This paper presents a numerical approach to predict the rheology of dense non-colloidal suspensions with a biviscous matrix. A biviscous matrix is characterized as a fluid with two shear rate dependent viscosities i.e. one above and below a critical shear rate ${\dot{\gamma }}_c$. The methodology is based on the lubrication dynamics which dominantly influence the suspension properties at high values of particle concentration. To efficiently handle the singular lubrication forces in the dense suspensions, a semi-implicit splitting integration scheme is employed. Using the presented approach, three dimensional simulations were performed and the predicted rheology of the suspension with a biviscous matrix is discussed under two regimes: (a) ${\dot{\gamma }}_c$ larger than the macroscopic applied shear rate where fluid slippage effect can be modeled in terms of the non-Newtonian properties of the matrix, and (2) ${\dot{\gamma }}_c$ smaller than the macroscopic applied shear rate where a biviscous model can be seen as a regularization of an apparent yield stress matrix. The results obtained at high ${\dot{\gamma }}_c$ show that the shear thinning of the biviscous matrix in the inter-particle gaps, which can be interpreted as an apparent fluid slipping on the particle surface, provides an alternative mechanism to explain the experimentally observed shear-thinning of non-colloidal suspension with Newtonian matrices. At low ${\dot{\gamma }}_c$ values, the predicted suspension properties and its microstructure corroborates the available experimental results on suspensions with yield stress fluids.

本文提出了一种数值方法来预测具有双粘稠度的稠密非胶体悬浮液的流变性。双粘性矩阵的特征是流体具有两种取决于剪切速率的粘度，即一种高于和低于临界剪切速率的粘度${\dot{\gamma }}_C$。该方法基于润滑动力学，该动力学主要影响颗粒浓度较高时的悬浮性能。为了有效处理稠密悬浮液中的奇异润滑力，采用了半隐式拆分积分方案。使用提出的方法，进行了三维模拟，并在两种情况下讨论了具有双粘弹性矩阵的悬浮液的预计流变学：（a）${\dot{\gamma }}_C$ 大于宏观应用的剪切速率，其中可以根据矩阵的非牛顿特性对流体滑移效应进行建模，以及（2） ${\dot{\gamma }}_C$小于宏观应用的剪切速率，其中双粘滞模型可以看作是表观屈服应力矩阵的正则化。高获得的结果${\dot{\gamma }}_C$结果表明，在颗粒间的间隙中双粘剂基质的剪切变稀，这可以解释为颗粒表面上明显的流体滑移，提供了另一种机制来解释用牛顿矩阵实验观察到的非胶体悬浮体的剪切稀化。在低${\dot{\gamma }}_C$ 值，预测的悬浮液特性及其微观结构证实了具有屈服应力流体的悬浮液的可用实验结果。