Thin-film deposition by a confined bubble moving in viscoelastic Boger fluids

Abstract

Thin-film deposition is ubiquitous in a wide range of engineering and biological applications. While viscous film deposition in Newtonian fluids has been extensively investigated, the film deposition dynamics for commonly encountered non-Newtonian complex fluids remain poorly understood, particularly with regard to experimentally validated scaling laws for film thickness. Here, we investigate thin-film deposition by a confined bubble moving in a circular capillary tube filled with constant-viscosity viscoelastic (i.e., Boger) fluids, which allows us to quantify the influence of the fluid elasticity on the film deposition. We performed systematic experiments to characterize the fluid rheology and measure the deposited film thickness across a wide range of flow conditions. Furthermore, we develop a scaling law based on hydrodynamic lubrication theory to rationalize the experimental results with a combination of capillary and Weissenberg numbers, which can be further interpreted as the Deborah number, comparing the viscoelastic relaxation timescale with the characteristic residence time in the capillary-transition region near the bubble front. The scaling relationship shows good agreement with the measured film thicknesses for all test fluids and flow conditions. Our results provide fundamental insights into confined multiphase viscoelastic flows and also help inform design principles for applications such as precision coating and advanced manufacturing involving complex fluids.