Instabilities of nanoparticle-laden non-isothermal flows in homogeneous porous media are investigated. The study is conducted for two representative systems; a hot fluid displacing a cold one (HDC) and a cold fluid displacing a hot one (CDH). The effects of Brownian diffusion and of thermophoresis, representing the average motion of the nanoparticles as a result of temperature gradients, are analysed. In the HDC case, the synergetic Brownian and thermophoretic effects induce a migration of nanoparticles towards the cold fluid and tend systematically to enhance the instability. In particular, because of these combined effects, an initially stable displacement can actually be destabilized. In the CDH case however, Brownian diffusion still acts towards the transport of nanoparticles downstream into the hot fluid while thermophoresis tends to resist such migration. These counteracting effects lead to the generation of local accumulations of nanoparticles at the front and engender the development of local stable regions in the flow. These stable regions hinder the growth of the instabilities, especially those of backward-developing fingers. It is concluded that, in this case, thermophoresis acts against Brownian diffusion and results in less unstable displacements compared to flows where thermophoresis is absent. This effect, exclusively associated with thermophoresis, will not be observed in nanoparticle-free non-isothermal displacements. Finally, it is found that the main effects of Brownian diffusion and thermophoresis arise mainly from their contributions to nanoparticle transport while their effects on the energy balance are negligible and can be disregarded.

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The interface of two approaching fluids in porous media becomes unstable at strong enough flow rates when the viscosity of the displacing fluid is less than that of the displaced one. This phenomenon is studied to address the effect of nanoparticles (NPs) dispersed in the displacing fluid assumed fully miscible with the displaced one. The problem is first studied under isothermal conditions. The effects of the NP-induced additional properties such as the viscosity of the nanofluid, the Brownian diffusivity and the NP deposition are addressed on both the flow instability and the flow configuration. It was found that NPs attenuate the instability of an initially unstable flow, but this effect is mitigated in the presence of NP deposition. Moreover, the Brownian diffusivity was found to have a destabilizing effect, but

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