Timeline for Fluid dynamics of a rotating liquid droplet
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2016 at 5:08 | comment | added | tom | Thinking further, the 2D problem (equivalent to a fluid in a rotating cylindrical shell) is very easy to solve, and the time for homogenisation is on the order of $r^2/\nu$, where $r$ is the cylinder's radius and $\nu$ is the kinematic viscosity. It seems reasonable that we'd expect a similar time scale for a rotating sphere also. For liquid water, this gives us roughly a 1 second homogenisation time for a droplet of 1mm radius. It seems a lot can happen inside rain-drops, but not inside droplets of diameter less $500 \mu m$ or so. | |
| May 6, 2016 at 2:29 | comment | added | tom | @WillieWong That is so simple I dismissed it off hand :) Given that this is the long-term solution, I guess the better question would be how quickly is it dynamically approached from the time the shell begins rotating. I imagine that would be a much more difficult problem to solve analytically though... | |
| May 5, 2016 at 13:31 | comment | added | Willie Wong | Let the $z$ axis be the axis of rotation. $$ u(x,y,z) = \begin{pmatrix} y \\ -x \\ 0\end{pmatrix}$$ is a steady-state solution to the incompressible Navier-Stokes equation that co-rotates with your spherical shell. The pressure is $\frac12 (x^2 + y^2)$. | |
| May 5, 2016 at 13:23 | history | edited | Willie Wong |
edited tags
|
|
| May 5, 2016 at 12:44 | review | First posts | |||
| May 5, 2016 at 12:52 | |||||
| May 5, 2016 at 12:43 | history | asked | tom | CC BY-SA 3.0 |