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