The Volume of Drips - An experimental study

[BilZ0r]

Re: recent discussions on the volume of drips. I conducted an experiment.


Methods: Drips of tap water from a plastic transfer pipette with ends of either 2.5 or 4.5 mm, and drips from and 30 gauge hypodermic needle (0.25mm diameter) were caught on a ±5µg balance. Drips were weighed and assuming 1g = 1mL, were converted to volume. The pipettes had approximately round holes in the end, but the needle was tapered.


Results: Drips from a 4.5mm pipette had a mean volume of 55.93 ± 6.7µL (n = 9) (Std Dev). Drips from the 2.5mm pipette had a mean volume of 29.11 ± 4.9µL (n = 9). Finally, drips from the 0.25 diameter needle had a mean volume of 3.45 ± 0.74µL (n = 9). Linear regression (Fig 1) showed a clear linear relationship between drip volume and dripper end diameter, which was best fit by the formula:

Drip Volume = 12.33 x Dripper Diameter - 0.3

The y-intercept constant of -0.3 had a 95% confidence interval of -3.564 to 2.964, so it is essentially zero. The slope constant of 12.33 had a 95% confidence interval of 11.23 to 13.43.

Fig 1. The relationship between drip volume and dripper diameter

Conclusion: If one measures the diameter of the a dripper, at least between 0.25 and 4.5mm, one can assume the volume (in µL) of the drips it will generate will be approximately 12 times the dripper diameter.

The error increases at smaller volumes/dripper diameters. In my sample of 9 drops, all drops were within 33% of the mean from the 4.5mm pipette, while from the 2.5mm needle, all drops were within 52% of the mean . Likewise, given the calculated standard errors, 95% of the drops from the 4.5mm pipette fell within 24% of the mean, while 95% of drops from a 0.25mm needle fell within 42% of the mean.

 

[vecktor]

great experiment,^
I did a different experiment years ago using a vertically mounted pointed solid needle and using dripping distilled water down the side from the top so it formed a drop attached to the needle tip, the whole setup was inside the draught shield and over a peice of tissue paper in a watch glass on a very accurate balance. the attached drop would grow then when the weight overcame the surface tension it would drop onto the tissue paper.
It was remarkably consistant. even when different diameter needles were used, we used machine sewing needles with the ends turned down and polished the needles were cleaned by boiling in 111-trichloroethane and air drying.

I will see if I can find the notes and references I had.

V

 

[BilZ0r]

^ well, a bit more fancy than mine.

From Wikipedia, the weight (mg) of a droplet formed from a tube is given by

weight = 3 x pi x a x λ x cos(a)


where a is the angle of contact with the tube and λ is the surface tension of the liquid

so for 4.5mm; 3 x 3.1415 x 0.0045 x ~60 x 72.86 x 0.5
=1.3mg = 1.3microL
hmm. That equation is supposed to be for the biggest possible drop. The angle of contact is the biggest unknown for me (i.e. the angle between the shaft of the pipette and where it contacts the forming droplet). If I reverse the equation, from a known weight.

68mg = 3 x 3.1415 x 0.0045 x 72.86 x a x cos(a)
68mg = 3.09 x a x cos(a)
22 = a x cos(a)
Angle = ~ 72 degrees I suppose that's believable.

And does that hold for 2.5mm; sure does, indeed, because, all those constants ~ approximately 15 (accepting for changes in magnitude), close to my 12.

 

[vecktor]

I am now wondering what effect certain interesting dissolved substances will have on surface tension, I expect that a substance like DOC which has a polar tail and a nonpolar head will act a little like a surfactant thus reducing surface tension as well as increasing the density of the water. though density/pressure would only effect the rate of dropet formation and this rapidly gets complicated with reynolds numbers and what have you.

I think a better approach is to use capillary tubes. use capillary action to pull up the liquid to a level on the tube and then wick all the fluid out by touching on an absorbant surface like for example extra strong mints.

 

[B9]

Drops are a more interesting branch of this subject. I refer to the product liquid acid, which is dispensed in 'drops' . One can alter the volume of these drops by a method known as 'squeezing the bottle firmly', and varying the squeezing pressure causes the drop size to alter.
Currently no empirical data, or basic measurements have yet been made available, although it is widely known that this method is tried and tested in the field.:D

In summation I heartily recommend it !

 

[kidamnesiac]

yes, one would assume that this is for only one pressure on the needle/dropper.
if you increased the pressure/flow rate, you will get smaller drops
one could liken this to the spit effect for 10 year old boys, trying to make the biggest, longest tailed luger they can. I believe Beavis and Butthead covered the subject once...
I think you should mention what your flow rate/pressure is

DOC shouldn't go into solution unless it is a salt. And the hydrophobicity/tail of the molecule will make significantly less difference than the ionic strength increase caused by the salt content, which will make drop sizes larger. I am not sure if this phenomenon would be relevant at lower [], say, 1mg/ml. But if you like it saturated, then things may be different to a noticable degree.

cool stuff blizor