Napoli Gaetano, Turzi Stefano
Dipartimento di Matematica e Fisica "E. De Giorgi," Università del Salento, Lecce 73100, Italy.
Dipartimento di Matematica, Politecnico di Milano, Milan 20133, Italy.
Phys Rev E. 2020 Feb;101(2-1):022701. doi: 10.1103/PhysRevE.101.022701.
Within the framework of the two-dimensional Ericksen-Leslie model, we explore the effect of geometric confinement on the spontaneous flow of active nematic gels. The nematic particles are assumed to flow on a cylindrical surface, while a degenerate tangential anchoring is enforced. Using the linear approximation of the motion equations, we show that there is a close interplay among extrinsic curvature, flow, director alignment, and activity. We find that the extrinsic curvature promotes the director alignment parallel to the cylindrical axis and is responsible for raising the critical threshold with respect to the flat case. Our analysis reveals a very rich scenario where the key quantities are the activity coefficient, the tumbling parameter, and the anisotropic viscosity ratio. Thus, solutions can exhibit a double periodicity in both the azimuthal and axial variables. As a consequence, the velocity field can make a finite angle with the cylinder axis and the active flow winds on the surface with a helical pattern, while the director oscillates around the cylinder generators. Our results can be validated on thin layers of nematic gels placed between two concentric cylinders and suggest which material properties are most suited for the design of active microfluidic devices.
在二维埃里克森 - 莱斯利模型的框架内，我们探讨了几何约束对活性向列型凝胶自发流动的影响。假设向列型粒子在圆柱表面流动，同时施加退化的切向锚定。通过运动方程的线性近似，我们表明外在曲率、流动、指向矢排列和活性之间存在密切的相互作用。我们发现外在曲率促进指向矢平行于圆柱轴排列，并导致相对于平面情况提高临界阈值。我们的分析揭示了一个非常丰富的情景，其中关键量是活性系数、翻滚参数和各向异性粘度比。因此，解在方位角和轴向变量上都可以呈现双周期性。结果，速度场可以与圆柱轴成有限角度，活性流以螺旋模式在表面上缠绕，而指向矢围绕圆柱母线振荡。我们的结果可以在置于两个同心圆柱之间的向列型凝胶薄层上得到验证，并表明哪些材料特性最适合用于设计活性微流控装置。
