Gravity-driven azimuthal flow of a layer of thixotropic fluid on the inner surface of a horizontal tube

Abstract

The gravity-driven azimuthal flow of a layer of thixotropic paint on the inner surface of a horizontal tube is studied, considering surface tension effects. Using the lubrication theory, it was shown that a non-linear, fourth-order partial differential equation governs the time evolution of the paint layer thickness distribution along the azimuthal coordinate. Three parameters arise in the analysis, namely, the Bond number and two rheology-related parameters. The governing equation is integrated via a second-order accurate finite-difference scheme. The results showed that, in situations where the capillary force dominates ( Bo < 1), displacement of the paint after application is very slow. For situations where the gravity force dominates ( Bo > 1), an undulation on the interface arises near the tube bottom at sufficiently large times.