Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium
Abstract
:1. Introduction
2. Formulation and Perturbation Equations
3. Normal Modes Analysis and Solutions
4. Boundary Conditions
- The kinematic boundary condition should be satisfied at the two interfaces, which states that the normal velocities of the liquid sheet at are
- The perturbed velocity of the gas far away from the interface should be vanishes, i.e.,
- The stress tensor’s tangential component must be continuous at the interfaces, i.e.,
- At the interfaces, the electric field’s tangential component is continuous.
- At interfaces, the electric displacement’s normal component is continuous.
- The stress tensor normal component is broken up at the interface by the surface tension coefficient, i.e.,Please note that for symmetric disturbances the boundary conditions that change forms are
5. The Antisymmetric Disturbance Case
5.1. Solutions in the Liquid Sheet Phase
5.2. Solutions in the Gas Medium (in the Upper and Lower Phases)
5.3. Solutions of the Electric Field (in the Upper and Lower Phases)
6. The Symmetric Disturbance Case
6.1. Solutions in the Liquid Sheet Phase
6.2. Solutions of the Electric Field (in the Upper and Lower Phases)
7. Non-Dimensional Dispersion Relations
8. Stability Analysis and Discussion
8.1. Effect of the Weber Number
8.2. Effect of Ohnesorge Number
8.3. Effect of Viscolasticity Parameter
8.4. Effect of Electric Field
8.5. Effect of Medium Permeability
8.6. Effect of Porosity of Porous Medium
8.7. Effect of Gas to Liquid Density Ratio
8.8. Effect of Gas to Liquid Velocity Ratio
8.9. Effect of Dielectric Constants
8.10. Effect of Gas to Liquid Viscosity Ratio
8.11. Effect of Porous Medium
8.12. Effect of Dimension
9. Concluding Remarks
- (1)
- When a system is placed in a two-dimensional configuration, it is more unstable when it is subjected to antisymmetric disturbance than when it is subjected to symmetric disturbance.
- (2)
- A porous medium makes the system more unstable, and it breaks down more quickly, compared to the lack of a porous medium.
- (3)
- Ohnesorge number, Weber number, and electric field all have a destabilizing effect on the system under consideration.
- (4)
- The system is stabilized by the viscoelasticity parameter, the medium permeability, the porous medium porosity, and the gas to liquid viscosity ratio.
- (5)
- We have found that the dielectric constants have a small stabilizing effect.
- (6)
- The gas to liquid velocity ratio affects system stability in two ways: it stabilizes when is less than one, and it destabilizes when is more than one.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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El-Sayed, M.F.; Alanzi, A.M. Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium. Fluids 2022, 7, 247. https://doi.org/10.3390/fluids7070247
El-Sayed MF, Alanzi AM. Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium. Fluids. 2022; 7(7):247. https://doi.org/10.3390/fluids7070247
Chicago/Turabian StyleEl-Sayed, Mohamed Fahmy, and Agaeb Mahal Alanzi. 2022. "Electrohydrodynamic Liquid Sheet Instability of Moving Viscoelastic Couple-Stress Dielectric Fluid Surrounded by an Inviscid Gas through Porous Medium" Fluids 7, no. 7: 247. https://doi.org/10.3390/fluids7070247