Viscoelastic responses of flow driven by a permeable disk investigated by ultrasound velocity profiling Takahiro Nakashima a , Takahisa Shiratori a , Yuichi Murai a,n , Yuji Tasaka a , Yasushi Takeda b , Eric J. Windhab b a Faculty of Engineering, Hokkaido University, N13W8, Sapporo 060-8628, Japan b Institute of Food, Nutrition and Health, ETH Zürich, 8092 Zürich, Switzerland article info Article history: Received 14 March 2015 Received in revised form 14 September 2015 Accepted 29 September 2015 Available online 21 October 2015 Keywords: Viscoelastic fluid Permeable object Flow visualization Ultrasound Doppler method abstract Ultrasound velocity profiling was applied to viscoelastic flow induced around a moving permeable disk. There were two objectives to this measurement. The first was to find technical advantages and restric- tions when applying ultrasonic Doppler velocimetry to a viscoelastic liquid. This issue has not been clarified even though ultrasonic pulses may interact with an elastic medium in the monitoring of the Doppler shift frequency. The second objective was to determine the fluid physics of a viscoelastic liquid around a permeable object, which will help in designing mixing process for materials subject to strong rheological resistance. In this paper, we report a representative response of a viscoelastic liquid in terms of its spatiotemporal velocity distribution. The response highlighted is cyclic lateral waves that form behind the disk, which were hardly detectable by particle image velocimetry. We discuss multiple rea- sons for this phenomenon considering not only fluid properties but also the measurement principle of ultrasound velocity profiling as applied to viscoelastic liquid. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Mixing is one of the greatest concerns in polymer processing since viscoelasticity resists local material displacement [1]. Similar issues are faced for heat transfer and chemical reactions when handling non-Newtonian fluids. To understand such behavior, scientists in the field of fluid mechanics have investigated parti- cular events arising for various configurations of internal flows [2– 10] and external flows [11–13]. It is known that a general way of enhancing mixing is to provide multiple streamlines that tangle complicatedly in the system [14]. Pellets or porous cells having complex shape in chemical facilities are placed in a reactor to control non-Newtonian flow by combining local external flows. Here we focus on a permeable disk as one such cell structure. The disk allows ambient fluid to penetrate through many small holes. Although the disk shape itself is simple to manufacture, the flow characteristics of the disk are difficult to predict theoretically, particularly in the case of viscoelastic fluids. Fig. 1 illustrates streamline patterns of three different disks. In the case of a solid disk (a), upstream fluid totally turns aside the disk. For Newtonian fluids having a range of Reynolds numbers, backward flow takes place behind the disk. For viscoelastic fluids, there is forward flow faster than the inflow velocity behind the disk, which is called negative wake [11]. No matter the fluid property, the backward and forward flow calms down as a hole is provided at the center of the disk as shown in (b). The rate of flow penetrating the hole depends on the flow resistance relative to the resistance of the external flow. The ratio of the flow rate is esti- mated analogously to parallel resistance. By increasing the number of holes, the flow behavior is governed by a doubled parallel re- sistance as shown in (c). For Newtonian fluids, such a permeable disk experiences drag stronger than that experienced by a solid disk because of viscous friction dominating the total drag [15–17]. For shear-thinning fluids, through-flows of the permeable disk are rather accelerated. For fluids with yield stress, the through-flow completely stops when the differential pressure acting on the disk surfaces is lower than the yield stress. For viscoelastic fluids, it becomes more difficult to predict the fluid behavior since viscoe- lasticity interacts among the many stream tubes that are provided by the through-flows. Additionally, the elasticity results in a re- sonance frequency along each streamline, which affects the global flow structure via the complexity of the doubled parallel re- sistance. Summarizing these issues, it is noted that the measure- ment of viscoelastic flows around a permeable disk requires careful consideration of multi-scale events emerging in both space and time. Against the background described above, ultrasound velocity Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/flowmeasinst Flow Measurement and Instrumentation http://dx.doi.org/10.1016/j.flowmeasinst.2015.09.009 0955-5986/& 2015 Elsevier Ltd. All rights reserved. n Correspondence to: Laboratory for Flow Control, Division of Energy & En- vironmental Systems, Faculty of Engineering, Hokkaido University, N13W8, Sap- poro 060-8628, Japan. Fax: þ81 11 706 6373. E-mail address: murai@eng.hokudai.ac.jp (Y. Murai). Flow Measurement and Instrumentation 48 (2016) 97–103