A momentum-conserving implicit material point method for surface tension with contact angles and spatial gradients

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying energies. These variations typically energy dependence on temperature and/or concentration. Furthermore, since the is an interfacial property depending types materials either side interface, spatial variation required for modeling contact angle at triple junction between liquid, solid and surrounding air. Our based itself, rather than associated traction condition most commonly used with particle methods. approach automatically captures gradients without explicit need to resolve them as in approaches. include implicit thermomechanical material coupling particle-based enforcement Robin boundary conditions convective heating. Lastly, we design resampling needed achieve perfect conservation linear angular momentum AffineParticle-In-Cell (APIC) [Jiang et al. 2015]. show our enables time stepping complex behaviors like Marangoni effect hydrophobicity/hydrophilicity. demonstrate robustness utility method by simulating exhibit highly diverse degrees effects, such water, wine wax.