# Are water molecules orientation absolutely independent of the flow direction?

Or is there a bias toward a specific angle in regards to the direction of the current?

These types of questions are tempting to ask in a yes-no way, and you currently have an answer that says "yes" and and answer that says "no." The physicist's approach is to ask how big the biggest effect might be; let's try that.

The current answer which proposes an aligning effect suggests an interaction between the electric dipole moment of the water molecule, $$p \approx 6\times10^{-30}\,\mathrm{C\,m} \approx 0.4\,e\,Å$$, and the Earths' magnetic field, via the Lorentz force, $$\vec F = q \vec v \times \vec B$$. The energy associated with this interaction is what you get if the force interacts over the length scale of the molecule, which has a bond length of about $$1\,Å$$. The typical thermal velocities obey $$kT \approx mv^2$$, or

\begin{align} v^2 \sim \frac{kT}{m} = \frac{25\rm\,meV}{18\,\mathrm{GeV}/c^2} &\approx \frac 43\times10^{-12}\ c^2 \\ v &\sim 10^{-6}\ c \approx 300 \rm\,m/s \end{align}

So a typical Lorentz-force polarization energy would be

\begin{align} U &\approx | p v B | %\\ &= 6\times10^{-30} \mathrm{C\,m}\cdot 3\times10^2\mathrm{m/s} \cdot \frac12\times10^{-4}\mathrm T %\\ &\approx 9\times10^{-32}\,\mathrm J %\times\frac{1\rm\,eV}{1.6\times10^{-19}\rm\,J} \\ &\approx \frac 58\times10^{-13} \rm\,eV \approx 60 \rm\,feV \end{align}

Those are femto-eV. But the water molecule's rotational degree of freedom also has milli-eV energy sloshing around. The ratio of the aligned and un-aligned populations will go like the Boltzmann factor for this energy difference,

$$e^{\Delta E/kT} = e^{\text{femto/milli}} = 1 + 10^{-12},$$

that is, a part-per-trillion difference. I've been involved in several experiments looking for part-per-billion asymmetries; each one took ten years. A few parts per trillion is a small effect, even if you go back through my arithmetic and futz around with some missing factors of two.

What's more, the preferred direction $$\vec v \times \vec B$$ is only well-defined if most of the water molecules are moving in generally the same direction. That only happens if the rate of flow is much faster than the typical thermal velocity --- which doesn't really happen unless the flow approaches the speed of sound in water.

If you tried to enhance the effect --- by, say, shooting a hypersonic jet of water through the bore of ten-tesla magnet, to bring the asymmetry up to the part-per-million range --- you'd probably just learn something sneaky about hydrogen bonding.

• I disagree with your philosophical approach: experience shows in physics that anything not forbidden is required. But we can compute whether an allowed behavior is common or rare.
– rob
Sep 10 '20 at 22:05
• Whatever. But ironically you do not address the rest of my comment. Sep 10 '20 at 22:10
• My expertise is in subatomic physics. Friction is a mesoscale effect. Those length scales usually don't talk to each other. If you have a model in mind, I might have more time to think about it, but it seems like that could have been part of your original question.
– rob
Sep 10 '20 at 23:03
• @nick012000 That was my first thought as well. The hydrogen bonds make the water molecules form chains in cold water (which consequently becomes "oily"). It's entirely conceivable that these line up with the flow in laminar flowing conditions, and potentially even interact. Sep 11 '20 at 9:21
• "shooting a hypersonic jet of water through the bore of ten-tesla magnet, to bring the asymmetry up to the part-per-million range " - I'd love to hear about that experiment actually having been done and what the results were. Sep 11 '20 at 19:32

No, there isn't a bias. Water molecules jiggle around so much in the liquid that any long-range order (like dipoles getting all lined up) has no chance to form, and if it did form for any reason, it would be very quickly erased.

• I read papers that describe long range interactions in water when it is steady, forming domains. I concur that this probably does not apply to an accelerating flow of water. Even if the effect is extremely small and whatever the reason behind it, I am interested though. Sep 10 '20 at 21:27