Ryan Shawn D, Haines Brian M, Berlyand Leonid, Ziebert Falko, Aranson Igor S
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):050904. doi: 10.1103/PhysRevE.83.050904. Epub 2011 May 16.
The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system.
对游动细菌悬浮液的粘度进行了分析和数值研究。我们提出了一个简单模型，可对大量细菌进行高效计算。我们的计算表明，粘性流体中自推进物体固有的长程流体动力学相互作用会导致有效粘度显著降低。与枯草芽孢杆菌悬浮液的实验结果一致，我们表明粘度降低与游泳者之间相互作用导致的大规模集体运动的开始有关。模拟结果表明，粘度降低仅发生在游泳者浓度相对较低的情况下：浓度进一步增加会导致粘度增加。我们根据已知物理参数推导出有效粘度的显式渐近公式，并表明在系统中不存在任何明确随机性的情况下，流体动力学相互作用表现为自诱导噪声。
