Velocity of Volume Fixed Frame and Its Application in Simulating Concentration Profiles in Multicomponent Diffusion

In non-ideal solutions, partial molar volumes change with composition, which means a diffusion process is always accompanied by change in volume of the system. To account for this change in volume while solving diffusion equation, it is necessary to know the velocity of the local center of volume (\({U}^{V}\)). An expression is derived for \({U}^{V}\), using a treatment that is applicable to a multicomponent system. Simulations of multicomponent diffusion profiles with composition dependent partial molar volumes have been absent in the literature so far. The expression derived in this work is also used to generate diffusion profiles in a hypothetical ternary diffusion couple. Significant difference is observed between the concentration profiles obtained with and without the assumption of constant molar volume. Exact calculation of \({U}^{V}\) also enables the estimation of the expansion or contraction accompanied by diffusion, which in turn would help in assessing diffusion induced stresses and dimensional changes.