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

• Published in: Journal of computational physics Vol. 353; pp. 435 - 459
• Main Authors: Ge, Zhouyang, Loiseau, Jean-Christophe, Tammisola, Outi, Brandt, Luca
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.01.2018; Elsevier Science Ltd; Elsevier
• Subjects: Colloidal droplet; Computational fluid dynamics; Computational physics; Computer simulation; Curvature; Depletion; Depletion force; Droplets; Engineering Sciences; Fluid Dynamics; Fluid flow; Fluid mechanics; Fluids mechanics; Ghost fluid method; Incompressible flow; Level set method; Mathematical models; Mechanics; Multiphase flow; Navier-Stokes equations; Numerical analysis; Numerical methods; Physics; Surface tension; Ghost fluid method; Depletion force; Multiphase flow; Colloidal droplet; Level set method; Physics and Astronomy (miscellaneous); Computer Science Applications
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2017.10.046

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.