Mass transport by advection and diffusion is involved in nearly all branches of science, but various scientific disciplines define the two mechanisms of transport differently. Models widely accepted for combining transport resulting from advection and diffusion are shown to be inconsistent with experimental observations. Experimental observations are cited to show that the barycentric velocity of a solution is not synonymous with velocity as determined by the Navier-Stokes equation of fluid motion. The physics of advection and diffusion is analyzed, and requirements for combining advection and diffusion are presented. Advection is defined here as transport responding to a pressure gradient or body force. Molecular diffusion is defined as transport responding to concentration or thermal gradients. Diffusion represents an average velocity component of molecules of a particular constituent relative to a fixed frame of reference external to the solution, rather than to the mean velocity of all constituents in a solution as defined in current literature. Advection and diffusion contribute independently to the total transport.