PHYSICAL REVIEW E 106, 014706 (2022) Anisotropic viscous effects of local flow by a rotating microparticle in nematic liquid crystal Jun-Yong Lee , 1 Jae Hoon Lee, 1 Bohdan Lev , 2 and Jong-Hyun Kim 1, 3 , * 1 Department of Physics, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon, 34134, Korea 2 Bogolyubov Institute for Theoretical Physics of the NAS of Ukraine, Metrolohichna Str.14-b, Kyiv, 03680, Ukraine 3 Institute of Quantum Systems, Chungnam National University, Daejeon, 34134, Korea (Received 10 October 2021; revised 16 May 2022; accepted 29 June 2022; published 25 July 2022) The presented study opens a perspective to investigate the effects of local flow on nematic liquid crystals. A particle rotated in nematic fluids typically generates a rotationally symmetric local flow, which causes a change in the director orientation. The director above the threshold velocity has a particular angle determined by the ratio of Leslie coefficients, α 2 /α 3 . In 5CB liquid crystals, this director angle with respect to the flow is approximately 13 ◦ . The angle is calculated through Ericksen-Leslie theory. The angle is not dependent on rotation frequency or particle size but temperature. The area of the influenced region increases with the rotation frequency and particle size. The changes in radius of the influenced region are calculated theoretically using Ericksen number. Further, an interference pattern appears at the edge of the influenced region by the refractive indexes mismatch between the influenced region and the rest. We experimentally obtain the thickness of the influenced region analyzing intervals of the pattern. DOI: 10.1103/PhysRevE.106.014706 I. INTRODUCTION Nematic liquid crystals (NLCs) have not only fluidity but also long-range orientational ordering between molecules, which distinguishes them from isotropic fluids. The most remarkable features of NLCs are an appropriate degree of elasticity and various anisotropies on the macroscopic scale [1,2]. Liquid crystal (LC) molecules tend to align in an orien- tation similar to that of adjacent molecules, where the average orientation is called the director. The director can be con- trolled by external fields, the properties of the substrates in which the LCs are constrained, and so on [3]. Furthermore, flow is also one of the most important factors that influence the director; in particular, the direction and gradient of the flow play a critical role. We can observe not only changes in the alignment of the director but also various instabilities of the system by generating a flow in a uniformly aligned LC cell [4–9]. Rich responses of the LC director can result from different types of shear flow and shapes of the cell confining the LCs [10–15]. In nematic fluid research, the anisotropy of viscosity in addition to flow is also important. Anisotropy of viscosity can be expressed through Miesowicz viscosity and Leslie coefficients, and the hydrodynamics of nematic fluids can be analyzed through the theories from Ericksen and Leslie [16–20]. From anisotropic viscosity, we can observe many interesting phenomena that do not appear in isotropic fluids [21–26]. For example, a Poiseuille flow in a uniformly and obliquely aligned LC to the flow creates transverse pressure [27]. Additionally, because the sign and magnitude of the coefficients play an important role in determining the size * Corresponding author: jxk97@cnu.ac.kr or orientation of the phenomena, many studies on various physical quantities of LCs have been conducted [28–32]. To date, most research on the behavior of LCs has focused on large-scale flow, while the effects of local flow on LCs have received relatively less attention. Among the studies on the effects of local flow, Rovner et al. observed various phenomena resulting from dispersed ferromagnetic discs ro- tated by a magnetic field in uniformly aligned LCs [33]. They pointed out that the alignment of the director around each disc changes when the angular velocity of the disc exceeds a cer- tain threshold, and also that the relaxation of the phenomena is affected by the ratio between elasticity and viscosity when rotation is stopped [33]. However, they did not investigate the alignment change of the director further or the cause of the change in detail. In the present work, we experimentally generate a local flow on the single-particle scale using micro- sized ferromagnetic spheres in NLCs and a rotating magnetic field. We apply Ericksen-Leslie theory on this scale and reveal not only the details of the director alignment in the region where the flow exceeds the threshold velocity and its cause but also the shape of the region where the alignment change happens. The related phenomena are calculated through the viscous torque exerted on the director and the proposed model that considers the distance from the substrate in the Ericksen number. II. EXPERIMENTS We used a mixture of NLCs and spherical ferromagnetic particles in a rotating magnetic field to generate a local flow. The mixture was prepared through the following process. Ferromagnetic spheres approximately 8–30 μm in diameter were dispersed into deionized water at a concentration of 1%. The ferromagnetic spherical particles (CFM-80-5 and CFM- 2470-0045/2022/106(1)/014706(9) 014706-1 ©2022 American Physical Society