Colloidal nanoparticle-assisted double diffusive gravitational fingering in a vertical Hele-Shaw cell: Theoretical and numerical studies

If one fluid layer contact with another layer having different density or viscosity, the interface can become unstable resulting in motions driven by density or viscous gradient. Here, the onset of colloidal particle assisted fingering motion in a Hele-Shaw cell is analyzed theoretically and numerically. By considering the mobility of colloidal nanoparticles, new governing equation for colloidal particle movement is obtained. Under the linear stability theory, new stability equations are derived and solved analytically and numerically. The linear stability analysis shows that the fingering without an adverse density gradient is possible for the present colloidal nanoparticle assisted fingering system. In addition, through the numerical simulations, we visualize the fingering motion and prove the results of the linear stability analysis. The present linear stability analysis and numerical simulations are in good agreement. Furthermore, the present analyses explain the recent experimental finding: fingering motion can be induced by adding a small amount colloidal particles into the initially stably stratified fluid layer.