Viscosity-gradient contributions to momentum diffusion at multiphase interfaces

This work investigates the influence of momentum diffusion model choice on meshless simulations of multiphase flows with discontinuous viscosity. Particular attention is given to the treatment of viscosity gradients at multiphase interfaces, where commonly used diffusion operators based on velocity gradients differ from the divergence of the symmetric Newtonian stress. Generalised Finite Difference (GFD) and Smoothed Particle Hydrodynamics (SPH) discretisations are used to distinguish effects associated with the diffusion model from those associated with the differential operator discretisation. For a 2D multiphase Poiseuille flow, the continuum formulations coincide for the selected unidirectional velocity field. Despite this, their discrete responses differ at the regularised interface, with similar behaviour obtained using both SPH and GFD and a relative difference that remains weakly dependent on resolution over the tested range. A 3D rising-bubble simulation then demonstrates the macroscopic sensitivity to the diffusion-model choice, with the standard operator predicting a terminal velocity 58.6% higher than a validated finite-volume benchmark solution, while the symmetric-stress formulation predicts a terminal velocity 0.8% higher than the benchmark.