Membranes, with selective permeability, separate 2 previously fully-mixed chemicals¶

The membranes are permeable to one of the chemicals, and impermeable to the other one.¶

See also experiment diffusion_3, where a transient separation is achieved WITHOUT membranes

TAGS : "membranes 1D", "basic", "diffusion 1D"¶

In [1]:

LAST_REVISED = "May 31, 2025"
LIFE123_VERSION = "1.0.0rc3"        # Library version this experiment is based on

In [2]:

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

In [26]:

#import sys, os
#os.getcwd()
#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 BioSim1D, ChemData, PlotlyHelper, check_version

In [4]:

check_version(LIFE123_VERSION)

OK

In [ ]:

Prepare the initial system¶

with two chemicals A and B

In [5]:

chem_data = ChemData(diffusion_rates=[2., 2.], plot_colors=["turquoise", "green"])   # Names "A", "B" automatically assigned

bio = BioSim1D(n_bins=9, chem_data=chem_data)

In [6]:

bio.set_bin_conc(bin_address=4, chem_label="A", conc=10.)
bio.set_bin_conc(bin_address=4, chem_label="B", conc=10.)

bio.set_membranes(membranes=[ (4,5) ])    # By default impermeable
bio.change_permeability("B", 1.)          # Permeable to `B` (and only to `B`)

bio.describe_state()

SYSTEM STATE at Time t = 0:
9 bins and 2 chemical species
Membranes present:  [(4, 5)]

Out[6]:

	Species	Diff rate	Bin 0	Bin 1	Bin 2	Bin 3	Bin 4	Bin 5	Bin 6	Bin 7	Bin 8
0	A	2.0	0.0	0.0	0.0	0.0	10.0	0.0	0.0	0.0	0.0
1	B	2.0	0.0	0.0	0.0	0.0	10.0	0.0	0.0	0.0	0.0

In [7]:

bio.system_snapshot()

Out[7]:

	A	B
0	0.0	0.0
1	0.0	0.0
2	0.0	0.0
3	0.0	0.0
4	10.0	10.0
5	0.0	0.0
6	0.0	0.0
7	0.0	0.0
8	0.0	0.0

In [8]:

bio.system_heatmaps()

In [ ]:

Request history-keeping for some bins¶

In [9]:

# Request to save the concentration history at the bin with the initial concentration injection, 
# and at a couple of other bins
bio.enable_history(bins=[0, 2, 4], frequency=3, take_snapshot=True)    

History enabled for bins [0, 2, 4] and chemicals None (None means 'all')

In [ ]:

Now, let's start the diffusion¶

In [10]:

bio.diffuse(time_step=0.02, n_steps=1)

Out[10]:

{'steps': 1, 'system time': '0.02'}

In [11]:

bio.system_snapshot()

Out[11]:

	A	B
0	0.0	0.0
1	0.0	0.0
2	0.0	0.0
3	0.0	0.2
4	10.0	9.6
5	0.0	0.2
6	0.0	0.0
7	0.0	0.0
8	0.0	0.0

In [12]:

bio.system_heatmaps()

In [13]:

bio.visualize_system()   # Line curve view

The concentrations of `A` and `B` start to differ¶

The membranes are impermeable to A but permeable to B

In [ ]:

Let's advance the diffusion¶

In [14]:

bio.diffuse(time_step=0.02, n_steps=4)

Out[14]:

{'steps': 4, 'system time': '0.1'}

In [15]:

bio.system_heatmaps()

In [16]:

bio.visualize_system()   # Line curve view

In [ ]:

In [17]:

bio.diffuse(time_step=0.02, n_steps=15)

Out[17]:

{'steps': 15, 'system time': '0.4'}

In [18]:

bio.system_heatmaps()

In [19]:

bio.visualize_system()   # Line curve view

In [ ]:

Finally, let's advance the diffusion to equilibrium¶

In [20]:

bio.diffuse(time_step=0.02, n_steps=600)

Out[20]:

{'steps': 600, 'system time': '12.4'}

In [21]:

bio.system_heatmaps()

In [22]:

bio.visualize_system()   # Line curve view

The membranes, with their selective permeability, have managed to separate the previously fully-mixed `A` and `B`|¶

In [ ]:

Verify that the total amount of each chemicals hasn't changed; in the case of `B`, it has simply shifted across bins¶

In [23]:

# Let's verify mass conservation
bio.check_mass_conservation(chem_label="A", expected=10.)

Out[23]:

True

In [24]:

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

Out[24]:

True

In [ ]:

Visualization of time changes at particular bins¶

Instead of visualizing the entire system at a moment in time, like in the previous diagrams, let's now look at the time evolution of the concentrations of `A` and `B` at selected bins (bins whose history-keeping we requested prior to running the simulation)¶

In [25]:

bio.plot_history_single_bin(bin_address=4, title_prefix="`A` and `B` get separated")

The transient separation of `A` and `B` is best seen by plotting the difference of their concentrations, as a function of time¶

In [28]:

bin4_hist = bio.conc_history.bin_history(bin_address=4)   # The bin where the initial concentration of `A` and `B` was applied
bin4_hist

Out[28]:

	SYSTEM TIME	A	B
0	0.00	10.0	10.000000
1	0.08	10.0	8.537110
2	0.16	10.0	7.383196
3	0.22	10.0	6.673179
4	0.28	10.0	6.068917
...	...	...	...
202	12.16	10.0	1.111178
203	12.22	10.0	1.111174
204	12.28	10.0	1.111171
205	12.34	10.0	1.111168
206	12.40	10.0	1.111165

207 rows × 3 columns

In [29]:

PlotlyHelper.plot_curves(x=bin4_hist['SYSTEM TIME'], y = bin4_hist['A'] - bin4_hist['B'], 
                         x_label="SYSTEM TIME", y_label="[A] - [B]", 
                         colors="purple", title="The separation of `A` and `B`, as seen in central bin 4")

In [ ]:

The separation of `A` and `B` is also seen in other bins...¶

In [30]:

bio.plot_history_single_bin(bin_address=0, title_prefix="The separation of `A` and `B` happens at other bins, too...")

In [31]:

bio.plot_history_single_bin(bin_address=2, title_prefix="The separation of `A` and `B` happens at other bins, too...")

In [ ]:

Membranes, with selective permeability, separate 2 previously fully-mixed chemicals¶

The membranes are permeable to one of the chemicals, and impermeable to the other one.¶

TAGS : "membranes 1D", "basic", "diffusion 1D"¶

Prepare the initial system¶

Request history-keeping for some bins¶

Now, let's start the diffusion¶

The concentrations of A and B start to differ¶

Let's advance the diffusion¶

Finally, let's advance the diffusion to equilibrium¶

The membranes, with their selective permeability, have managed to separate the previously fully-mixed A and B|¶

Verify that the total amount of each chemicals hasn't changed; in the case of B, it has simply shifted across bins¶

Visualization of time changes at particular bins¶

Instead of visualizing the entire system at a moment in time, like in the previous diagrams, let's now look at the time evolution of the concentrations of A and B at selected bins (bins whose history-keeping we requested prior to running the simulation)¶

The transient separation of A and B is best seen by plotting the difference of their concentrations, as a function of time¶

The separation of A and B is also seen in other bins...¶

The concentrations of `A` and `B` start to differ¶

The membranes, with their selective permeability, have managed to separate the previously fully-mixed `A` and `B`|¶

Verify that the total amount of each chemicals hasn't changed; in the case of `B`, it has simply shifted across bins¶

Instead of visualizing the entire system at a moment in time, like in the previous diagrams, let's now look at the time evolution of the concentrations of `A` and `B` at selected bins (bins whose history-keeping we requested prior to running the simulation)¶

The transient separation of `A` and `B` is best seen by plotting the difference of their concentrations, as a function of time¶

The separation of `A` and `B` is also seen in other bins...¶