ReactiveWetting2
This page is continued from [wiki:reactiveWetting].
There is a 2D case currently running. The convergence for the 1D solid vapor case was an issue. This, as it turned out, may just have been becasue I didn't leave the simulation running for long enough. I've set off another 1D simulation to see if better convergence can be had by waiting longer. The 2D takes a lot of steps to reach equilibrium. This is most probably because of the time step limit.
The following are a list of items that were raised
* 2D calculation comparison with analytical results * W epsilon_phi simulations need to be evaluated * 1D convergence issues, impact of epsilon_1 * lower viscosity simulations * volume before and after for each state * interface thickness numbers * 1D plot thruogh 2D simulation * change temperature as a function of time. * point and click GUI tool for Bill. * increased viscosity simulations
Other things that I think are important
* improve 1D efficiency * start using trilinos
The following plot shows the *somewhat* classical analytical solution that does not include the non-classical concentration deviations with the 2D solution. Image(plot4900.png, 60px) The curvatures of both interfaces look good. The solid height is certainly a bit low. It still hasn't finished running so I'll wait to see what happens with that. The interfaces are quite thick compared with the analytical solution so it could be something to do with that, i.e non-classical effects. If I plot the maximum velocity in the domain and the solid height far away from the drop I get the following Image(height-velocity.png, 1px)
It seems that changing epsilon_1 back to 1e-16 drammatically improves the time step restriction and equilibrium accuracy without sacraficing the contact angle for these numbers. I am now using the following parameters,
The equilirium results were for the solid-liquid (dataTue-Oct--2-16:06:50-2007, out-1D-billsNewParams7.2579.0)
$ \rho_1^s = 7593.1 (7489.1), \;\;\; \rho_1^l = 769.56 (767.67), \;\;\; \rho_2^s = 360.22 (349.29), \;\;\; \rho_2^l = 6643.2 (6586.67), \;\;\; \gamma_{sl}^1 = 33.507, \;\;\; \gamma_{sl}^2 = 33.876, \;\;\; \max \left( |v| \right) = 1 \times 10^{-9} $
for the solid-vapor (dataThu-Sep-27-11:50:53-2007, out-1D-billsNewParams7.2443.0)
$ \rho_1^s = 7470.5 (7489.1), \;\;\; \rho_1^v = 8.6036 (8.6488 ), \;\;\; \rho_2^s = 368.24 (349.29), \;\;\; \rho_2^v = 78.426 (74.207), \;\;\; \newline \gamma_{sv}^1 = 39.839, \;\;\; \gamma_{sv}^2 = 39.057, \;\;\; \max \left( |v| \right) = 5 \times 10^{-9} $
for the liquid-vapor (dataTue-Oct--2-16:08:28-2007, out-1D-billsNewParams7.2581.0)
$ \rho_1^l = 689.27 (767.67)), \;\;\; \rho_1^v = 7.7531 (8.6488 ), \;\;\; \rho_2^l = 6665.1(6586.67), \;\;\; \rho_2^v = 75.164 (74.207), \;\;\; \newline \gamma_{lv}^1 = 18.904, \;\;\; \gamma_{lv}^2 = 19.114, \;\;\; \max \left( |v| \right) = 5 \times 10^{-7} \text{still running and decreasing dt=1e-7} $
The approximated contact angle is ~70. Get a good contact angle. Convergence to
equilibrium is much better. Parasitic velocity is much smaller.
The following are a list of items that were raised
* viscosity differential * mbar differential * different initial data, temperature change A's function of temperature * look for gradients in the Xs while changing the temperature by varying the viscosity up and Mbar down.
Jim would like to see the following.
* In the 2D simulation, the rate of melting and depositio (or equivalent). * fraction of each phase over time, * 2D simulation with an increased driving force (possibly temperature, but maybe concentration) * Bill's stuff for mbar, viscosity and temperature in 1D
Here is the 2D [attachment:wiki:oct11-10.mov]. Looks great and good agreement with analytical. There was a mistake in the analytical (now fixed) calculation and the solid height now agrees well.
Run some examples with the solid velocity set to zero.
Conversation with Jim and Bill
- get the 1D problem working with an initial condition - run 1D s-l-v system with Mbar=1e-7 and viscosity=2e+4 with a temperature drop of 50. - find a time step such that the above system works. - try decreasing the viscosity to 2e-3 and find a time step that works for that - try running this problem in 2D with a small enough time step - increase the solid visocisty from 2e-3 as much as possible - decrease the solid Mbar to 1e-11.
Where are we? Currently I am working on a graphs of viscosity versus time step. The bottom line is this, I can run with simulations with all the right numbers apart from the viscosity in the fluid, whcih can be at about 10^1. Meeting with Bill - Bill wants me to check the concentartion gradients with a temperature drop.
Still working on 1D simulations to obtain a somewhat stable concentration gradient during the interface motion transient. The following figure shows the gradient in X2 in the solid region and the liquid region as well as the interface position. These are simulations that start at a solid-liquid equilibrium condition for a temperature of 650, but the temperature is 550 for the simulations. During the simulation the position of the interface should go from .5 * L to .78 * L, where L is the box length.
The lines end because the time steps were too large. I'm running cases that have a smaller time step size. for the lower solid viscosities. The decrease in the solid viscosity makes the problem more unstable (bigger velocities in the solid). The other issue is that the interface width is probably too large for the box size. We really don't want gradients initially in the far field. There is a secondary problem due to having a small boz size. If we look at the interface position, we see that there is a very fast initial movement of the interface. My guess is that the initial movement will be independet of box size. It would be good if this initial movement is small compared with the box size. It is clear that the initial movement does not induce concentration gradients in the far fields. Most of these simulations have not evolved to the final equilibrium position so it is hard to know whether a fixed concentration gradent will be induced. It is clear that a decrease in solid viscosity increases X2 gradinets.
The follwoing figure shows the same for a large solid viscosity with varying liquid viscosity. A lower solid viscosity is included for reference. When the solid viscosity is large the interface motion does not stop at the correct equilibrium position. See also the [attachment:wiki:ReactiveWetting2:largemu.mov]. The movie is for the case when mu_s=1e+12 and mu_l=1e+2.
What now?
- running job with smaller time step for mu_s = 1, mu_l = 1e-2, dt = 1e-10 - running job with twice the box size to find equilibrium. mu_s=1e+4, mu_l=1e+4, dt=1e-6 - increase the efficency of 1D simulations. - run jobs for the larger box size and compare.
What is happening in the 1D simulations? The pressure is equilibrating first manifesting as "sloppy" fluid behaviour. Once this first stage is over and the viscosity is low enough, the next stage may reveal the slow transient behaviour we are looking for. The size of the box will have no effect on this behaviour. The amount of relaxation due to the pressure will be in proportion to the size of the box. The solid has to expand to equilibrate the pressure.
[attachment:wiki:ReactiveWetting2:X2difference.mov] Binary solid liquid system with a non-varying mu and mbar of 1e+4 and 1e-9.