In a companion paper, a continuum model for simulating transport phenomena occurring during solidification of a binary metal alloy is extended to allow for treatment of effects such as solutal undercooling and solid transport in the form of floating and settling crystals. However, inclusion of such features requires auxiliary models which, in large part, depend on microscopic considerations. Such models are developed in this study and specifically deal with relations for solid and liquid velocities under conditions involving solid motion, as well as determination of solutal undercooling as a function of the solidification rate and stereological characteristics of the solid/liquid interface. The models also permit determination of final grain density and size.