Recent studies on the spreading phenomena of liquid dispersions of nanoparticles (nanofluids) have revealed that the self-layering and two-dimensional structuring of nanoparticles in the three-phase contact region exert structural disjoining pressure, which drives the spreading of nanofluids by forming a continuous wedge film between the liquid (e.g., oil) and solid surface. Motivated by the practical applications of the phenomenon and experimental results reported in Part I of this two-part series, we thoroughly investigated the spreading dynamics of nanofluids against an oil drop on a solid surface. With the Laplace equation as a starting point, the spreading process is modeled by Navier-Stokes equations through the lubrication approach, which considers the structural disjoining pressure, gravity, and van der Waals force. The temporal interface profile and advancing inner contact line velocity of nanofluidic films are analyzed through varying the effective nanoparticle concentration, the outer contact angle, the effective nanoparticle size, and capillary pressure. It is found that a fast and spontaneous advance of the inner contact line movement can be obtained by increasing the nanoparticle concentration, decreasing the nanoparticle size, and/or decreasing the interfacial tension. Once the nanofluidic film is formed, the advancing inner contact line movement reaches a constant velocity, which is independent of the outer contact angle if the interfacial tension is held constant.