  Aiming for the simulation of colloidal droplets in microfluidic devices, we
present here a numerical method for two-fluid systems subject to surface
tension and depletion forces among the suspended droplets. The algorithm is
based on an efficient solver for the incompressible two-phase Navier-Stokes
equations, and uses a mass-conserving level set method to capture the fluid
interface. The four novel ingredients proposed here are, firstly, an
interface-correction level set (ICLS) method; global mass conservation is
achieved by performing an additional advection near the interface, with a
correction velocity obtained by locally solving an algebraic equation, which is
easy to implement in both 2D and 3D. Secondly, we report a second-order
accurate geometric estimation of the curvature at the interface and, thirdly,
the combination of the ghost fluid method with the fast pressure-correction
approach enabling an accurate and fast computation even for large density
contrasts. Finally, we derive a hydrodynamic model for the interaction forces
induced by depletion of surfactant micelles and combine it with a multiple
level set approach to study short-range interactions among droplets in the
presence of attracting forces.
