ON CONVECTION INDUCED BY MOLECULAR-DIFFUSION

Irreversible thermodynamic interpretations of experimental data involv ing molecular diffusion are usually based upon the assumption that in closed containers the local velocity v(o) of the so-called center of v olume (relative to the fixed container walls) vanishes at every point of the system at every instant of time. This assumption greatly simpli fies the interpretation of diffusion data, since by referring the conv ective-diffusive species flux vector to a local reference frame in whi ch the convective component of the flux is v(o) and hence vanishes, th e transport process occurs by molecular diffusion alone. In turn, this furnishes a straightforward, classical linear scheme for determining diffusion coefficients from experimental measurements of transient spe cies concentrations in the closed diffusion cell. Were this not the ca se, one would have to determine the transient hydrodynamic velocity fi eld v induced by the diffusional process, simultaneous with the soluti on of the transient species concentration field-a highly nonlinear ana lysis owing to the coupling between these fields, similar to that occu rring in natural convection problems. In this paper, we first give a p hysical argument proving that v(o) does indeed describe the volume flu x in a mixture. Subsequently, we derive a simple expression-valid for isothermal incompressible binary mixtures-connecting the barycentric o r mass-average velocity field v to. the volume-average velocity field v(o), i.e., relating the mass and volume flows. Later on, after showin g that the generic kinematic argument found in the literature 'proving ' that v(o) vanishes in closed containers is incompatible with hydrody namics and even internally inconsistent, we expose an alternative, mor e general development incorporating hydrodynamic effects, one that sup plies a (necessary but insufficient) compatibility condition based upo n the Navier-Stokes equation. This criterion permits one to identify a priori those classes of systems for which the possibility exists that v(o) = 0. These circumstances are shown to include all laterally unbo unded one-dimensional transport processes as well as all unbounded thr ee-dimensional Navier-Stokes flows for which inertial effects are smal l compared with viscous effects. Such physicochemically low-Reynolds-n umber flows arise in the latter case in circumstances wherein the Schm idt number v/D (v = kinematic viscosity, D = molecular diffusivity) is large compared with unity, a situation that arises for most liquid-ph ase diffusion experiments but not for most gases.