A study on capillary actions of power-law fluids in porous fibrous materials via W-M function

Abstract

The study of fluid diffusion is an important aspect of heat and mass transfer of the porous fibrous materials. This work established a fractal model for the diffusion of power-law fluids in porous fibrous materials by considering the pore size distribution and the tortuosity of the capillary. Adopting the Darcy’s law and the Hagen–Poiseuille’s law, the diffusion coefficient of power-law fluids is derived as a function of the tortuosity fractal dimension, the pore size fractal dimension and the flow behavior index, in which the phase transition and the adsorption effect of fiber as well as the influence of gas diffusion and temperature change are taken into consideration. And the Weierstrass–Mandelbrot (W-M) function is applied to manifest the detailed fractal characters of the pores. Focusing on an analytical expression of the diffusion of power-law fluids in porous fibrous materials, the changes of liquid volume fraction, gas concentration and temperature distribution subjected to the specification initial and boundary conditions are simulated numerically. The test of this approach on the height of fluids when the bottom of cotton fabrics is immersed in the water display the clear diffusion of fluid in fiber. Our preliminary results indicate the important roles that the porosity and flow behavior index play in the fluids transfer in the porous fibrous materials: the fluids with lower power law index rise higher heights and diffuse more rapidly, meanwhile, the height increases with the porosity.