This paper reports the results of detailed studies of the combined effect of the viscous flow and diffusive flow in the transient diffusion of a mixture containing N species in a capillary, and in the transient adsorption of a mixture of hydrocarbons in an activated carbon particle. The Maxwell-Stefan approach is applied to describe the interaction of diffusing species in the large pore network, where the viscous flow mechanism operates in conjunction with the other diffusion mechanisms. In the pure diffusion systems, the viscous flow affects significantly the overall diffusion flux when the molecular weights of the diffusing species are significantly different or when the pore size is small. In the adsorption systems, the viscous flow can enhance the adsorption process as the loss of mass from the gas phase may render the viscous flow significant. We test the theory with the adsorption of nitrogen/ethane/propane onto activated carbon, and it is shown that the theory describes well the adsorption kinetics of this mixture.