Motion of deformable drops in pipes and channels using Navier-Stokes equations

The motion of deformable drops in pipes and channels is studied using a level set approach in order to capture the interface of two fluids. The interface is described as the zero level set of a smooth function, which is defined to be the signed normal distance from the interface. In order to solve the Navier-Stokes equations, a second-order projection method is used. The dimensionless parameters of the problem are the relative size of the drop to the size of the pipe or channel cross-section, the ratio of the drop viscosity to the viscosity of the suspending fluid and the relative magnitude of viscous forces to the surface tension forces. The shape of the drop, the velocity field and the additional pressure loss due to the presence of the drop, varying systematically with the above-mentioned dimensionless parameters, are computed. Copyright (C) 2000 John Wiley & Sons, Ltd.