An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces
Résumé
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 pressurecorrection 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.
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