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Initial Number Density of Ink Particles

  1. Mar 13, 2010 #1
    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:

    [tex]f(x) = 2Nx[/tex] ; for [tex]0 < x < 1[/tex]

    [tex]f(x) = 0[/tex] ; otherwise.

    Suppose also add a point source containing [itex]N[/itex] molecules at the point [itex]x = − 1[/itex].

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

    (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 [itex]t[/itex] at the point [itex]x = 0[/itex].

    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 :frown:
     
  2. jcsd
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