A modified SPH method to model the coalescence of colliding non‐Newtonian liquid droplets

Abstract

Summary This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non‐Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas‐to‐liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head‐on binary collision of vdW liquid droplets. Both Newtonian and non‐Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off‐center binary collision of non‐Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non‐Newtonian liquid droplets without tensile instability.

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

“…There are also studies on colliding and coalescence process of droplets by SPH [47,48]. Simulation of bubbles in liquid is similar, but can encounter special challenges [49], due to the reverse density/viscosity ratio as that of droplet in gas.…”

Numerical simulation of complex fluid flows with moving interfaces

“…In the second round of validations, we have reproduced numerical results considering the coalescence case of shear-thinning fluids. A numerical-numerical comparison was performed between the modified SPH of YU, 2020) and the front-tracking/markerand-cell approach of this current work. For this comparison, we simulated the head-on binary collision using the same viscosity function adopted in (XU; TANG; YU, 2020), the Cross fluid model, with the same parameters: η 0 = 1, η ∞ = 0.1η 0 , K = 1, and m = 0.1.…”

“…Front-Tracking, in general do not join the two droplets in an automated manner, which causes them to favour the bouncing output (see . The investigations of binary droplets collision with non-Newtonian fluids are mainly restricted to numerical approaches with Carreau-type viscosity functions with special emphasis on the shear-thinning branch BOTHE, 2011;SUN et al, 2015;HIRSCHLER et al, 2017;YU, 2020;CONG;ZHU, 2020). An emblematic exception is the experimental work of Finotello et al (FINOTELLO et al, 2018).…”