与加载速率相关的细菌鞭毛相变和运动的多尺度问题

The bacterial flagellum, working as a propeller, plays a very important role in the bacterial movement. Recent experiments show that the flagellar filament can undergo a cyclic phase transition under the viscous fluid flowing, now we are working on the martensite phase transition of bacterial flagellar filament under the support of the NSFC. Firstly we made mechanical analysis of the phase transition experiment of the flagellar filament, and got its transition rule; based on this we establish the theoretical model to describe filament’s phase transition under the Kirchhoff rod theory and Ginzberg-Landau phase transition theory, and got the loading (force and displacement) conditions of phase transition instability through the stability analysis; finally based on non-local and non-convex continuum modeling we use finite element method to simulate its phase transition process and successfully capture the main features of flagellar phase transition, such as two-phase coexistence with an interface of finite thickness, phase nucleation and phase growth with interface propagation. Moreover, we find that flagellar phase transition and motion closely relate to the velocity of viscous fluid. The key is the multi-scale problem in the phase transition and motion of flagella. We will further study this problem based on the previous work. Here multi-scale effects include both multi-scale size effect and multi-scale time effect. Since flagella motion involves two time scales: one is characteristic loading time or loading frequency, the other is the viscous time of fluid-solid relative motion. These two time scales have relation with flagellar geometry, at the same time the completion of two time scales leads to a new internal length scale (the domain spacing). Considering both multi-scale of size and time effects, the concrete content of our analysis are as following: phase transition load criteria and motion of flagella; the microstructure domain spacing of the new phase during the phase transition; the stress hysteresis and damping capacity of bacterial flagella. After study, our simulation can predict behaviors of bacterial flagella in different environments (of different fluid viscosity and different flow speed). Although there are limited experiments (because of the difficult experimental techniques), our theoretical study can help get general relations for various bacteria in various ambient.

鞭毛作为细菌运动的推进器，在细菌运动中起重要作用。实验发现细菌鞭毛在粘性流体作用下会发生马氏体相变, 目前正在对其进行研究。我们以实验分析为基础，建立相变模型描述鞭毛相变过程并进行稳定性分析；在非局部和非凸连续介质力学基础上用有限元法对实验现象进行模拟，描述其相变典型特征（形核、长大和两相共存）。进一步实验发现鞭毛相变和运动跟粘性流体流速密切相关，其科学问题为鞭毛相变和运动的多尺度问题，课题将就此展开研究。这里的多尺度涉及空间多尺度和时间多尺度，两个时间尺度：一、加载特征时间尺度（加载率）；二、鞭毛与粘性液体间运动产生的粘性时间尺度。这两个时间尺度除与鞭毛几何尺度有相互作用外，两个时间尺度的相互竞争还会引起一个新的空间涌现尺度（相变带之间的间距）。内容包括多尺度效应下：相变载荷条件和其运动规律，相变过程中形核微结构、应力滞后和能量耗散。通过以上工作，预测鞭毛在不同粘性流体中相变和运动规律。

鞭毛作为细菌运动的推进器，在细菌运动中起重要作用。实验发现细菌鞭毛在粘性流体作用下会发生马氏体相变, 而且其力学相变的过程跟加载速率有关。鞭毛的力学相变过程与组成鞭毛的鞭毛蛋白的重构有关。我们以实验分析为基础，建立了二维相变模型描述鞭毛细丝力学相变过程并进行稳定性分析；在非局部和非凸连续介质力学基础上运用有限元法对实验现象进行模拟，描述其相变典型特征（形核、长大和两相共存），研究在不同加载速率影响下鞭毛的相变特点；还分析了鞭毛马达在不同离子载荷下的工作效率。进一步，我们把研究对象由单个细菌细胞扩展的多个细菌细胞，对由多个细菌细胞形成的生物膜的动力学生长过程和力学特性进行了系统的实验、数值和模拟分析。具体开展了以下方面的工作：.1. 根据细菌鞭毛细丝的相变特点，建立以扭转率和曲率为序参量的朗道相变模型，该模型考虑非凸弹性能用来描述鞭毛相变引起的失稳；非局部梯度能描述两相之间的界面能；粘弹性耗散能描述非平衡条件下材料的松弛过程，即相变动力学。运用有限元方法对模型进行数值模拟来描述鞭毛的相变过程。.2. 在以上模型和模拟算法的基础上，对细菌鞭毛相变进行稳定性分析，得到相变发生的载荷条件；以及加载速率对鞭毛相变的影响。在加载速率非常慢的情况下，即加载时间远远大于材料的特征时间参数，鞭毛会发生相变；当加载速率非常快时，即加载时间远远小于材料特征参数，鞭毛不发生相变，只发生弹性变形。同时得到了不同加载速率下力和应变的定量关系。.3. 鞭毛马达是由于细胞壁内外的离子浓度差来驱动的，我们分析了不同的离子浓度对马达效率的影响，以及马达的结构，及定子和转子在不同的离子浓度驱动力下的结构和工作特点。.4. 我们建立了用于观测细菌生物膜的实验平台，用来观测细菌在形成生物膜的过程中细胞的分化，细菌生物膜的表面形貌，以及力和其他生长环境对细菌生物膜的表面形貌以及力学特性的影响。