Electrohydrodynamic instability in an annular liquid layer with radial conductivity gradients

Area of Science:

• Fluid Dynamics
• Electrohydrodynamics
• Non-equilibrium Thermodynamics

Background:

• Investigates electrohydrodynamic stability in an annular liquid layer.
• Considers a radial electrical conductivity gradient and an applied radial electric field.
• Incorporates a weak axial shear flow driven by a pressure gradient.

Purpose of the Study:

• Analyze the influence of key parameters on fluid layer dynamics.
• Determine the nature of the critical unstable mode (oscillatory or stationary).
• Understand the impact of inner radius, conductivity gradient, shear flow, and ionic diffusion.

Main Methods:

• Employs three-dimensional linear instability analysis.
• Examines the effects of dimensionless inner radius (a).
• Evaluates the role of the electrical conductivity gradient and Reynolds number.

Main Results:

• The critical unstable mode can be oscillatory or stationary.
• Instability increases with the dimensionless inner radius (a).
• Conductivity gradients and the electrical Schmidt number exhibit complex, dual effects on stability.

Conclusions:

• Inner radius and shear flow generally promote instability.
• Conductivity gradients can shift the unstable mode from oscillatory to stationary.
• Ionic diffusion, represented by the electrical Schmidt number, has a dual impact on system stability.