Thermocapillary instabilities in thin liquid films on a rotating cylinder

Abstract

Thin liquid films flowing along rotating cylinders are crucial in many industrial processes such as centrifugal thin-film evaporators. The thermocapillary instability in these films often leads to operational inefficiencies and stability concerns. To improve the design and operation of these systems under thermal effects, achieving a uniform distribution of the coating layer is crucial. This challenge becomes even more complex when the cylinder is simultaneously heated and rotated. A comprehensive understanding of these coupled effects is essential for uplifting the efficiency and effectiveness of these systems in practical applications. In this study, we present a model for a thin liquid film flowing along the inner surface of a rotating cylinder subjected to nonuniform heating. Using a long-wave approximation to describe interface dynamics, our study formulates a full lubrication equation incorporating thermal boundary conditions, nonlinear curvature terms, and rotational effects. Linear stability analysis indicates that the Rayleigh-Plateau instability can be suppressed by rotating the cylinder. When the wall is uniformly heated, the reinforced instability can also be suppressed by introducing rotation. Additionally, we investigate the influence of thermocapillarity and rotation on wave speed and the stability of traveling wave solutions. Furthermore, we numerically study the self-similar solution in plug formation and obtain the scaling ${\left(t_c-t\right)}^{1/5}$, where $t_c$ is the choke time. We find the exponent 1/5 is independent of rotation but $t_c$ increases with higher rotation. Numerical simulation reveals that nonuniform heating exacerbates surface wave instability and plug formation (or choke behavior), while cylinder rotation can potentially delay plug formation. Our analysis shows that an increasing Biot number can induce choke behavior in a uniformly heated cylinder, but the introduction of rotation can delay the onset of choking.