Displacement flow inside a capillary tube — the impact of boundary conditions on the dynamic contact angle

Abstract

Accurately modelling multiphase flows requires a thorough understanding of advancing contact line behaviour, which is crucial for predicting interface dynamics in applications like microfluidics and coating processes. This research investigates how the contact angle boundary condition and slip length influence the dynamic contact angle and interface shape within a horizontal cylindrical capillary tube at low velocities. We conduct numerical simulations of Newtonian fluid flow using the volume of fluid (VOF) method to analyse the impact of these factors across different length scales. We explore three approaches for specifying the contact angle at the triple line, comparing velocity-dependent and velocity-independent models. Our results indicate that employing a velocity-dependent relation reduces the critical capillary number for air entrainment and overestimates the apparent contact angle compared to Hoffman’s experimental findings. Imposing a contact angle based on Kistler’s relation enlarges the viscous bending zone compared to the constant contact angle model. Additionally, increasing slip length influences the apparent contact angle differently depending on the contact angle model used. The best agreement with experimental data is achieved using a constant quasi-static advancing contact angle in the low to intermediate capillary number range. A detailed analysis of the interface shape highlights the role of slip length in regulating viscous bending extent. These findings offer valuable insights for enhancing the accuracy of numerical simulations of multiphase flows involving contact lines, with significant implications for practical applications.