surface. Using a cleanly drawn tube worked, as did pre-wetting the tube with fluid. But it took us awhile to figure it out...hmmm, maybe being ignorant in that case was not so bad...
. I mentioned the wall effect, which you have described in much more accurate detail. Wish I'd had that knowledge lo these many years ago, when a colleague (a very cute one too) was trying to measure surface tension, and not getting very repeatable results, nor could she correlate her tests to "book" values. Turned out she had drawn her own glass capillary tubes, by using a wire as a mandrel. She had coated the wire with something (silicone?) that affected how the liquid wetted the surface. Using a cleanly drawn tube worked, as did pre-wetting the tube with fluid. But it took us awhile to figure it out...hmmm, maybe being ignorant in that case was not so bad...BTW, the angle of contact [θ], in [σ] = 0.5 rg[ρ]lh/cos [θ] is an important factor.
For example, if a given capillary tube is cut down to half the height of the liquid rise, the rising liquid wouldn't overflow the shorter tube, but would stop at the rim forming a new angle of contact whose cosine would be proportional to h, in this case, 0.5.
If the original angle was zero with its cosine = 1, the new meniscus would be flattened to a contact angle whose cosine = 0.5, meaning the new [θ] = 60 degrees.
Thus, to avoid having to cope with measuring [θ] , when dealing with a glass-wetting liquid, it would be wise to use a sufficiently long (longer than the liquid rise) capillary tube.![[smile]](/data/assets/smilies/smile.gif "[smile] [smile]")
For example, if a given capillary tube is cut down to half the height of the liquid rise, the rising liquid wouldn't overflow the shorter tube, but would stop at the rim forming a new angle of contact whose cosine would be proportional to h, in this case, 0.5.
If the original angle was zero with its cosine = 1, the new meniscus would be flattened to a contact angle whose cosine = 0.5, meaning the new [θ] = 60 degrees.
Thus, to avoid having to cope with measuring [θ] , when dealing with a glass-wetting liquid, it would be wise to use a sufficiently long (longer than the liquid rise) capillary tube.
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