The droplet contact angle and morphology of the growth interface (vertical, tapered or truncated facets) are known to affect the zincblende (ZB) or wurtzite (WZ) crystal phase of III-V nanowires (NWs) grown by the vapor-liquid-solid method. Here, we present a model which describes the dynamics of the morphological evolution in self-catalyzed III-V NWs in terms of the time-dependent (or length-dependent) contact angle or top nanowire radius under varying material fluxes. The model fits quite well the contact angle dynamics obtained by in situ growth monitoring of self-catalyzed GaAs NWs in a transmission electron microscope. These results can be used for modeling the interface dynamics and the related crystal phase switching and for obtaining ZB-WZ heterostructures in III-V.