In　this　paper,　we　investigate　the　wave　phenomena　associated　with　a　fluid-particle　model　described　by　the　multi-dimensional　compressible　Euler　or　Navier-Stokes　equations　coupled　with　the　Vlasov-Fokker-Planck　equation　(denoted　by　Euler-VFP　or　NS-VFP　in　abbreviation)　through　the　relaxation　drag　force　on　the　fluid　momentum　equation　and　the　Vlasov　force　on　the　particle　transport.　First,　we　prove　the　globally　nonlinear　time-asymptotical　stability　of　the　planar　rarefaction　wave　to　3D　Euler-VFP　system,　which　as　we　know　is　the　first　result　about　the　nonlinear　stability　of　basic　hyperbolic　waves　for　the　multi-dimensional　compressible　Euler　equations　with　low　order　dissipative　effects　(i.e.,　relaxation　friction　damping).　This　new　(hyperbolic)　wave　phenomena　comes　essentially　from　the　fluid-particle　interactions　through　the　relaxation　friction　damping,　which　is　different　from　the　interesting　diffusive　phenomena　for　either　the　compressible　Euler　equations　with　damping　(Hsiao　and　Liu　in　Commun　Math　Phys　143:599-605,　1992)　or　the　pure　Fokker-Planck　equation　(Lin　et　al.　in　Q　Appl　Math　77(4):727-766,　2019).　To　prove　the　nonlinear　stability　of　a　planar　rarefaction　wave,　we　introduce　a　new　micro-macro　decomposition　around　the　local　Maxwellian　to　the　Vlasov-Fokker-Planck　equation　(kinetic　part　of　the　3D　Euler-VFP　system),　which　presents　an　unified　framework　to　investigate　the　time-asymptotic　stability　of　basic　wave　patterns　to　multi-D　Euler-VFP　or　NS-VFP　system.　In　particular,　a　new　viscous　compressible　fluid-dynamical　model　is　first　derived　from　the　Chapman-Enskog　expansion　for　the　Vlasov-Fokker-Planck　equation,　equipped　with　the　isothermal　pressure　and　the　density-dependent　viscosity　coefficient,　which　takes　the　same　form　of　the　well-known　viscous　Saint-Venant　model　for　shallow　water.　Moreover,　the　nonlinear　stability　of　planar　rarefaction　wave　is　also　shown　for　3D　NS-VFP　system　in　terms　of　the　unified　framework,　and　it　is　further　proved　that　as　the　shear　and　bulk　viscosities　tend　to　zero,　the　global　solution　to　3D　compressible　NS-VFP　system　around　the　planar　rarefaction　wave　converges　to　that　of　3D　Euler-VFP　system　at　the　uniform　rate　with　respect　to　the　viscosity　coefficients.