An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions
An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions
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DOI：
10.1007/s003970100171
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发表时间：
2001-09-01
期刊：
影响因子：
2.3
通讯作者：
Willenbacher, N
中科院分区：
文献类型：
--
作者：
Dames, B;Morrison, BR;Willenbacher, N
浓分散体的粒度分布与粘度之间的关系具有重要的工业意义，因为它是获得高固体分散体或悬浮体的关键。这个问题在这里处理实验以及理论上的特殊情况下，强相互作用的胶体粒子。基于广义Quemada方程eta =（1 - phi/phi（max））（-ψ）的经验模型用于描述作为单峰和多峰分散体的体积分数的函数的eta。前置因子解释了eta的剪切速率依赖性，并且不影响eta vs phi曲线的形状。它在这里示出的第一次，胶体的相互作用不出现在最大的包装参数和phi（最大）可以计算出的粒度分布，而无需进一步的知识之间的相互作用的悬浮颗粒。另一方面，指数λ由粒子之间的相互作用控制。对于非相互作用的胶体或非胶体颗粒，从极限值2开始，随着颗粒尺寸的减小，λ通常强烈地增加。对于给定的颗粒系统，它可以表示为数均粒径的函数。因此，双峰分散体的粘度不仅随着大颗粒与小颗粒的尺寸比而变化，而且还取决于随着尺寸比增加而经历最小值的绝对粒度。此外，众所周知的粘度最小值双峰分散体的体积混合比约为30/70的小到大的颗粒显示消失，如果胶体相互作用作出重大贡献。
The relationship between particle size distribution and viscosity of concentrated dispersions is of great industrial importance, since it is the key to get high solids dispersions or suspensions. The problem is treated here experimentally as well as theoretically for the special case of strongly interacting colloidal particles. An empirical model based on a generalized Quemada equation eta = (1 - phi/phi (max))(-epsilon) is used to describe eta as a function of volume fraction for mono- as well as multimodal dispersions. The pre-factor accounts for the shear rate dependence of eta and does not affect the shape of the eta vs phi curves. It is shown here for the first time that colloidal interactions do not show up in the maximum packing parameter and phi (max) can be calculated from the particle size distribution without further knowledge of the interactions among the suspended particles. On the other hand, the exponent epsilon is controlled by the interactions among the particles. Starting from a limiting value of 2 for non-interacting either colloidal or non-colloidal particles, epsilon generally increases strongly with decreasing particle size. For a given particle system it then can be expressed as a function of the number average particle diameter. As a consequence, the viscosity of bimodal dispersions varies not only with the size ratio of large to small particles, but also depends on the absolute particle size going through a minimum as the size ratio increases. Furthermore, the well-known viscosity minimum for bimodal dispersions with volumetric mixing ratios of around 30/70 of small to large particles is shown to vanish if colloidal interactions contribute significantly.