Collaborative Research: Smoluchowski Equations: Analysis of Dynamics, Singularities and Statistics in Complex Fluid-Particle Mixtures

在这个合作项目中，研究人员研究了流体和颗粒分布之间的相互作用。他们研究了与环境流体既有被动相互作用又有主动相互作用的非线性Smoluchowski方程。具体目标是：研究高浓度极限下向列态的转变、剪切效应、复杂动力学和耦合模式。特别注意了与流体的活泼相互作用、奇点的形成、高浓度悬浮液的稳定以及由于插入而产生的耗散效应。许多生物和人造材料都涉及熔体或流体携带插入颗粒的过程。颗粒的取向及其总体分布影响混合物的物理化学性质。研究人员对这种混合物的模型进行了数学研究。我们的目标是定性地描述由粒子形成的图案，这些图案中哪些是稳定的，在图案中产生不连续的条件是什么，以及与它们相关的能量学和整体物理性质是什么。更好地理解小尺度非平衡动力学对复杂颗粒-流体系统中大尺度输运的影响，例如这里所讨论的粘性聚合物悬浮液，在化学、生物和工程中具有重要意义。

In this collaborative project, the investigators study theinteraction between fluids and particle distributions. Theyexamine the nonlinear Smoluchowski equations with both passive andactive interaction with an ambient fluid. The specific goals are:a study of the transition to nematic states in the highconcentration limit, effects of shear, complex dynamics and modesof coupling. Particular attention is given to the activeinteractions with fluids, singularity formation, the stabilizationof high concentration suspensions, and the dissipation effects dueto the insertions. Many biological and artificial materials are involved inprocesses in which melts or fluid flows carry inserted particles. The orientation of the particles and their overall distributioninfluence the physical and chemical properties of the mixture. The investigators carry out a mathematical study of models of suchmixtures. The goals are to describe qualitatively the patternsformed by the particles, which of these patterns are stable, whatare the conditions for the creation of discontinuities in thepatterns, and what are the energetics and bulk physical propertiesassociated with them. Better understanding of the effects ofsmall-scale nonequilibrium dynamics on large-scale transport incomplex particle-fuid systems, such as the viscous polymersuspensions considered here, is important in chemistry, biology,and engineering.