标题： 多流体张量方程用于半稀释单分散悬浮液的流动 显示英文标题

标题： Multifluid tensorial equations for the flow of semi-dilute monodisperse suspensions

摘要： 使用Jackson（1997）的体积平均技术，我们推导出一组双流体方程，用于描述半稀释区域中单分散非布朗胶体悬浮液的动力学。 这些方程是张量形式的，可以应用于任意几何结构。 开发了闭合模型，该模型将每个粒子周围的应力表示为由于流体通过固定颗粒床流动产生的应力之和，以及由于颗粒之间相互作用产生的应力之和。 强调实用性，所开发的闭合模型与这些系统中颗粒相互作用的当前知识一致，但采用可调整的参数以表示特定颗粒悬浮液的微观结构。 在相互作用模型中，使用了一个关于每个颗粒周围颗粒分布的模型，该模型依赖于应变率场，允许在响应任意应变场时在悬浮液中发展出微观结构的各向异性（从而产生法向悬浮应力）。 在颗粒相互作用期间作用于颗粒上的力矩通过求和颗粒对之间的水动力贡献来计算，但进行了调整以认识到多颗粒相互作用可以增加每次相互作用产生的有效应力。 最后，对推导出的动量方程进行了数量级分析，以确定哪些项是重要的，最终方程中只保留了预测目标半稀释区域内层流行为所需的项。 在一篇配套论文（称为论文II，Noori等，2024）中，我们选择了预测实验测得的宏观悬浮液行为的微观结构参数，建立了颗粒特性（即粗糙度）、悬浮液微观结构以及任意流动场中的剪切诱导颗粒迁移之间的联系。 显示英文摘要

摘要： Using the volume averaging technique of Jackson (1997), we derive a set of two-fluid equations that describe the dynamics of a mono-disperse non-Brownian colloidal suspension in the semi-dilute regime. The equations are tensorial and can be applied in arbitrary geometries. Closure models are developed that represent the stress surrounding each particle as a sum of stresses due to fluid movement through a fixed bed of particles, and those due to interactions between particles. Emphasising pragmatism, the developed closure models are consistent with current knowledge of particle interactions in these systems but employ parameters that can be tuned to represent the microstructure of specific particle suspensions. Within the interaction model, a model for the particle distribution around each particle is used that depends on the strain rate field, allowing anisotropy of the microstructure (and hence normal suspension stresses) to develop within the suspension in response to arbitrary strain fields. Force moments acting on particles during particle interactions are calculating by summing hydrodynamic contributions between particle pairs, but adjusted to recognise that multi-particle interactions can increase the effective stress generated during each interaction. Finally, an order of magnitude analysis is performed on the derived momentum equations to determine what terms are significant, leaving only terms in the final equations that are required to predict behaviour during laminar flow within the targeted semi-dilute regime. In a companion paper (referred to as paper II, Noori et. al., 2024) we chose sets of microstructure parameters that predict experimentally measured bulk suspension behaviour, creating a link between particle properties (i.e. roughness), suspension microstructure and shear-induced particle migration in arbitrary flow fields.