Dynamics of Fiber Suspensions and their Applications

研究人员将开发稳健、准确和经济有效的方法来模拟柔性纤维悬浮在斯托克流体中的动力学。柔性纤维构成了悬浮物的微观结构，表现出强烈的非牛顿体行为，如弹性、剪切变薄和剪切流动中的正常应力差异。通过采用非标准方法来解决这个问题，并设计一个基于非局部细长体近似的流体动力相互作用的数值算法，可以模拟用标准方法不可行的问题。由于该数值方法具有坚实的数学基础，因此可以将方法设计视为数值分析问题，在算法设计中仔细处理精度和稳定性问题。需要解决的技术障碍是当细丝彼此接近时精确包含润滑力，以及开发和应用快速求和策略来评估细丝-细丝相互作用。研究人员还将为刚性细丝的特殊情况开发特别有效的方法。他们将把这些方法应用于一系列当前的理论问题，如柔性纤维悬浮液中正常应力差异的发展，流体微观结构中储存和释放弹性应力对流体混合的影响，以及棒状自移动元件的大规模动力学（如在模拟细菌浴中出现的）。浸入流体中的微观柔性纤维的动力学对于理解当前在生物学、工程、和物理。例如，从纸浆和造纸工业的制造过程到在小型设备中混合流体的新提出的方法，再到微生物的运动。这些都是复杂的系统，其动力学尚未得到很好的理解，部分原因是流动的大规模动力学可能取决于微观纤维的详细非线性动力学。为了增加我们对这类问题的理解，研究人员正在开发有效和准确的方法来数值模拟具有许多相互作用纤维的这类系统的动力学。他们将把这些方法应用到当前的一系列应用中，这些应用来自流体、工程和生物学的基础物理学。

The investigators will develop robust, accurate, and cost-effectivemethods for simulating the dynamics of suspensions of flexible fibersin a Stokesian fluid. Flexible fibers make up themicro-structure of suspensions that show strongly non-Newtonian bulkbehavior, such as elasticity, shear-thinning, and normal stressesdifferences in shear flows. By taking a nonstandard approach to thisproblem, and designing a numerical algorithm based on a nonlocalslender-body approximation to hydrodynamical interactions, it ispossible to simulate problems not feasible with standard methods. Asthis numerical method has a firm mathematical foundation, methoddesign can be approached as a numerical analysis problem, carefullytreating issues of accuracy and stability in algorithm design.Technical obstacles to be addressed are the accurate inclusion oflubrication forces when filaments approach each other, and thedevelopment and application of fast summation strategies forevalluating filament-filament interactions. The investigators willalso develop especially efficient methods for the special case ofrigid filaments. They will apply these methods to a set of currenttheoretical issues, such as the development of normal stressdifferences in flexible fiber suspensions, the effect on fluid mixingof storing and releasing elastic stress in the fluidic microstructure,and the large-scale dynamics of rod-like self-locomoting elements (asarises in modeling bacterial baths)The dynamics of microscopic flexible fibers immersed in a fluid areessential to understanding many current problems arising in biology,engineering, and physics. Examples range from manufacturing processesin the pulp and paper industries to new proposed methods for mixingfluids in small devices to the locomotion of micro-organisms. Theseare all complicated systems whose dynamics are not well understood, inpart because the large-scale dynamics of the flow can depend on thedetailed nonlinear dynamics of the microscopic fibers. To helpincrease our understanding of such problems, the investigators aredeveloping efficient and accurate methods for numerically simulatingthe dynamics of such systems with many interacting fibers. They willapply these methods to a set of current applications, drawn from thebasic physics of fluids, engineering, and biology.