Diffusion in fluids between K nudsen and F ickian limits: Departure from classical behavior

The finite‐difference equation of diffusion (consistent with Einstein's evolution equation of diffusion) without the assumption of small mean free path is discussed. This equation predicts significant deviations from classical behavior for the simplest geometry: fluid in a pipe with a large density gradient, such that one end is at the Fickian limit, the other end is at Knudsen limit and there can be a transition zone between them. This has not been considered in previous studies. The analysis indicates that significant deviations from classical (Fickian) behavior arise due to the large change in mean free path which is important in numerous situations, including vacuum technology and propulsion in space. Other examples of deviations from Fick's law include cases where the mean free path is not small compared to system size (nanoscale systems and low density systems) and cases where there are large gradients. These are important in a variety of practical applications, including vacuum distillation, vacuum pumps, and adsorption measurements. © 2015 American Institute of Chemical Engineers AIChE J , 61: 3138–3143, 2015