Solving a diffusion problem involves breaking down the problem into smaller, more manageable steps. First, identify the type of diffusion problem (e.g. Fickian or non-Fickian). Then, determine the boundary conditions and initial conditions. Next, use the appropriate diffusion equation (e.g. Fick's first or second law) to solve for the concentration profile. Finally, check your solution for accuracy and make any necessary adjustments.
Fick's first law describes the diffusion of a solute in a stationary medium, while Fick's second law takes into account the diffusion of a solute in a moving medium. Fick's first law assumes a constant diffusion coefficient, while Fick's second law allows for the diffusion coefficient to vary with time and position.
Non-Fickian diffusion refers to situations where the solute does not diffuse according to Fick's laws. This can occur when there are other factors at play, such as chemical reactions or convection. In these cases, the appropriate diffusion equation must be used (e.g. Stefan-Maxwell equation for multicomponent diffusion) and additional information about the system may be needed to solve the problem.
Some common assumptions made in solving diffusion problems include: a dilute solution, constant diffusion coefficient, steady-state conditions, and one-dimensional diffusion. These assumptions may not always hold true in real-world situations, so it is important to carefully consider the problem and make any necessary adjustments to the assumptions.
One way to check the accuracy of your solution is to compare it to experimental data or previous solutions for similar problems. You can also check if your solution satisfies the boundary and initial conditions, as well as any physical constraints (e.g. concentration cannot be negative). Additionally, you can perform sensitivity analysis by varying the input parameters to see how they affect the solution.