title: Shear dispersion in a capillary tube with a porous wall.
abstract: An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.
authors: Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada.
authors: Morteza
authors: M
authors: Dejam
authors: Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada. Electronic address: hhassanz@ucalgary.ca.
authors: Hassan
authors: H
authors: Hassanzadeh
authors: Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada.
authors: Zhangxin
authors: Z
authors: Chen
mesh_terms: D004058:Diffusion; D062070:Hydrology / Q000379:methods*; D008962:Models, Theoretical; D016062:Porosity; D012996:Solutions
chemical_list: D012996:Solutions
keywords: Advection–diffusion; Coupled system; Dispersion; Double-porosity; Mass storage; Solute transport