Electrohydrodynamic instability between a newtonian and a non-newtonian fluid in a microchannel

When two immiscible liquids flow in a microchannel, the challenge is to generate droplets. Applying an electric field is an effective method which enables to generate droplets. The focus of this study is the linear stability analysis between a Newtonian and a non-Newtonian fluid in a microchannel in the presence of an electric field. The effects of the dimensionless groups, the electric number, the ratio of the fluid to electric time scales, the Reynolds number, the ratios of the physical properties and the direction of the electric field are analyzed. The maximum growth rates versus the power-law index and the neutral stability curves, i.e. the plot of the power-law indexes versus the critical dimensionless wavenumbers are examined for different thickness ratios which change the effect of the power-law index on the stability. Moreover, the practical ways to destabilize the stable system are investigated, i.e. the electric number related to the applied voltage, the thickness ratio related to the flow rate ratio and the viscosity ratio. The electric number versus the critical dimensionless wavenumbers are plotted to observe the effect of the length of the electrode on the critical electric number.