Unsteady mass transport from a sphere immersed in a porous medium at finite Peclet numbers

A singular perturbation method is employed in order to develop an analytica l solution to the problem of the unsteady mass transfer from a sphere immer sed in an unbounded saturated porous medium. Al the inception of the proces s. the sphere is suddenly leaking a contaminant, which spreads in the porou s medium by convection and diffusion. The boundary conditions at the surfac e of the sphere are either constant concentration or constant mass flux. Th roughout the process the Peclet number is small but finite. The time and le ngth domains of the problem are separated in four subdomains, which result from the combinations of short and long times, and inner and outer regions. Based on the physical analysis of the problem, the governing equations in these regions are derived and solved in the time domain or the Laplace doma in. A matching technique is used to derive the final expressions for the co ntaminant concentration field and the mass transfer coefficients. Hence, an alytical asymptotic solutions for the concentration of the contaminant in t he entire space and time domains are derived in terms of the Peclet numbers . The solutions are validated by comparison with known analytical results. (C) 1998 Elsevier Science Ltd. All results reserved.