Thermophoretic effects on instabilities of nanoflows in porous media

Abstract

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.

Instabilities of nanofluid flow displacements in porous media

“…x < 0 and depletion at the center. Following a previous flow analysis [105], this behavior is a direct consequence of the temperature gradient driven convective transport of the NPs from the center to either sides of the channel. More specifically, the convected NPs from the center increase the local concentration of NPs at either side while NP concentration is decreased at the center, in the position of positive and negative Src respectively.…”

“…In particular based on Einstein equation (D n = k B T 3πµ bf dp ) it is assumed that D n varies linearly with temperature while following Piazza and Parola [93] and Buongiorno [84], D T in Eq. 5.5 is a linear function [105] and incorporating constant K into the viscosity definition, the equations are then made dimensionless. Accordingly, the length, time and pressure are scaled with Daφ U , Daφ 2 U 2 , D a φµ a , viscosity with µ a , velocity with U , C j with C 0 and C n with C n0 .…”

A review on the flow instability of nanofluids

“…Waki et al [43][44] showed that flow stability depends on the nanoparticle concentration and size as well as the magnetic Chandrasekhar number for a flow between two impermeable boundaries and heated underneath by considering an external magnetic force. Dastvareh and Azaiez [45] concluded that the thermophoresis hinders particle Brownian diffusion and leads to less displacement compared with the case in which thermophoresis in homogeneous porous media is not considered. Zargartalebi and Azaiez [46] showed that the flow instability was controlled by the properties of nanoparticles that behave differently at various temperatures.…”

A revised work on the Rayleigh-Bénard instability of nanofluid in a porous medium layer

“…According to the experimental report in the literature, 26 the range nanoparticle concentration commonly used is between 0.1~2% (corresponding to Rn=2.65~52.9), which means that the onset of convection always occurs once the nanofluid within the porous layer is heated from below. The intrinsically unstable phenomenon also occurs at other systems, such as the interface of two approaching fluids in a porous medium, 18 in which the thermophoretic effect plays a determinant role at the onset of instability.…”

“…Such a problem could be resolved by introducing nanofluids, which have been investigated by many studies focusing on the thermal instability of nanofluid flow. [10][11][12][13][14][15][16][17][18] These studies revealed that the instability of convection could be enhanced by employing nanofluids in the porous medium layer.…”