Tiribocchi Adriano, Wittkowski Raphael, Marenduzzo Davide, Cates Michael E
SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.
Department of Physics and Astronomy, University of Padua, I-35131 Padova, Italy.
Phys Rev Lett. 2015 Oct 30;115(18):188302. doi: 10.1103/PhysRevLett.115.188302. Epub 2015 Oct 28.
We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation, we introduce a dimensionless scalar concentration field ϕ with advective-diffusive dynamics. Activity creates a contribution Σ_{ij}=-κ[over ^][(∂{i}ϕ)(∂{j}ϕ)-(∇ϕ)^{2}δ_{ij}/d] to the deviatoric stress, where κ[over ^] is odd under time reversal and d is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus, there is a subtle interplay of activity and hydrodynamics, even without alignment interactions.
我们提出了一种自推进粒子的连续介质理论，该理论适用于无排列相互作用且动量守恒的溶剂中的粒子。为了研究相分离，我们引入了一个具有平流扩散动力学的无量纲标量浓度场ϕ。活性对偏应力产生贡献Σ_{ij}=-κ[上标^][(∂{i}ϕ)(∂{j}ϕ)-(∇ϕ)^{2}δ_{ij}/d]，其中κ[上标^]在时间反演下为奇函数，d为空间维度数；这导致了一个有效的界面张力贡献，对于收缩性游动者来说是负的。我们预测，在一个长度尺度上，域生长会停止，在这个尺度上，扩散粗化与界面的主动拉伸达到平衡，并通过数值计算证实了这一点。因此，即使没有排列相互作用，活性和流体动力学之间也存在微妙的相互作用。
