An SPH model to simulate the dynamic behavior of shear thickening fluids

Abstract

While significant research has been dedicated to the simulation of fluids, not much attention has been given to exploring new interesting behavior that can be generated with different types of non-Newtonian fluids with nonconstant viscosity. Going in this direction, this paper introduces a computational model for simulating the most interesting phenomena observed in non-Newtonian shear thickening fluids, which are fluids where viscosity increases with increased stress. These fluids have unique and unconventional behavior, and they often appear in real-world scenarios such as when sinking in quicksand or when experimenting with popular cornstarch and water mixtures. The fluid exhibits unique phase changes between solid and liquid states, great impact resistance in its solid state, and strong hysteresis effects. Our proposed approach builds on existing non-Newtonian smoothed particle hydrodynamics (SPH) fluid models in computer graphics and introduces an efficient history-based stiffness term that is essential to produce the most interesting types of shear thickening phenomena. The history-based stiffness is formulated through the use of fractional derivatives, leveraging the fractional calculus ability to depict both the viscoelastic behavior and the history effects of history-dependent systems. Simulations produced by our method are compared against real experiments, and the results demonstrate that the proposed model successfully captures key phenomena specific to discontinuous shear thickening fluids.

Flow-to-fracture transition and pattern formation in a discontinuous shear thickening fluid

“…Cornstarch in other interstitial fluids can have no DST response 18 but cornstarch suspensions in water have been routinely used for experiments designed to study the DST phenomenon. Experiments have advanced our understanding through detailed rheological studies 17,[19][20][21][22] , careful characterisation of impact generated shear-jamming (SJ) fronts [23][24][25][26][27][28][29][30][31][32] , and benchmarking of DST models [33][34][35][36] .…”

Review on shear thickening fluid and its applications in vibration reduction

“…The constitutive model of STF highlights its material properties, with several literature sources introducing STF constitutive models [36,[80][81][82][83][84]. The WC model [36] is widely acknowledged as the primary STF constitutive model.…”

Improved smoothed particle dynamics simulation of eXtended Pom-Pom viscoelastic fluid

“…改进方案。例如，为了提高计算精度，Liu 等 [12] 利用积分再生核思想发展了再生核粒子方法 (Reproducing Kernel Particle Method, RKPM)；Liu 等 [13] 推导了具有较高计算精度的有限粒子 法(Finite Particle Method, FPM)； Fang 等 [14] 提出了模拟黏性不可压缩流动的高精度 SPH 方法。 为了改善 SPH 方法的数值稳定性，Yang 等 [15] 提出了一种新的核函数，克服了黏性液滴形成 过程中的张力不稳定；Antuono 等 [16] 在密度方程中引入密度耗散项，以解决流动过程中出现 的压力不稳定；Lyu 等 [17] 发展了粒子迁移技术，保证流动过程中流体粒子的规则分布。为了 施加边界条件，Monaghan 等 [18] 提出了只施加一层粒子在边界的边界排斥力法；Morris 等 [19] 发展了布置多层粒子在边界的虚拟粒子法；Liu 等 [20] 结合排斥力法和虚拟粒子法的优势，建 立了两者相耦合的动力学边界处理技术。虽然这些改进方法已被成功提出并得到一定的应 用，但它们在黏弹性流体力学领域中的应用并不多见。 对于黏弹性流体的 SPH 模拟，Fang 等 [21] 将 SPH 方法推广到含自由面的 Oldroyd-B 黏弹 性液滴撞击固壁问题的模拟中。Hashemi 等 [22] 研究了两个相互作用的固体颗粒在 Oldroyd-B 剪切流场下的迁移运动，分析了 Deborah 数对固体颗粒运动轨迹的影响。Xu 等 [23] 提出了改 进 SPH 方法模拟基于 Oldroyd-B 模型的黏弹性液滴撞击固壁和挤出胀大问题。Ozgen 等 [24] 利用 SPH 方法捕捉了非连续剪切增稠流体特有的流动现象。Vahabi 等 [25] 基于 SPH 方法数值 模拟了气泡在 Giesekus 黏弹性溶液中的上升和变形。King 等 [26] 将对数构象公式耦合到 SPH 方法模拟了高 Weissenberg 数下的黏弹性圆柱绕流问题。 eXtended Pom-Pom(XPP)模型是由 Verbeeten 等 [27] 在 Pom-Pom 模型的基础上基于支链聚 合物的分子理论推导得到的。与传统的简单模型(如 Oldroyd-B、上随体 Maxwell 模型)相比， XPP 模型能够更合理地描述聚合物溶液的剪切和拉伸行为，且在一定程度上克服了应力奇 点问题。此外，大量的实验 [27]…”