...steady state
'The Tea Is A Lie' (TTIAL) is a C++ software for calculating membrane concentration-profiles, fluxes, permeabilities, and so forth in steady-state based on Mesh Analysis. The software is built around a 2D rectangular membrane which is laterally periodic and therefore infinite, suitable for for example brick and mortar systems. The program is fundamentally constructed to model mass diffusion however it can also be used to model temperature flux and change diffusion. The major restriction of the scheme is that it assumes one constant concentration profile at the upper boundary of the system while utilizing a sink, i.e. zero concentration, at the lower boundary. For thermal/electric diffusion the temperature/electric potential is constant at those boundaries. Included is also the non-steady state software 'Ad Vacuum' which gives concentration-profiles and flows. That software is in many ways compatible with TTIAL, for example much of the input data is similar.
- C++14 compiler
- CMake
- The Eigen matrix library
The CMake build will automatically download Eigen.
cmake .
makeA steady state example of a Brick and Mortar system can be run by executing the following commands
cd examples/steadystate
../../ttial input.txtAlternatively it is possible to use the Jupyter Notebook brick_and_mortar.ipynb in the same folder.
jupyter-notebook brick_and_mortar.ipynbFinally, in order to use IPython to run the software and produce figures simply convert the ipynb-file and run the produced py-file.
jupyter nbconvert --to script brick_and_mortar.ipynb
ipython brick_and_mortar.pyA non steady state example of a Brick and Mortar system can be run by executing the following commands
cd examples/nonsteadystate
../../advacuum input.txtAll input to the software is retrieved from the input.txt file which must be in the same folder as where the program is executed from. In the following we define the diffusion coefficient as D=URT where U is the mobility, R the gas constant, and T the temperature. The solubility is defined by S = c0 / gamma / exp(mu0/RT) where c0 is the standard concentration, gamma the activity coefficient, and mu0 the standard chemical potential.
For charge diffusion c_out divited by S_out is the electric potential difference over the system and the resistances are the products between the solubilities S and diffusion coefficients D.
For heat diffusion c_out divited by S_out is the temperature difference over the system and the thermal conductivities are the products between the solubilities S and diffusion coefficients D.
Important! Note that the input-file must end at the last input-row. If empty rows are present at the end of the file the program will crash.
| Input parameter | Unit | Type | Description |
|---|---|---|---|
model_nbr |
unitless | integer | Model number, 0 gives Brick and Mortar |
d |
m | double | Width of bricks |
s |
m | double | Horizontal spacing between bricks |
g |
m | double | Vertical spacing between bricks |
t |
m | double | Brick thickness |
N |
unitless | integer | Number of layers of bricks |
omega |
unitless | double | Offset ratio, negative gives random |
c_out |
kg/m^3 | double | Concentration outside system at upper boundary |
S_out |
kg/m^3 | double | Solubility outside system |
S_mv |
kg/m^3 | double | Mortar solubility (verticle) |
S_mh |
kg/m^3 | double | Mortar solubility (horizontal) |
S_bv |
kg/m^3 | double | Brick solubility (verticle) |
S_bh |
kg/m^3 | double | Brick solubility (horizontal) |
S_mtv |
kg/m^3 | double | Mortar solubility (verticle) at upper boundary. Only used for model_nbr equal one |
S_mth |
kg/m^3 | double | Mortar solubility (horizontal) at upper boundary. Only used for model_nbr equal one |
D_mv |
m^2/s | double | Mortar diffusion coefficient (verticle) |
D_mh |
m^2/s | double | Mortar diffusion coefficient (horizontal) |
D_mtv |
m^2/s | double | Mortar diffusion coefficient (verticle) at upper boundary. Only used for model_nbr equal one |
D_mth |
m^2/s | double | Mortar diffusion coefficient (horizontal) at upper boundary. Only used for model_nbr equal one |
D_bv |
m^2/s | double | Brick diffusion coefficient (verticle) |
D_bh |
m^2/s | double | Brick diffusion coefficient (horizontal) |
z_break |
m | double | Cross-over point between linear and constant regions of the membrane. Only used for model_nbr equal one |
seed |
unitless | integer | Seed, negative gives random |
Nc |
unitless | integer | Number of columns of nodes |
Nr |
unitless | integer | Number of rows of nodes |
height |
m | double | Height of system, only relevant when loading an external mesh |
width |
m | double | Width of system, only relevant when loading an external mesh |
load_external |
- | bool | Load external mesh, default: false |
input_folder |
- | string | Folder from which input is loaded, default: current directory, only relevant when loading an external mesh |
output_folder |
- | string | Folder in which output is put, default: current directory |
output_file |
- | string | Name of output-file, default: output.txt |
| Input parameter | Unit | Type | Description |
|---|---|---|---|
time_steps |
unitless | integer | Number of iterations in time |
sample |
unitless | integer | Interval for output samples |
dt |
s | double | Time-step |
time_periodic |
s | double | Time between applying c_out at upper boundary |
evaporate |
- | bool | Evaporate volume at upper boundary, default: false |
display |
- | bool | Display progressbar or not, default: true |
evap_time |
s | double | Time after which evap_left volume fraction is left at upper boundary. Only used if evaporate is true. |
evap_left |
unitless | double | Volume fraction at upper boundary after which evap_time is left. Only used if evaporate is true. |
| Output files | Unit | Description |
|---|---|---|
output.txt |
- | Miscellaneous data |
Dh_matrix.txt |
m^2/s | Diffusion coefficients in the horizontal cells |
Dv_matrix.txt |
m^2/s | Diffusion coefficients in the vertical cells |
sh_matrix.txt |
kg/m^3 | Solubility in the horizontal cells |
sv_matrix.txt |
kg/m^3 | Solubility in the vertical cells |
sn_matrix.txt |
kg/m^3 | Solubility in the nodes [FIX no such for steay-state] |
Data in output.txt |
Unit | Description |
|---|---|---|
model |
unitless | Name of used model |
K_{M_ver/out} |
unitless | Partition coefficient between mortar (vertical) and outside |
K_{B_ver/out} |
unitless | Partition coefficient between bricks (vertical) and outside |
K_{M_ver/B_ver} |
unitless | Partition coefficient between mortar and bricks (both vertical) |
K_{M_hor/B_hor} |
unitless | Partition coefficient between mortar and bricks (both horizontal) |
height |
m | Height of system |
width |
m | Width of system |
Time |
- | Time to run the software [Days/Hours/Minutes/Seconds] |
| Output files | Unit | Description |
|---|---|---|
conc_hor_matrix.txt |
kg/m^3 | Concentration in the horizontal cells |
conc_ver_matrix.txt |
kg/m^3 | Concentration in the vertical cells |
j_hor_matrix.txt |
kg/m^2 s | Flux in the horizontal cells |
j_ver_matrix.txt |
kg/m^2 s | Flux in the vertical cells |
j_hor_vector.txt |
kg/m^2 s | Mean of amplitude of flux in each row of the horizontal cells |
j_ver_vector.txt |
kg/m^2 s | Sum of flux in each row of the vertical cells |
V_matrix.txt |
unitless | Potential in nodes in between cells |
res_hor.txt |
m s / kg | Resistance in the horizontal cells (inverse of 'Solubility times Diffusion coefficients' ) |
res_ver.txt |
m s / kg | Resistance in the horizontal cells (inverse of 'Solubility times Diffusion coefficients' ) |
vec_error.txt |
- | Error in conjugate gradient method (if used) |
V_vec_last_iteration.txt |
- | Last iteration in conjugate gradient method (if used) |
Data in output.txt |
Unit | Description |
|---|---|---|
j_ver |
kg/m^2 s | Mean value of flux into/out of the system, i.e. mean value of data in jv_vector.txt |
j_hor |
kg/m^2 s | Mean of absolute value of lateral flux in the system, i.e. mean value of data in jh_vector.txt |
P_eff |
m / s | Effective permeability of the whole system, P_eff = -j_ver / c_out |
D_eff |
m^2 / s | Effective diffusion coefficient of the whole system, D_eff = -j_ver * height / c_inside |
I_bot_sum |
kg/m^2 s | Flux out of the system, sum over all columns. Should equal I_top_sum otherwise not steady-state |
I_top_sum |
kg/m^2 s | Flux into the system, sum over all columns. Should equal I_bot_sum otherwise not steady-state |
R_eff |
s m / kg | Effective resistance of the whole system |
- |
- | Information about conjugate gradient method (if used) |
| Output files | Unit | Description |
|---|---|---|
conc_X.txt |
kg/m^3 | Concentration profile, sample X |
lambda_X.txt |
unitless | Absolute activity profile, sample X |
j_ver_X.txt |
kg/m^2 s | Vertical flux matrix, sample X |
j_hor_X.txt |
kg/m^2 s | Horizontal flux matrix, sample X |
volume_change.txt |
m^3 | Volume of elements outside of upper boundary, vector in time |
mass_out.txt |
kg | Mass flowing out of the lower boundary, vector in time |