Trying to implement Fick's first law of diffusion in a simulation of water movement across cell membrane
<p>I want to do the above simulation using fick's law with the use of finite differences.
My problem is at the set up of the whole problem.</p>

<p>I will list some values and declarations from the paper and how i tried to implement them.(the cell is divided into 6 compartments)</p>

<p><strong>Physical properties:</strong></p>

<ol>
<li>The initial volume of the cell ,V0.</li>
<li>The initial volume of osmotically active water within the cell,Viw0.</li>
</ol>

<p>Here, i did :</p>

<pre><code>V0 = ... # just a variable
V = sc.zeros(5) 
V[0] = ...  # this goes for Viw0
</code></pre>

<p><strong>Boundary conditions:</strong></p>

<ol>
<li>Initial concentration of solute within the cell , Ci0</li>
<li>Concentration in the bulk medium C7 (this goes out of the cell)</li>
</ol>

<p>Here, I did:</p>

<pre><code>C = sc.zeros(5)
C[0] = ... #this goes for Ci0
C7 = ...
</code></pre>

<p><strong>Fick's first law:</strong></p>

<p><code>F = -D * dc/dx</code></p>

<blockquote>
  <p># F the rate of transfer per unit of a section</p>
  
  <p># c the concentration of diffusing substance</p>
  
  <p># x the space coordinate measured normal to the section</p>
</blockquote>

<p>Here, I don't know what the argument of the function must be :</p>

<pre><code>def F(what to put here?):

        dc = 0.1    # I don't know what to do with the dc!
        return -(D*dc)/dx
</code></pre>

<p>Also, how to implement the finite difference method? (I have a class in which i implement the method).</p>

<p>Below, links to the paper:</p>

<p><a href="http://i.stack.imgur.com/kjsLh.png" rel="nofollow">Page 1</a><br>
<a href="http://i.stack.imgur.com/48zPx.png" rel="nofollow">Page 2</a><br>
<a href="http://i.stack.imgur.com/TXbRb.png" rel="nofollow">Page 3</a><br>
<a href="http://i.stack.imgur.com/P2MDF.png" rel="nofollow">Page 4</a>  </p>
