Yes dear we should may two phase modeling for nanofluids in LBM .
Several important studies have been drawn considering single phase nanofluids which try to explain the observed anomalous enhancement in heat transfer.
But it becomes necessary to consider two-phase approach, which claims a better model to describe the nanofluids thermal conductivity enhancement. Slip velocity between the particle and base fluid plays an important role on the heat transfer performance of nanofluids. Different slip mechanism are responsible for this, which are inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage and gravity settling. Out of these seven slip mechanisms Brownian motion and Thermophoresis plays important role.