Non-isothermal flow of a liquid film on a horizontal cylinder

Abstract

We consider the flow of a viscous liquid film on the surface of a cylinder that is heated or cooled. Lubrication theory is used to study a thin film under the influence of gravity, capillary, thermocapillary, and intermolecular forces. We derive evolution equations for the interface shapes as a function of the azimuthal angle about the cylinder that govern the behaviour of the film subject to the above coupled forces. We use both analytical and numerical techniques to elucidate the dynamics and steady states of the thin layer over a wide range of thermal conditions and material properties. Finally, we extend our derivation to the case of three-dimensional dynamics and explore the stability of the film to small axial disturbances.

A depth-averaged model for non-isothermal thin-film rimming flow

“…Temperature profiles in rimming and coating flows have been extensively studied using lubrication theory with inertia and heat convection typically negligible, for example [6], and good reviews of work on this is available in the recent publications [7,8]. Our paper aims to extend the thin film analysis by including these effects which may become important in the aero-engine application.…”

An analytical film drainage model and breakup criterion for Taylor bubbles in slug flow in inclined round pipes

“…Also, the intermolecular forces are included through the intermolecular potential function in the liquid, Φ, accounting for the difference behavior between a thin film and a bulk liquid [35]. To include these effects, we first look at the Navier-Stokes equation in the…”

“…Such criterion can be used to determine under which conditions the lubricating film is present, which is a key input for both numerical simulations [15,42,4,22] and mechanistic modeling of slug flow in order to determine correctly the Taylor bubble velocity and pressure drop. Also, it can be applied in flow assurance 35 studies of high-viscosity oil slug flows, a critical aspect in oil and gas systems:…”

Numerical investigation of the coupled interaction between an unsteady aerodynamic flow field and a water film coating on a circular cylinder

“…given by Lemaitre et al (2007) in the case of flow on a static cylinder and with an earlier equation (Reisfeld and Bankoff, 1992) for the case without aerodynamic loading.…”