# Initial Number Density of Ink Particles

1. Mar 13, 2010

### Hart

1. The problem statement, all variables and given/known data

Suppose an initial number density of ink particles (i.e. number per unit length) is
given by:

$$f(x) = 2Nx$$ ; for $$0 < x < 1$$

$$f(x) = 0$$ ; otherwise.

Suppose also add a point source containing $N$ molecules at the point $x = − 1$.

(a) Showing that the initial total number of molecules at $x > 0$ is equal to the initial total number of molecules at $x < 0$.

(b) Using the standard time-dependent solution of the 1-D diffusion equation with initial conditions to find an expression
for the number density of molecules as a function of $t$ at the point $x = 0$.

2. Relevant equations

Within the problem statement and solutions.

3. The attempt at a solution

I have no idea how to even go about where to start