Dendritic microstructures are most dominant patterns in solidified alloys. The microstructural features of these structures control the segregation profiles of solute elements in the interdendritic regions, thus determining the mechanical properties of cast structures. In this study, a 2D model of solid/liquid interface instability in a low carbon steel was introduced, using the multi-phase-field software code MICRESS (R) combined with an in-situ study of solidification in a laser-scanning confocal microscope. The use of a moving-frame boundary condition and a linear temperature gradient within the simulation allows further optimization of the solidification studies in the laser-scanning confocal microscope. By analysing the shape of the delta-ferrite grain boundary at the solid/liquid interface, in-situ and at temperature, it was possible to experimentally determine the Gibbs-Thomson coefficient and the solid/liquid interfacial energy of the alloy. The interface mobility of the solid/liquid interface was calibrated in the model so as to reproduce the experimentally measured interface velocity at the onset of interface instability. The proposed model was used to describe the morphological transitions from planar to cellular to dendritic modes during solidification and solute segregation under a variety of processing conditions such as cooling rate and temperature gradient. The importance of this approach is that the verified model has been used to extend the prediction of microstructural development to cooling rates well beyond what can be achieved experimentally and into the regime pertinent to high-speed continuous casting. Significant microstructural differences that arise as a result of varying processing conditions are discussed.