Viscous potential flow analysis of capillary instability

Study on hydro-magnetic capillary instability with mass transfer through porous media

“…The undisturbed cylindrical interface is taken at radius R. In the formulation the superscripts 1 and 2 denote the variables associated with the fluid inside and outside the interface, respectively. In undisturbed state, viscous fluid layer of thickness h 1 , density ρ (1) , viscosity μ (1) and magnetic permeability μ (1) m occupies the inner region r 1 < r < R and viscous fluid layer of thickness h 2 , density ρ (2) , viscosity μ (2) and magnetic permeability μ (2) m occupies the outer region R < r < r 2 where h 1 = R − r 1 and h 2 = r 2 − R. Surface tension at the interface is taken as σ . The bounding surfaces r = r 1 and r = r 2 are considered to be rigid.…”

“…where H t (= |n × H|) is the tangential component of the magnetic field and [x] represents the difference in a quantity across the interface, it is defined as [x] = x (2) − x (1) . There is discontinuity in the normal current across the interface; charge accumulation within a material element is balanced by conduction from bulk fluid on either side of the surface.…”

“…Substituting the values of η, φ (1) , φ (2) , ψ (1) m and ψ (2) m in Eq. (22) we get the dispersion relation…”

“…μ∇ 2 u in the Navier-Stokes equation is identically zero but the viscosity is not zero, where μ denotes the viscosity and u denotes the velocity of the fluid flow. To study the capillary instability of a viscous fluid cylinder surrounded by another viscous fluid, Funada and Joseph [1] have applied the VPF theory and observed that the VPF theory gives good agreement with the experimental results. Funada and Joseph [2] have also applied the VPF theory to study the capillary instability of viscoelastic fluid of Maxwell type surrounded by a viscous fluid and found that the elastic property of the fluid enhances the instability.…”

“…The effect of heat and mass transfer on the Kelvin-Helmholtz instability was studied by Asthana and Agrawal [6] when both fluids are miscible and viscous. Kim et al [7] extended the work of Funada and Joseph [1] including the effect of interfacial heat and mass transfer. They have found that the interfacial heat and mass transfer phenomenon resists the growth of disturbance waves.…”