Long bubbles in tubes filled with viscoplastic fluid

An analysis is presented of the thin viscoplastic film coating the wall of a slot or tube as a long bubble is displaced down the conduit by ambient fluid flow (the viscoplastic version of a classical viscous problem studied by Bretherton). Lubrication theory is used to analyse the limit of low Capillary number and examine primarily the effect of a yield stress. The predictions are compared with the results of numerical simulations with the open source code Gerris.