I was studying the process of coalescence in emulsions. We considered $N$ bubbles of liquid 1 floating in liquid 2. The result we derived, is that if there are some dissipative forces (diffusion) the most stable configuration is for the $N$ bubbles to coalesce/fusion and become 1 bubble (to reduce surface tension).
So I tried to make the experiment at home to see how long would it take. I emulsified oil in water. After one day, it has not changed much.
I tried to estimate the time it would take using Stokes-Einstein equation:
\begin{equation}
D=\frac{k_{\rm B}T}{6\pi \eta r}
\end{equation}
where $\eta$ is the viscosity of (olive) oil (?) and $r$ the radius of the bubbles (about 1 mm).
And then using the result of Brownian motion for 2D: $$\overline{x^2}=4Dt$$ I replaced $\overline{x^2}$ by the surface of my container, about $R=$ 4 cm of radius so $\overline{x^2}=\pi R^2$. Mixing both equations, I can derive the time it takes (for room temperature). But I get an enormous duration of $10^5$ years.
Is this the true value or I am doing something wrong?
Update: Day five, the smallest bubbles ($r<1$ mm) are gone but still $N>100$.
Update2: Day six. No coalescence. I stopped the experiment.
Update3: Obvious problem of leaving the experiment for so long is that the water starts to evaporate.