Non-expert summaryThe Lattice-Boltzman numerical method is used to solve the Navier-Stokes equations describing the displacement of a viscoplastic fluid from a cylindrical pipe by the injection of a Newtonian liquid. The equations are written in dimensionless form so no particular time or length scale is specified. Gravity and surface tension effects are included. The average velocity of the Newtonian liquid is such that its flow is laminar. The numerical code is able to resolve several features of the process: the growth of a 'finger' of Newtonian liquid as it pushes the viscoplastic fluid out and the development of waves at the liquid-fluid interface. The impact of key dimensionless groups, particularly the Bingham number (ratio of critical or yield stress to stress induced by the flow) and Reynolds number.
Scale1e-6 to 1e-3 m, 1e-3 m, 1e-3 to 1 m, 1 to 10 m
[... Show more]