Darish Jeswin Dhas | Searcharxiv

arXiv2026

Evidence of an inertialess Kapitza instability due to viscosity stratification

The classical Kapitza instability of a gravity-driven falling film requires finite inertia to operate. We show that a surface-mode instability can arise in the complete absence of inertia when the film possesses a continuous viscosity stratification, a feature relevant to particle-laden films with shear-induced migration, thermally stratified coatings, and concentration-graded flows. The viscosity field, prescribed as a linear profile across the film thickness, evolves through an advection-diffusion equation characterized by a P$é$clet number. Using long-wave asymptotics and Chebyshev spectral computations, we solve the coupled eigenvalue problem for the perturbation streamfunction and viscosity fields and demonstrate that viscosity stratification destabilizes the surface mode in the zero-inertia (Stokes) limit. The instability is confined to a finite window of P$é$clet numbers. Increasing the stratification parameter lowers the critical P$é$clet number, broadens the range of unstable wavenumbers, and increases the growth rate. The instability mechanism is traced to the phase relationship between perturbation vorticity and the interface displacement: viscosity stratification shifts the vorticity to a lagging configuration, which reinforces interface deformation, following the framework of Hinch (1984). The mechanism bears a structural resemblance to the surfactant-driven Marangoni instability in creeping two-layer flows, extending this class of scalar-mediated, inertialess instabilities to bulk viscosity stratification.

physics.flu-dyn↗

arXiv2022

Instability of a dusty vortex

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian-Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$. Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh-Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as m increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas, modes above it remain unstable but with lower growth rates compared to the non-inertial case. Comparison with Eulerian-Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiraling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays similar pattern which lead to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

physics.flu-dyn↗