Finger-shaped patterns, also known as viscous fingering (VF) or Saffman–Taylor instabilities, often develop when the interface of two approaching fluids in a porous medium becomes unstable due to a low viscosity fluid displacing a more viscous one. In some cases, this phenomenon is favorable, e.g., in micromixers, while it becomes unfavorable in instances such as, cleaning of oils spills, chromatographic columns and contaminant transport. There are two classes of VF: miscible and immiscible; the former considers molecular diffusion and mechanical dispersion, while the latter includes surface tension. So far, the phenomena have been widely studied and the effects of various parameters analyzed.
The wide usage of nanofluids in different applications, however, raises the question of the potential effects of the presence of nanoparticles on the instability. This is due to the fact that nanoparticles alter the properties of the base fluid, and hence their effects on VF cannot be ignored. Regardless, there are only few studies focusing on this issue, particularly with respect to miscible displacements.
Recently, Behnam Dastvareh (PhD candidate) and Professor Jalel Azaiez from the Schulich School of Engineering at the University of Calgary in Canada presented a study where they focused on investigating the role of parameters affecting the development and growth of VF instabilities of non-isothermal nanoflows in homogeneous porous media. In particular, they analyzed the combined effects of Brownian diffusion and thermophoresis, the average motion of NPs resulting from temperature gradients, on the flow dynamics, particle distribution and instability. Their work is published in the Journal of Fluid Mechanics.
The authors first assessed the effects of Brownian diffusion and thermophoresis in two representative unstable systems: HDC (hot fluid displacing cold fluid) and CDH (cold fluid displacing hot fluid). This analysis was conducted using concentration distribution of the displaced fluid obtained through nonlinear simulations of the flow. The resultant phenomena were explained after which physical interpretations of the observed trends were provided. Lastly, the two scholars extended their study and examined the effects of thermophoresis in the case of initially stable systems.
Dastvareh and Azaiez observed that for the HDC case, the synergetic Brownian and thermophoretic effects induced a migration of nanoparticles towards the cold fluid and tended systematically to enhance the instability. On the contrary, for the CDH case, the Brownian diffusion continued to act towards the transport of nanoparticles downstream into the hot fluid while thermophoresis was seen to resist such migration. Consequently, the counteracting effects were noted to lead to the generation of local accumulations of nanoparticles at the front and to engender the development of local stable regions in the flow.
In summary, the University of Calgary scientists investigated flow instability in homogeneous porous media in the presence of thermal effects and nanoparticles dispersed in the displacing fluid. Generally, they observed that the synergic effect of Brownian diffusion and thermophoresis in the HDC system can increase the viscosity mismatch and enhance the flow instability. On the other hand, in the CDH system thermophoresis acts against Brownian diffusion and results in less unstable displacements compared to flows where thermophoresis is absent. Specifically, stable regions generated as a result of the nanoparticles accumulations in the CDH hindered the growth of instabilities, particularly those of backward-developing fingers. Altogether, they found out that the main effects of Brownian diffusion and thermophoresis arose mainly from their contributions to nanoparticle transport while their effects on the energy balance were negligible and could be disregarded.
B. Dastvareh, J. Azaiez. Thermophoretic effects on instabilities of nanoflows in porous media. Journal of Fluid Mechanics (2018), volume 857, page 173–199.Go To Journal of Fluid Mechanics