Fluid-particle model is extensively used in many industries such as sprays, aerosols etc. In this paper, we investigate the wave phenomena to a fluid-particle model described by the three-dimensional Vlasov-Fokker-Planck equation coupled with Euler equations. First, we prove the time-asymptotically nonlinear stability of the planar rarefaction wave for both 3D E-VFP systems. Consequently, a new two-fluid model with one fluid equipped with the isothermal pressure and the degenerate viscosity coefficients depending on the corresponding density function linearly is derived from the Chapman-Enskog expansion of the Vlasov-Fokker-Planck equation around the local Maxwellian.