EHD azimuthal instability of two rigid-rotating columns with Marangoni effect in porous media

Abstract

This current work is concerned with the analysis of the azimuthal instability of a circular interface between two rotating cylindrical nano-fluids under the influence of a uniform azimuthal electric field. The fluids are considered as dielectric, viscous, homogeneous, incompressible, and saturated in porous media. To simplify the mathematical manipulation, the viscous potential theory along with the normal modes analysis is employed. Motivated by the potential implication of mass and heat transfer in physics, engineering and biology, the existing configuration is intended to be a miscible one. Additionally, apart from Hsieh’s simplified formulation (J Basic Eng 94:156, 1972, Phys Fluids 21:745, 1978), the governing equations of motion include energy as well as volumetric nanoparticles fraction equations. The surface tension depends on temperature and concentration distributions. Consequently, the influence of Marangoni convection takes place. The linear stability results in an exceedingly complicated transcendental dispersion relation. Typically, this equation has no exact (closed) solution. Subsequently, numerical calculations are performed to validate the theoretical outcomes and describe the relationship between the real part of the growth rate and the radius of the cylindrical interface. The analysis reveals a set of non-dimensional numbers, all of which are restricted by the stability criteria.