Extensional and shear flows, and general rheology of concentrated emulsions of deformable drops
Extensional and shear flows, and general rheology of concentrated emulsions of deformable drops
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可变形液滴浓缩乳液的拉伸流动和剪切流动以及一般流变学
DOI：
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发表时间：
2015
影响因子：
3.7
通讯作者：
Robert H. Davis
中科院分区：
文献类型：
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作者：
A. Z. Zinchenko;Robert H. Davis
通过对三种类型的稳定宏观流动进行严格的多点数值模拟，研究了高浓度单分散乳液的流变学：(i) 简单剪切 ( $dot{{itgamma}}x_{2}$ , 0 0)，(ii) 平面延伸 (PE) ( $dot{{itGamma}}x_{1},-dot{{itGamma}}x_{2},0$ ) 和 (iii) 混合 ( $dot{{itgamma}}x_{2}$ , $dot{{itgamma}}{itchi}x_{1}$ , 0)，其中 $dot{{itgamma}}$和$dot{{itGamma}}$是变形率，${itchi}in (-1,1)$是流动参数，以便构建和验证具有任意运动学的乳液流动的通用本构模型。该算法是 Zinchenko & Davis 的多极加速边界积分 (BI) 代码的开发（J. Fluid Mech.，第 455 卷，2002 年，第 21-62 页）。它还包含 (ii) 和 (iii) 的周期性边界条件（基于 Kraynik-Reinelt for PE 的可再现晶格动力学）、表面重叠控制、用于长时间模拟的更鲁棒的可控表面三角测量以及更高效的加速。在液滴体积分数 $c=0.45{-}0.55$ 、液滴与介质粘度比 ${itlambda}=0.25{-}10$ 和各种 毛细管数 $mathit{Ca}$ ，周期单元中有 100–400 滴，每滴有 2000–4000 个边界单元。高表面分辨率对于小 $mathit{Ca}$ 下的所有三种流动都很重要。在某些剪切流模拟中，大系统尺寸和高达数千的应变 $dot{{itgamma}}t$ 对于识别相变到部分有序状态的开始至关重要，并评估（尽管仍然不精确）该状态下的粘度函数。在相变点以下，剪切粘度与 $mathit{Ca}$ 的关系显示出扭结行为，局部最小值在 ${itlambda}=1$ 和 $c=0.55$ 处最为明显。即使当 $c=0.45$ 时，${itlambda}=0.25$ 乳液也会在较宽的 $mathit{Ca}$ 范围内以部分有序的方式流动。将 ${itlambda}$ 增加到 3–10 会将排序的开始转移到更小的 $mathit{Ca}$ ，通常超出模拟范围。与简单剪切相反，在 PE 或混合流中从未观察到相变。具有可变系数的广义五参数 Oldroyd 模型适合任意流动强度（但在相变范围之外）的引伸测量和粘度测量函数。模型预测与强混合流 ${itchi}=0.25$ 的精确模拟结果非常吻合。还考虑了与时间相关的 PE 流量。讨论了克服本构建模中相变和液滴破碎限制的方法。
The rheology of highly concentrated monodisperse emulsions is studied by rigorous multidrop numerical simulations for three types of steady macroscopic flow, (i) simple shear ( $dot{{itgamma}}x_{2}$ , 0 0), (ii) planar extension (PE) ( $dot{{itGamma}}x_{1},-dot{{itGamma}}x_{2},0$ ) and (iii) mixed ( $dot{{itgamma}}x_{2}$ , $dot{{itgamma}}{itchi}x_{1}$ , 0), where $dot{{itgamma}}$ and $dot{{itGamma}}$ are the deformation rates, and ${itchi}in (-1,1)$ is the flow parameter, in order to construct and validate a general constitutive model for emulsion flows with arbitrary kinematics. The algorithm is a development of the multipole-accelerated boundary-integral (BI) code of Zinchenko & Davis (J. Fluid Mech., vol. 455, 2002, pp. 21–62). It additionally incorporates periodic boundary conditions for (ii) and (iii) (based on the reproducible lattice dynamics of Kraynik–Reinelt for PE), control of surface overlapping, much more robust controllable surface triangulations for long-time simulations, and more efficient acceleration. The emulsion steady-state viscometric functions (shear viscosity and normal stress differences) for (i) and extensiometric functions (extensional viscosity and stress cross-difference) for (ii) are studied in the range of drop volume fractions $c=0.45{-}0.55$ , drop-to-medium viscosity ratios ${itlambda}=0.25{-}10$ and various capillary numbers $mathit{Ca}$ , with 100–400 drops in a periodic cell and 2000–4000 boundary elements per drop. High surface resolution is important for all three flows at small $mathit{Ca}$ . Large system size and strains $dot{{itgamma}}t$ of up to several thousand are imperative in some shear-flow simulations to identify the onset of phase transition to a partially ordered state, and evaluate (although still not precisely) the viscometric functions in this state. Below the phase transition point, the shear viscosity versus $mathit{Ca}$ shows a kinked behaviour, with the local minimum most pronounced at ${itlambda}=1$ and $c=0.55$ . The ${itlambda}=0.25$ emulsions flow in a partially ordered manner in a wide range of $mathit{Ca}$ even when $c=0.45$ . Increase of ${itlambda}$ to 3–10 shifts the onset of ordering to much smaller $mathit{Ca}$ , often outside the simulation range. In contrast to simple shear, phase transition is never observed in PE or mixed flow. A generalized five-parameter Oldroyd model with variable coefficients is fitted to our extensiometric and viscometric functions at arbitrary flow intensities (but outside the phase transition range). The model predictions compare very well with precise simulation results for strong mixed flows, ${itchi}=0.25$ . Time-dependent PE flow is also considered. Ways to overcome the phase transition and drop breakup limitations on constitutive modelling are discussed.