Truby J M, Mueller S P, Llewellin E W, Mader H M
Department of Earth Sciences , Durham University , Durham DH1 3LE, UK.
Institute of Geosciences, Johannes Gutenberg University Mainz , 55099 Mainz, Germany.
Proc Math Phys Eng Sci. 2015 Jan 8;471(2173):20140557. doi: 10.1098/rspa.2014.0557.
We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an 'effective-medium' approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction ([Formula: see text]) and bubble volume fraction ([Formula: see text]). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.
我们建立了一个用于描述牛顿流体中气泡和颗粒三相悬浮体系在稳定流动下的流变学模型。我们采用“有效介质”方法，将含气泡液体视为悬浮颗粒的连续介质。由此得到的三相模型结合了分别来自文献的气泡悬浮流变学和颗粒悬浮流变学的两相模型。该模型通过在低气泡毛细管数区域收集的气泡和球形颗粒三相悬浮体系的新实验数据进行了验证。在颗粒体积分数（[公式：见正文]）和气泡体积分数（[公式：见正文]）的实验范围内发现了良好的一致性。与模型预测一致，实验结果表明，在低毛细作用下向稀颗粒悬浮液中添加气泡会增加其粘度，而向浓颗粒悬浮液中添加气泡会降低其粘度。该模型考虑了颗粒的各向异性，并且易于扩展以考虑可变毛细作用，但尚未针对这些情况进行实验验证。
