The operational properties of liquid metal ion sources (LMIS) have been studied extensively the last three decades. Nevertheless, debate still exists on the emitter shape and the mechanism(s) responsible for ion emission. It is generally believed that prior to onset, the applied electric field causes a (cuspidal) deformation of the liquid emitter surface. This study will use the cone-sphere as a prototype for the emitter surface. The advantage of the cone-sphere model is its ability to replicate analytically the emitter shapes seen experimentally, since one can independently choose the radius of curvature, R, the "form factor" k (which determines the amount of "necking") and the asymptotic cone angle. The I-V characteristics of a cone-sphere model of a Au LMIS were calculated using the image hump (IH) and charge exchange (CE) models for the field evaporation process. Field evaporation is assumed to be thermally activated and follow an Arrenhius expression of the form exp(-Q(n)/kT), where Q(n) is the activation energy. The multidimensionality of the source is accounted for in the calculation of the exact field variation on the three-dimensional surface of the liquid emitter. The calculation of Q(n) in the image hump model follows a standard procedure. However, the evaluation of Q(n) for the charge exchange model differs from that done by others. First, the atomic energy curve for Au is calculated using the universal binding energy curve of Smith et al. [J. R. Smith, J. Ferrante, and J. H. Rose, Phys. Rev. B 25, 1149 (1982)]. The intersection of the atomic and ionic potential energy curves is determined as a function of field. The quantity Q(n) is then the energy difference between the minimum of the atomic energy curve and its value at the intersection. The I-V characteristics for Au obtained using the CE model are in better qualitative agreement with experimental results for Au and Cs than the IH model in the voltage range from 1 to 10 kV. In paricular, the calculated curves exhibit a definitive onset voltage, a sharp rapid rise, and saturation behavior.