Solar energy is an alternative source of energy that can be used to replace fossil fuels. Various types of solar cells have been developed to harvest this seemingly endless supply of energy, leading to the construction of solar cell devices, such as dye-sensitized solar cells. An important factor that affects energy conversion efficiency of dye-sensitized solar cells is the distribution of dye molecules within the porous semiconductor (TiO2). In this paper, we formulate a continuum model for the interaction between the dye molecule Tris(2,2'-bipyridyl)ruthenium(II) (Ru(bpy) and titanium dioxide (TiO2) semiconductor. We obtain the equilibrium position at the minimum energy position between the dye molecules and between the dye and TiO2 nanoporous structure. Our main outcome is an analytical expression for the energy of the two molecules as a function of their sizes. We also show that the interaction energy obtained using the continuum model is in close agreement with molecular dynamics simulations.