In the vapor-liquid-solid (VLS) nanowire growth, nanowires can be constructed utilizing the difference in the mechanism of crystallization between the vapor-solid (VS) process (outside the solvent droplet) and the VLS process (inside the droplet). We performed a series of separate molecular dynamics simulations for a VLS system and a VS system under equivalent nonequilibrium conditions to clarify the different mechanisms of the solid growth process in both systems and to understand how a liquid substance can catalyze the solidification. The detailed observation of the chemical potential distribution during the steady solid growth state clearly outlines the processes that limit the growth rate. We found that the most dominant process limiting the growth rate is mass transport in the solvent liquid. We also show numerically and analytically that the mass transport rate is proportional to the diffusion constant and also to the solubility of in the solvent, and that a high solubility in the solvent can almost compensate for the disadvantage of a small diffusion constant. Although remarkable catalytic effect by the solvent at least in the linear nonequilibrium region could not be observed, our results suggest that the VLS process would catalyze the solid growth using liquid substance with higher solubility or in a nonlinear nonequilibrium state.