Non-expert summaryThe flushing of a viscous fluid from a pipe or cavity by a less viscous one is widely used in cleaning operations. This paper reports the numerical modelling of the transient displacement of a viscoplastic material from straight or suddenly constricted (square entry) concentric cylindrical tubes of finite length, simulating a gas at higher pressure displacing the geometry initially filled with liquid. A mixed finite element method is coupled with a quasi-elliptic mesh generation scheme in order to follow the very large deformations involved. The gas bubble grows in length and leaves a thin liquid film on the duct wall (so it does not remove all the liquid). The shape of the bubble is computed for various Reynolds and Bingham numbers (ratio of yield stress to viscous stress). The 'tip splitting' instability that can arise in flow of a gas along a tube filled with a viscous Newtonian fluids is suppressed with viscoplastic fluids at higher Bingham numbers. The shape of the bubble as it passes through the constriction is also studied.
Non-expert summaryThe use of pressurised air to displace a viscoplastic liquid from a complex duct geometry is simulated using detailed numerical modelling. The transient displacement of Newtonian and viscoplastic liquids by air in cylindrical tubes of finite length with a concentric expansion followed by a contraction in their cross section is considered. The change in diameter is not sudden. Various expansion and contraction ratios are studied. Papanastasiou's formula is employed to regularize the discontinuous Bingham model. Results are presented for a range of fluid and geometrical parameters, and some cases are compared to analytical results.
Non-expert summaryImpinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. This paper investigates what is observed when a coherent, turbulent, water jet impinges normally on a thin layer of an immiscible viscoplastic material. Removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Previously Glover et al. [2016, J. Food Eng.. 178, 95-109] presented a semi-empirical model relating the rate of removal (location of the berm) to the momentum flow rate in the liquid film. The authors present a first-order model for cleaning thin layers of these materials based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the Glover et al. model, with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and in this work they were obtained by fitting to the data. New and existing experimental results are compared with the model for three soft solids immiscible with water: two petroleum jellies and a soft paraffin, which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000. The ratio of average film depth and layer thickness was in the range 0.1-1.5.