Process modeling is a valuable tool for process design and optimization. Nonetheless, the extent of its use depends on the physical complexity of each particular application. Flotation is one of the most complex processes to model. In particular, in mechanical flotation cells, turbulent flow prevails and promotes bubble particle collisions. Many size and time scales of both hydrodynamic and physicochemical nature have to be resolved to model the process. The only way to achieve this is a combination of co-current (pulp and froth) and sequential multiscale modeling. A generalized framework for modeling the pulp phase from the device scale to thin film scale separating bubbles and particles is presented here. The core of the model is the term describing the collision frequency between bubbles and particles. Existing approaches to derive this term are reviewed and critically commented demonstrating several inconsistencies. A unified and consistent approach for deriving this collision frequency term is described overcoming all the inconsistencies of previous approaches. Specific results are presented for the case of flotation of fine particles, being practically the only case for which a simplified collision frequency expression of algebraic complexity can be derived.

流程建模是用于流程设计和优化的宝贵工具。但是，其使用范围取决于每个特定应用程序的物理复杂性。浮选是最复杂的建模过程之一。特别地，在机械浮选池中，湍流占优势并促进气泡颗粒碰撞。必须解析流体动力学和物理化学性质的许多大小和时间尺度，以对过程进行建模。实现此目的的唯一方法是并流（纸浆和泡沫）和顺序多尺度建模的组合。这里介绍了一个通用的框架，用于建模从设备规模到将气泡和颗粒分离的薄膜规模的纸浆相。该模型的核心是描述气泡与颗粒之间的碰撞频率的术语。现有的推导此术语的方法已被审查并进行了批判性评论，表明存在一些不一致之处。描述了一种用于推导该碰撞频率项的统一且一致的方法，以克服先前方法的所有不一致性。对于浮选微粒的情况，给出了具体的结果，实际上是唯一可以推导代数复杂度的简化碰撞频率表达式的情况。