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Mixing Oils and Strange Math
By Micheal D. Holloway, CLS, OMA I, MLT I, Manager - Strategic Accounts and External Training

There are times when someone accidently adds the wrong oil to the oil reservoir. If the oils are the same viscosity and the manufacturers have determined that they are compatible then the only issue may be when a sample is submitted and the organometallic additives of the blend do not agree with the information that was put on the sample identification form. It is important to always provide information about repairs as well as incorrect top-fills. There have been instances when someone will add gear oil to a hydraulic sump or add hydraulic oil to an engine crankcase. These situations are not uncommon but what is perplexing is the time when someone added a gear oil to a hydraulic sump then took that mixture and added the same amount back into the gear oil drum. When samples were taken from the gear oil drum and the hydraulic sump, a very interesting result was discovered. At first glance, the results were perplexing until you considered the concept of ‘entropy of mixing’. Consider the following scenario.

If you took 1 gallon of gear oil from a drum that had 30 gallons of gear oil in it, and put it into a 30 gallon hydraulic sump, then you took 1 gallon of the mixed oil and put it back to gear oil drum and sampled both the oil mixture now in the gear oil drum and the oil mixture in the hydraulic sump - what would be the amount of gear oil be in the hydraulic sump? And what would be the amount of hydraulic oil be in the gear oil drum? Choose between a, b, or c.
    a) There will be more hydraulic oil in the gear oil drum than gear oil in the hydraulic sump.
    b) There will be more gear oil in the hydraulic sump than hydraulic oil in the gear oil drum.
    c) The amount of hydraulic oil in the gear oil drum will be the same as the amount of gear oil in the hydraulic sump.
The answer may surprise you, even frustrate you because you will consider that a certain percentage taken must influence what goes back in but your math with deceive you. The answer is c) The amount of hydraulic oil in the gear oil drum will be the same as the amount of gear oil in the hydraulic sump.

Here is the proof: It is true that the 2nd gallon taken is not 100% hydraulic oil, as opposed to the 1st gallon which is 100% gear oil. How do the two transfers which are not even end up with an even amount? The 2nd gallon is (100% - X%) of hydraulic oil. The hydraulic oil that is moved to the gear oil drum is not enough to balance the gear oil that was moved to the hydraulic sump in the 1st gallon. But, that means X% of gear oil is also moved back to the gear oil drum, which is the exact amount that is needed to balance the discrepancy and make them even. The 2 balance to zero difference. Some will argue that the temperature had something to do with it or even agitation. Neither are a consideration. It is the concept of the entropy of mixing. When we think of entropy, we think that temperature is a consideration. With the entropy of mixing – the gain of entropy in the hydraulic sump is exactly the same as the gain of entropy in the gear oil drum, even if hydraulic oil and gear oil are totally different oils. The 2 are balanced out. In the oil analysis results for both samples, it was determined that the amount of hydraulic oil in the gear oil drum was be the same as the amount of gear oil in the hydraulic sump.

ALS Tribology offers oil, fuel, coolant, and grease analysis for wear, contamination and lubricant condition. Contact your local lab to learn more about the various services ALS Tribology can perform for you.

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