Abstract We selected a 1.4 wt% Octadecyl trimethyl ammonium chloride (OTAC) concentration wormlike micellar fluid with broad relaxation time spectrum and another single relaxation Maxwell fluid of 4.0 wt% OTAC concentration with a constant weight ratio of OTAC to NaSal of 5:1. The shear viscosity, dynamic modulus as well as the extensional viscosity were tested. The steady and unsteady motion of spheres were investigated by high-speed video images in these two wormlike micellar fluids. Extremely slow settling velocity is found when smaller spheres with diameters of 3.2 and 4.0 mm settles in the 1.4 wt% OTAC solution. Stronger rebound of these spheres occurs in this fluid. Comparing with particle settling velocity in inelastic power law fluid, we concluded that this extremely slow sedimentation in the 1.4 wt% OTAC solution seems to be dominated by the slowest stress relaxation of this solution. The rheology test demonstrated that this wormlike micellar fluid has more tensile hardening, low viscosity and strong elasticity. The oscillation of sphere results from the elasticity of the entangled microstructures of wormlike micelles. For a Maxwell viscoelastic 4.0 wt% OTAC solution, settling behaviors of spheres agree with previous literatures that the flow becomes instability as the Wi number exceeds a critical value. Graphic Abstract Steady and unsteady motion of Particles settling in two kinds of wormlike micellar fluids, one with broad relaxation time spectrum and another with single relaxation Maxwell fluid, were investigated by high speed video camera. The shear viscosities, dynamic modulus as well as the extensional viscosities were tested. Extremely slow settling velocity is found when smaller spheres settles in the broad relaxation time spectrum solution. Stronger rebound of these spheres occurs in this fluid. Comparing with inelastic power law fluid settling velocity, we concluded that this extremely slow sedimentation in broad relaxation time spectrum solution seems to be dominated by the slowest stress relaxation of this solution. The oscillation of sphere results from the elasticity of the entangled microstructures of wormlike micelles with tensile hardening in extensional rheology.

中文翻译：

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粒子在具有广谱弛豫时间的稀释蠕虫状胶束流体中的极慢沉降行为

摘要 我们选择了具有宽弛豫时间谱的 1.4 wt% 十八烷基三甲基氯化铵 (OTAC) 浓度的蠕虫状胶束流体和另一种 OTAC 浓度为 4.0 wt% 且 OTAC 与 NaSal 重量比为 5:1 的单一弛豫 Maxwell 流体。测试剪切粘度、动态模量以及拉伸粘度。通过这两种蠕虫状胶束流体中的高速视频图像研究了球体的稳态和非稳态运动。当直径为 3.2 和 4.0 毫米的较小球体在 1.4 wt% OTAC 溶液中沉降时，发现沉降速度极慢。这些球体在这种流体中会发生更强的反弹。与非弹性幂律流体中的颗粒沉降速度相比，我们得出结论，这种在 1. 4 wt% OTAC 解决方案似乎受该解决方案最慢的应力松弛支配。流变测试表明，这种蠕虫状胶束流体具有更强的拉伸硬化、低粘度和强弹性。球体的振荡是由蠕虫状胶束缠结的微结构的弹性引起的。对于 Maxwell 粘弹性 4.0 wt% OTAC 解决方案，球体的沉降行为与之前的文献一致，即随着 Wi 数超过临界值，流动变得不稳定。图形摘要 用高速摄像机研究了颗粒在两种蠕虫状胶束流体中的稳态和非稳态运动，一种具有宽弛豫时间谱，另一种具有单一弛豫麦克斯韦流体。测试剪切粘度、动态模量以及拉伸粘度。当较小的球体在宽弛豫时间谱解决方案中沉降时，会发现沉降速度非常慢。这些球体在这种流体中会发生更强的反弹。与非弹性幂律流体沉降速度相比，我们得出结论，在宽弛豫时间谱解决方案中这种极其缓慢的沉降似乎是由该解决方案的最慢应力弛豫控制的。球体的振荡是由蠕虫状胶束的纠缠微观结构的弹性引起的，在拉伸流变学中具有拉伸硬化。我们得出结论，在宽弛豫时间谱溶液中这种极其缓慢的沉降似乎是由该溶液的最慢应力弛豫所支配的。球体的振荡是由蠕虫状胶束的纠缠微观结构的弹性引起的，在拉伸流变学中具有拉伸硬化。我们得出结论，在宽弛豫时间谱溶液中这种极其缓慢的沉降似乎是由该溶液最慢的应力弛豫所支配的。球体的振荡是由蠕虫状胶束的纠缠微观结构的弹性引起的，在拉伸流变学中具有拉伸硬化。