A novel implementation of surface tension and adhesion for smoothed particle hydrodynamics (SPH)

In this communication a novel implementation was outlined to simulate surface tension and adhesion by weakly compressible Smoothed Particle Hydrodynamics (SPH). Physical effects in a liquid phase of surface tension and adhesion toward a solid surface were generated by including proper particle-particle interactions within the SPH scheme. The analytical relationship describing intensities of such forces as a function of mutual distance, was derived from the literature and was given a dimensionally consistent form. Four computational approaches were compared, including as ingredients: Monaghan or Riemann solvers, for the viscous/dissipative term of momentum conservation equation; two diverse strategies to compute the overall adhesion force acting onto each liquid particle, one exploiting as sampling points “ghost” particles (already present for boundary conditions), another one based on numerical quadrature within the support of the approximating Kernel. For very preliminary simulations a single phase scenario was considered, describing in a simplified fashion a sessile droplet experiment for wettability assessment. A semicircular liquid droplet was discretized by particles, and subjected to surface tension and adhesion forces exerted by a solid, flat substrate, coincident with a boundary of the problem domain. On the basis of results so far available, Monaghan solver exhibited superior robustness; on the other hand, Riemann solver was preferable as for the smoothness of pressure field. However, severe numerical problems were met: locally, within the droplet, spurious and unphysical negative pressure were predicted by both solvers, endowed by unexpected instability of particle flow and by a global lack of robustness at varying the analysis parameters.