# Mixing two different liquids at different temperatures

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1. Dec 15, 2015

### RobertHutchison

When I pour two different liquids at different temperatures, into the same container, the temperature will be uneven at the start but then will approach equilibrium. Similarly, the concentrations of each liquid will be uneven but when mixing is complete, there will be the same concentrations throughout the liquid. I am wondering whether the temperature will reach equilibrium first or whether the concentrations will reach equilibrium first.
A bit of a tricky one I think.

2. Dec 15, 2015

### RobertHutchison

P.S. the liquids are completely miscible with each other.

3. Dec 16, 2015

### Staff: Mentor

If you're stirring the system, both will happen very fast. In any case, to ascertain which will happen faster, you need to compare the thermal diffusivity with the molecular diffusivity. The ratio of the thermal diffusivity to the mass diffusivity is called the Lewis Number (a dimensionless group).

Chet

4. Dec 16, 2015

### RobertHutchison

Thanks Chet.

I have quickly looked at the Lewis number and it is certainly relevant to the problem. I will chase this through. The particular problem I am investigating is injecting water into a concentrated salt solution at 250C. I am wanting to find out whether the water will boil before it is absorbed or it will be absorbed before it boils. Any suggestions?

Robert

5. Dec 16, 2015

Of course the Lewis number tells you a lot about the problem. It it will also depend on the initial conditions, i.e. What is the temperature of each liquid at the beginning and what is(are) the initial concentration(s).

6. Dec 16, 2015

### Staff: Mentor

Well, I think you can get a handle on it by doing some modeling. But, it would have to include some simulation of the mixing. Maybe you could start by modeling an array of alternate striated slabs of water and salt water. This is how I might begin to approach something like this.

Chet

7. Dec 16, 2015

Getting any more detailed than that may be... problematic. This problem reeks of turbulent mixing in a jet, which is an active area of modern fluid dynamics research.

8. Dec 17, 2015