text: Ficks second law can be derived from Ficks first law and the mass conservation in absence of any chemical reactions:
  Assuming the diffusion coefficient  to be a constant, one can exchange the orders of the differentiation and multiply by the constant:
  and, thus, receive the form of the Fick's equations as was stated above.
  For the case of diffusion in two or more dimensions Fick's second law becomes
  which is analogous to the heat equation.
  If the diffusion coefficient is not a constant, but depends upon the coordinate or concentration, Fick's second law yields
  An important example is the case where  is at a steady state, i.e. the concentration does not change by time, so that the left part of the above equation is identically zero. In one dimension with constant , the solution for the concentration will be a linear change of concentrations along . In two or more dimensions we obtain
  which is Laplace's equation, the solutions to which are referred to by mathematicians as harmonic functions.