micromachines Article Numerical Investigation of T-Shaped Microfluidic Oscillator with Viscoelastic Fluid Chao Yuan 1 , Hongna Zhang 2, *, Xiaobin Li 2 , Masamichi Oishi 3 , Marie Oshima 3 , Qinghe Yao 1, * and Fengchen Li 2   Citation: Yuan, C.; Zhang, H.; Li, X.; Oishi, M.; Oshima, M.; Yao, Q.; Li, F. Numerical Investigation of T-Shaped Microfluidic Oscillator with Viscoelastic Fluid. Micromachines 2021, 12, 477. https://doi.org/10.3390/ mi12050477 Academic Editor: Gaetano D’Avino Received: 16 March 2021 Accepted: 20 April 2021 Published: 22 April 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China; yuanch9@mail2.sysu.edu.cn 2 School of Mechanical Engineering, Tianjin University, Tianjin 300350, China; lixiaobin@tju.edu.cn (X.L.); lifch@tju.edu.cn (F.L.) 3 Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; oishi@iis.u-tokyo.ac.jp (M.O.); marie@iis.u-tokyo.ac.jp (M.O.) * Correspondence: hongna@tju.edu.cn (H.Z.); yaoqhe@mail.sysu.edu.cn (Q.Y.) Abstract: Oscillatory flow has many applications in micro-scaled devices. The methods of realizing microfluidic oscillators reported so far are typically based on the impinging-jet and Coanda effect, which usually require the flow Reynolds number to be at least at the order of unity. Another approach is to introduce elastomeric membrane into the microfluidic units; however, the manufacturing process is relatively complex, and the membrane will become soft after long-time operation, which leads to deviation from the design condition. From the perspective of the core requirement of a microfluidic circuit, i.e., nonlinearity, the oscillatory microfluidic flow can be realized via the nonlinear characteristics of viscoelastic fluid flow. In this paper, the flow characteristics of viscoelastic fluid (Boger-type) in a T-shaped channel and its modified structures are studied by two-dimensional direct numerical simulation (DNS). The main results obtained from the DNS study are as follows: (1) Both Weissenberg (Wi) number and viscosity ratio need to be within a certain range to achieve a periodic oscillating performance; (2) With the presence of the dynamic evolution of the pair of vortices in the upstream near the intersection, the oscillation intensity increases as the elasticity-dominated area in the junction enlarges; (3) Considering the simplicity of the T-type channel as a potential oscillator, the improved structure should have a groove carved toward the entrance near the upper wall. The maximum oscillation intensity measured by the standard deviation of flow rate at outlet is increased by 129% compared with that of the original standard T-shaped channel under the same condition. To sum up, with Wi number and viscosity ratio within a certain range, the regular periodic oscillation characteristics of Oldroyd-B type viscoelastic fluid flow in standard T-shaped and its modified channels can be obtained. This structure can serve as a passive microfluidic oscillator with great potential value at an extremely low Reynolds number, which has the advantages of simplicity, no moving parts and fan-out of two. Keywords: microfluidic oscillator; oscillating flow; viscoelastic fluid; T-shaped channel; elastic instability 1. Introduction A fluid oscillator is a device that utilizes the instability of fluid flow to produce a continuous pulsating jet. It has a wide variety of applications, such as jet mixing enhance- ment [1–3], heat transfer enhancement [4–6], cavity resonance suppression [7,8], etc. In addition, as a flow control actuator, the fluid oscillator is utilized in aerospace industries because of its unique features and its simplicity with no moving parts, such as missile con- trol [9] and jet thrust vector control [10]. A comprehensive overview of the fluid oscillator can be found in the review literature [9,11]. Micromachines 2021, 12, 477. https://doi.org/10.3390/mi12050477 https://www.mdpi.com/journal/micromachines