Modeling surface tension of a two-dimensional droplet using smoothed particle hydrodynamics

Surface tension plays a significant role at the dynamic interface of free-surface flows especially at the microscale in capillary-dominated flows. A model for accurately predicting the formation of two-dimensional viscous droplets in vacuum or gas of negligible density and viscosity resulting from axisymmetric oscillation due to surface tension is solved using smoothed particle hydrodynamics composed of the Navier-Stokes system and appropriate interfacial conditions for the free-surface boundaries. The evolution of the droplet and its free-surface interface is tracked over time to investigate the effects of surface tension forces implemented using a modified continuous surface force method and is compared with those performed using interparticle interaction force. The dynamic viscous fluid and surface tension interactions are investigated via a controlled curvature model and test cases of nonsteady oscillating droplets; attention is focused here on droplet oscillation that is released from an initial static deformation. Accuracy of the results is attested by demonstrating that (i) the curvature of the droplet that is controlled; (ii) uniform distribution of fluid particles; (iii) clean asymmetric forces acting on the free surface; and (iv) nonsteady oscillating droplets compare well with analytical and published experiment findings. The advantage of the proposed continuous surface force method only requires the use of physical properties of the fluid, whereas the interparticle interaction force method is restricted by the requirement of tuning parameters.