Study on the effective diffusion coefficient of nano-magnetic fluid and the geometrical factors in tumor tissues

Based on the Fick’s First law, the effective diffusion coefficient of nano-magnetic fluid in tumor tissues is deduced by considering the tumor tissues as porous media and assuming the shapes of tumor to be circle or ellipse or a combination of them. The deduced expression of effective diffusion coefficient is generally a function of geometrical factors with no empirical constants and presents good agreements with the existed values especially in biological tissues (porosity is about 60%), with relative error less than 3%. The irregular structure can be transformed into regular structure (circle or ellipse) by using the irregular factor. The expression of the effective diffusion coefficient can be widely used in both regular and irregular structures and may provide theoretical basis for the study of transportation especially in drug delivery research.