Fick's Law (one dimensional diffusion with time)

The Fick's Law (one dimensional diffusion with time) calculator computes the concentration along the x-axis after some period, t.

• [n₀] Concentration maintained at the boundary
• (D) Diffusion Coefficient (units: m²/s )
• (x) Distance in x-direction
• (t) Time

Concentration n(x,t): The calculator returns the concentration in moles per cubic meter.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The flux of solute, `J_x`, is proportional to the the concentration gradient along the x-axis, across the boundary.  The Fick's Law equation for one dimensional fusion is:

   `n(x,t) = n_0*[1 -  (x/( sqrt(D*t*pi) ))]`

where:

• n(x,t) = concentration along the x axis after a period of time
• n₀ = concentration maintained on the boundary
• D = Diffusion Coefficient
• x = distance in x direction
• t = time