Study of a thin film of colloidal suspension flowing over a vertical cylinder
Phys. Rev. Fluids 10, 084005 – Published 28 August, 2025
DOI: https://doi.org/10.1103/g44d-38zc
Abstract
This study investigates the stability of a liquid film containing colloidal particles flowing along the exterior surface of a vertical cylinder due to gravity. The governing equation for the location of the liquid-gas interface is derived by simplifying the mass and momentum balance equations within the lubrication approximation. The evolution of bulk concentration is modeled by simplifying the advection-diffusion equation assuming dominant radial diffusion. Following the Krieger-Dougherty and Stokes-Einstein equations, the suspension viscosity and colloidal diffusion coefficients are considered functions of bulk concentration. These coupled film and concentration evolution equations are subsequently perturbed using a normal mode analysis to obtain the eigenvalue problem. The resulting dispersion relation is analyzed to study the influence of bulk concentration, surface concentration, particle diffusion, and the solutal Marangoni number on the stability of the system. The presence of bulk colloids leads to an increase in the viscosity and stabilizes the flow. The Marangoni stress due to concentration gradient at the liquid-gas interface stabilizes the curvature pressure-driven instability at moderate Marangoni numbers while introducing another unstable mode driven by surfactant at larger Marangoni numbers. The nonlinear analysis recovers the growth rates predicted by the linear analysis. The pattern for the first mode indicates in-phase evolving waves for film thickness and surface concentration, while a phase lag is observed between the two waves for the second mode. The mechanisms for the two modes are highlighted by using a flux analysis. At larger values of the Bond number, the film behavior asymptotically approaches that of the flow over a planar substrate. A rigid interface limit is attained at large values of the Marangoni number and the predicted growth rate is found to be independent of the concentration profile.
