Uphill Diffusion in Silicate Melts.

Diffusion in silicate melts often shows uphill diffusion, the diffusion of a component up its own concentration gradient. As discussed by Zhang (1993: J. Geophys. Res., 98, 11901-11920), there has been no practical model until now that can predict whether uphill diffusion will occur in a given system. This paper presents a new nonlinear diffusion equation which can describe uphill diffusion in a ternary system and provide a criterion in what conditions uphill diffusion will take place. Cross coefficients Dij(i≡j) in a multicomponent diffusion equation describe the strength in coupling between diffusional flows, which may cause uphill diffusion. Irreversible thermodynamics shows that cross coefficients are dependent on con-centration, although their functional form is unknown. To estimate it, in this paper an irreversible thermodynamic approach by Miller (1959: J. Phys. Chem., 63, 570-578) and an eigenvector analysis by Gupta and Cooper (1971: Physica, 54, 39-59) is combined. The functional form satisfying the two conditions above is:D12=Φ2(D22-D11) and D21=Φ1(D11-D22). These cross coefficients give a nonlinear diffusion equation which satisfactorily describes uphill diffusion.