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Consider the U-tube water experiment below with the left red block at 10C and the right red block at 90C. I think the right level will become about 3% higher than the left level simply because hotter water is 3% less dense than colder water, but I'm assuming negligible pressure change along the bottom portion of the tube. I'm guessing this effect is small since I can't find papers for liquids like I can for gases (gas moves from cold to hot via thermal transpiration).

So, what is the pressure change along the bottom?

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If there was a horizontal pressure gradient, this unbalanced force would begin to redistribute the fluid. So by assuming the fluid settles in a static equilibrium configuration, you've implied that there is no pressure change along the bottom.

Of course, in a realistic situation (with a tube that is not infinitesimal in cross-section), you'd expect to see convection occurring inside the tube between the two blocks, transferring heat via dynamic and chaotic turbulence of the fluid (i.e., across the junction the pressure would continually fluctuate slightly).

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  • $\begingroup$ I am thinking the steady state might have flow from right to left in the tube's center ("pressure" from hot) and compensating flow from left to right along the tube's perimeter ("creep" from cold). This flow and the pressure difference is smaller for wider tubes, but still finite. Anyway, if the water were replaced by gas, thermal transpiration experiments show that pressure does change along the bottom, despite a steady state, so I don't think I've "implied that there is no pressure change along the bottom". $\endgroup$ – bobuhito Dec 7 '15 at 1:19
  • $\begingroup$ In your scenario, is there anything to prevent convection (because I think those turbulent currents will confound the observation you want to make)? Note, thermal transpiration tends to be only encountered in gases when at very low pressures, i.e. fluids in the limit farthest from liquid behaviour (e.g., see fig 2.26 of Phys. Meth. of Chem. vol.6 1992). $\endgroup$ – benjimin Dec 12 '15 at 4:27
  • $\begingroup$ No, nothing prevents convection which I think is fine. Honestly, I chose this experiment because it seemed like the best way to check for thermal transpiration in liquids, but after quantifying things since posting this, I now believe the pressure difference is unmeasurable. So, that leaves me looking for a better experiment... $\endgroup$ – bobuhito Dec 12 '15 at 15:38

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