This thesis describes two seperate results in the study of solar neutrinos. The first is a measurement of the $\ce{^{8}B}$ solar neutrino flux using a 69.2,kt-day dataset acquired with the SNO+ detector during its water commissioning phase. Using an energy range of 5,MeV to 15,MeV, fits of the solar neutrino event direction yielded an observed flux of $2.53^{+0.31}{-0.28}$(stat.)$^{+0.13}{-0.10}$(syst.)$\times10^6$,cm$^{-2}$s$^{-1}$, assuming no neutrino oscillations. This flux is consistent with standard matter enhanced neutrino oscillations and measurements done by other experiments. At energies above 6,MeV the dataset is an extremely pure sample of solar neutrino elastic scattering events, allowing an accurate measurement with relatively little exposure. In that energy region the best fit background rate is $0.25^{+0.09}{-0.07}$,events/kt-day, significantly lower than the measured solar neutrino event rate in that energy range, which is $1.03^{+0.13}{-0.12}$,events/kt-day. The second topic is the development of a novel model for neutrino mixing that allows for a potential that couples to neutrino flavor and is only significant in areas of near zero matter density. A neutrino mixing simulation of this model was developed and is described. Special consideration is given to a previously observed tension in the measured value for $\Delta m^{2}_{21}$ by the KamLAND reactor experiment and a combined solar neutrino experiment measurement. Performing a fit to solar neutrino and reactor neutrino data it's determined that this new neutrino mixing model reduces the tension between solar neutrino measurements and the KamLAND measurement from $\Delta \chi^{2}=4.2$ to $\Delta \chi^{2}=.85$ with two new degrees of freedom. Providing a modest preference for this new model over standard neutrino mixing. Finally, future improvements and generalizations to this result are discussed.