Diffusion of 2 chemicals¶

Identical to experiment `diffusion_2_a` EXCEPT for some extra rows of bins at the top of the system (high y-bin values), which breaks the previously-perfect symmetry of the 2 chemicals: now, one of them (`A`) is more "hemmed in by the walls", compared to the other one¶

TAGS : "diffusion 2D", "basic"¶

In [1]:

LAST_REVISED = "Jan. 20, 2025"
LIFE123_VERSION = "1.0.0rc2"        # Library version this experiment is based on

In [2]:

#import set_path                    # Using MyBinder?  Uncomment this before running the next cell!

In [3]:

#import sys
#sys.path.append("C:/some_path/my_env_or_install")   # CHANGE to the folder containing your venv or libraries installation!
# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try:  import set_path   

from life123 import BioSim2D, ChemData, check_version

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

In [5]:

# Prepare the initial system, with two concentration pulses, at almost-opposite ends of the system, with the same diffusion rate coefficient
chem_data = ChemData(names=["A", "B"], diffusion_rates=[0.05, 0.05])

bio = BioSim2D(x_bins=7, y_bins=10, chem_data=chem_data)  # 3 more rows, compared to experiment `diffusion_2_a` 

bio.set_bin_conc(bin_address = (1,1), chem_label="A", conc=10.)
bio.set_bin_conc(bin_address = (5,5), chem_label="B", conc=10.)

Different ways to visualize the system¶

Notice the bin with the initial concentration of A and the other bin with the initial concentration of B

In [6]:

bio.describe_state()

SYSTEM STATE at Time t = 0:
Species `A`:
     0     1    2    3    4    5    6
9  0.0   0.0  0.0  0.0  0.0  0.0  0.0
8  0.0   0.0  0.0  0.0  0.0  0.0  0.0
7  0.0   0.0  0.0  0.0  0.0  0.0  0.0
6  0.0   0.0  0.0  0.0  0.0  0.0  0.0
5  0.0   0.0  0.0  0.0  0.0  0.0  0.0
4  0.0   0.0  0.0  0.0  0.0  0.0  0.0
3  0.0   0.0  0.0  0.0  0.0  0.0  0.0
2  0.0   0.0  0.0  0.0  0.0  0.0  0.0
1  0.0  10.0  0.0  0.0  0.0  0.0  0.0
0  0.0   0.0  0.0  0.0  0.0  0.0  0.0
Species `B`:
     0    1    2    3    4     5    6
9  0.0  0.0  0.0  0.0  0.0   0.0  0.0
8  0.0  0.0  0.0  0.0  0.0   0.0  0.0
7  0.0  0.0  0.0  0.0  0.0   0.0  0.0
6  0.0  0.0  0.0  0.0  0.0   0.0  0.0
5  0.0  0.0  0.0  0.0  0.0  10.0  0.0
4  0.0  0.0  0.0  0.0  0.0   0.0  0.0
3  0.0  0.0  0.0  0.0  0.0   0.0  0.0
2  0.0  0.0  0.0  0.0  0.0   0.0  0.0
1  0.0  0.0  0.0  0.0  0.0   0.0  0.0
0  0.0  0.0  0.0  0.0  0.0   0.0  0.0

In [7]:

bio.system_snapshot(chem_label="A")

Out[7]:

	0	1	2	3	4	5	6
9	0.0	0.0	0.0	0.0	0.0	0.0	0.0
8	0.0	0.0	0.0	0.0	0.0	0.0	0.0
7	0.0	0.0	0.0	0.0	0.0	0.0	0.0
6	0.0	0.0	0.0	0.0	0.0	0.0	0.0
5	0.0	0.0	0.0	0.0	0.0	0.0	0.0
4	0.0	0.0	0.0	0.0	0.0	0.0	0.0
3	0.0	0.0	0.0	0.0	0.0	0.0	0.0
2	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1	0.0	10.0	0.0	0.0	0.0	0.0	0.0
0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

In [8]:

bio.system_snapshot(chem_label="B")

Out[8]:

	0	1	2	3	4	5	6
9	0.0	0.0	0.0	0.0	0.0	0.0	0.0
8	0.0	0.0	0.0	0.0	0.0	0.0	0.0
7	0.0	0.0	0.0	0.0	0.0	0.0	0.0
6	0.0	0.0	0.0	0.0	0.0	0.0	0.0
5	0.0	0.0	0.0	0.0	0.0	10.0	0.0
4	0.0	0.0	0.0	0.0	0.0	0.0	0.0
3	0.0	0.0	0.0	0.0	0.0	0.0	0.0
2	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1	0.0	0.0	0.0	0.0	0.0	0.0	0.0
0	0.0	0.0	0.0	0.0	0.0	0.0	0.0

In [9]:

bio.system_heatmaps()

Notice that the bins with the initial concentration pulses lie on a diagonal from each other, but one is closer to the system "walls"

In [ ]:

Request history-keeping for some bins¶

In [10]:

# Request to save the concentration history of all chemicals at selected bins 
bio.enable_history(bins=[(1,1), (3,3), (1,6)], frequency=5, take_snapshot=True)    # Taking a snapshot to include the current initial state in the history

History enabled for bins [(1, 1), (3, 3), (1, 6)] and chemicals None (None means 'all')

In [ ]:

Initial Diffusion Step¶

In [11]:

delta_time = 2.5

In [12]:

status = bio.diffuse(total_duration=delta_time, time_step=0.1)
print("\n", status)

bio.system_heatmaps(title_prefix="Diffusion")

 {'steps': 25}

In [13]:

# MASS-CONSERVATION CHECK. Verify that that sum of all the entries in each of the above matrices is still the initial 10.
bio.check_mass_conservation(chem_label="A", expected=10.) \
and \
bio.check_mass_conservation(chem_label="B", expected=10.)

Out[13]:

True

A second step¶

In [14]:

status = bio.diffuse(total_duration=delta_time, time_step=0.1)
print("\n", status)

bio.system_heatmaps(title_prefix="Diffusion")

 {'steps': 25}

In [ ]:

This is still an early stage in the diffusion process; let's advance it more... (Visualization from results shown at selected times)¶

In [15]:

for i in range(300):
    status = bio.diffuse(total_duration=delta_time, time_step=0.2)

    if i==3 or i==20 or i==50 or i==100 or i==299:
        fig = bio.system_heatmaps(title_prefix="Diffusion")
        fig.show()

All bins now have essentially uniform concentration. The diffusion has reached equilibrium¶

Notice how B, further away from walls compared to A, has an opportunity to spread out more quickly, in spite of the same diffusion rate coefficient

Mass conservations: the initial "10. units of concentration" are now uniformly spread across the 70 (7x10) bins, leading to a near-constant concentration of 10./60

In [16]:

10./70

Out[16]:

0.14285714285714285

In [17]:

# Mass conservation for both `A` and `B` can also be verified as follows:
bio.check_mass_conservation(chem_label="A", expected=10.)

Out[17]:

True

In [18]:

bio.check_mass_conservation(chem_label="B", expected=10.)

Out[18]:

True

In [ ]:

Visualization of concentration changes with time at particular bins¶

In [19]:

bio.plot_history_single_bin(bin_address=(1,1))    # The bin with the initial pulse of `A`

In [ ]:

In [20]:

bio.plot_history_single_bin(bin_address=(3,3))    # The bin halfway between the initial pulses of `A` and `B`

Even thought bin (3,3) is exactly halfway between the bins with the initial pulses of A and B, an asymmetry develops because A is more "hemmed in by walls", and has fewer directions to spread out, including towards (3,3), while B also dilutes away towards the top (high y-bin values) of the system. Thus A arrives more quickly.
(Compare to the perfect overlap in experiment diffusion_2_a)

In [ ]:

In [21]:

bio.plot_history_single_bin(bin_address=((1, 6))) # Distance from (1,1), with the initial pulse of `A`, is 5;  
                                                  # distance from (5,5), with the initial pulse of `B`, is 4.12

B arrives more quickly at this bin, until A eventually catches up

In [ ]:

Diffusion of 2 chemicals¶

Identical to experiment diffusion_2_a EXCEPT for some extra rows of bins at the top of the system (high y-bin values), which breaks the previously-perfect symmetry of the 2 chemicals: now, one of them (A) is more "hemmed in by the walls", compared to the other one¶

TAGS : "diffusion 2D", "basic"¶

Different ways to visualize the system¶

Request history-keeping for some bins¶

Initial Diffusion Step¶

A second step¶

This is still an early stage in the diffusion process; let's advance it more... (Visualization from results shown at selected times)¶

All bins now have essentially uniform concentration. The diffusion has reached equilibrium¶

Visualization of concentration changes with time at particular bins¶

Identical to experiment `diffusion_2_a` EXCEPT for some extra rows of bins at the top of the system (high y-bin values), which breaks the previously-perfect symmetry of the 2 chemicals: now, one of them (`A`) is more "hemmed in by the walls", compared to the other one¶