How can you prove mathematically that rinsing several times with a small volume is better than rinsing 1 x with the total volume?

In the lab you have to wash or rinse things regularly so that you have transferred everything. In the past I’ve seen that you could prove mathematically that 3x rinsing with say 5ml is better than 1x rinsing with 15ml. But how did this come together?

Asker: David, 38 years old

Answer

Hi David,

I base myself on your example, and assume that there is always 0.5ml of liquid left behind after emptying, and that you empty your recipient (except for 0.5ml) before you start rinsing.

In the first case you have 0.5ml of contamination and 15ml of flushing agent, so a contamination of 0.5/15.5 = 3.2% in your one and last flush.
If you now pour out your recipient, 0.5ml*3.2%=0.016ml contamination remains.

In the second case, with a first flush you have 0.5 to 5.5 = 9.1% contamination.
If you pour out your test tube (or whatever) you will be left with 0.5ml in this assumption, with a contamination of 9.1%, or 0.5ml*9.1%=0.045ml contamination.
With a second rinse you will have 0.045ml contamination per 5.5ml liquid in your test tube, or 0.8% contamination.
After pouring, 0.5*0.8%=0.0041ml contamination remains. You can see that after the second rinse your fluid is already less contaminated than if you used the 15ml in one go.
With the third rinse you have 0.0041ml of contamination at 5.5ml=0.075%.
If you pour this out again, you are left with 0.5 ml of rinsing at 0.075% contamination = 0.00038 ml contamination.

Kind regards,
Luc.

Answered by

ir Luc Bosmans

Technology in the audiovisual sector

How can you prove mathematically that rinsing several times with a small volume is better than rinsing 1 x with the total volume?

Erasmus University College Brussels
Industrial quay 170 B-1070 Brussels
http://www.erasmushogeschool.be/

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