Aiming for the simulation of colloidal droplets in microfluidic devices, wepresent here a numerical method for two-fluid systems subject to surfacetension and depletion forces among the suspended droplets. The algorithm isbased on an efficient solver for the incompressible two-phase Navier-Stokesequations, and uses a mass-conserving level set method to capture the fluidinterface. The four novel ingredients proposed here are, firstly, aninterface-correction level set (ICLS) method; global mass conservation isachieved by performing an additional advection near the interface, with acorrection velocity obtained by locally solving an algebraic equation, which iseasy to implement in both 2D and 3D. Secondly, we report a second-orderaccurate geometric estimation of the curvature at the interface and, thirdly,the combination of the ghost fluid method with the fast pressure-correctionapproach enabling an accurate and fast computation even for large densitycontrasts. Finally, we derive a hydrodynamic model for the interaction forcesinduced by depletion of surfactant micelles and combine it with a multiplelevel set approach to study short-range interactions among droplets in thepresence of attracting forces.
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