Effectiveness Factor and Mass Transfer Coefficient in Wedge and Funnel Pores Using a Generalized Fick–Jacobs Model

In this work we study the diffusion–adsorption process in porous media and analyze the effect that the irregular geometry of the pores has on the efficiency of two types of adsorption processes: (a) when there is a net flux along the pore and (b) when the pore is completely saturated. In the first case, we measured the mass transfer coefficient, which is the constant of proportionality between the net flux and the difference of concentration. In the second case, we measure the effectiveness factor, which is the ratio between the actual rate of adsorption and the rate which would be achieved if the entire surface were at the same external concentration. In order to perform this analysis, we use a generalized Fick–Jacobs equation that considers the net effect of diffusion and adsorption along the direction of transport. For this analysis we have used wedge-shaped and conical pores, due to the simplicity of the treatment and their importance in the elaboration of a new brand of artificial materials. We have proved that the enhancement or diminution of the mass transfer coefficient or the effectiveness factor depend upon the specific rate of adsorption; therefore, they can be controlled using our model as a prediction tool in order to build artificial materials with a specific output flux of material. Additionally, our work allows to find how the Thiele modulus locally depends on the geometry of the pore for a linear reaction.